Chapter Eleven. Dimensioning


After studying the material in this chapter, you should be able to:

1. Use conventional dimensioning techniques to describe size and shape accurately on an engineering drawing.

2. Create and read a drawing at a specified scale.

3. Correctly place dimension lines, extension lines, angles, and notes.

4. Dimension circles, arcs, and inclined surfaces.

5. Apply finish symbols and notes to a drawing.

6. Dimension contours.

7. Use standard practices for dimensioning prisms, cylinders, holes, and curves.

8. List practices for dimensioning a solid model as documentation.

9. Identify guidelines for the dos and don’ts of dimensioning.

Refer to the following standards:

• ANSI/ASME Y14.5 Dimensioning and Tolerancing

• ASME Y14.41 Digital Product Definition Data Practices

• ASME B4.2 Preferred Metric Limits and Fits

Different views of a hood drum module are shown.

Dimensioned Drawing from a Solid Model. This dimensioned drawing for the sheet metal drum module hood was created from a 3D model using SolidWorks. (Courtesy of Dynojet Research, Inc.)


It is essential to describe not only the shape of the features you design but also their sizes and locations. Dimensions and notes define the size, finish, and other requirements to fully define what you want manufactured.

Standards organizations prescribe how dimensions should appear and the general rules for their selection and placement in the drawing and in digital models, but it takes skill and practice to dimension drawings so that their interpretation is clear and unambiguous.

Whether you are creating 2D drawings or 3D models, CAD systems are great for producing dimensions that follow standards for the appearance of the dimensions themselves. However, the job of selecting which dimension to show or where to place it in a drawing takes a level of intelligence that is not part of most CAD systems. Those important decisions are still up to the CAD user—or in other words, you.

Learning good practices for dimensioning and tolerancing to define part geometry can also help you create better 3D models. If you have a good understanding of how the sizes and locations of model features will be defined, you can plan how to capture this information clearly in the model.

Understanding Dimensioning

You can describe an object’s shape using different types of drawing views. By providing dimensions, you describe the sizes and locations of design features.

The need for interchangeability of parts is the basis for modern part dimensioning. Drawings for products must be dimensioned so that production personnel all over the world can make mating parts that will fit properly when assembled or when used to replace parts.

The increasing need for precision manufacturing and interchangeability has shifted responsibility for size control to the design engineer or detail drafter. The production worker must properly interpret the instructions given on the drawings to produce the required part or construct the building or system. You should be familiar with materials and methods of construction and with production requirements to create drawings that define exactly what you want to have manufactured.

Practices for dimensioning architectural and structural drawings are similar in many ways to those for dimensioning manufactured parts, but some practices differ. The portfolio section throughout this book shows a variety of drawings that you can use to familiarize yourself with practices from other disciplines.

Figure 11.1 shows a dimensioned CAD drawing created from a solid model. Although CAD can be a great help for proper dimensioning technique, you must provide the intelligence to choose and place the dimensions to create a drawing that conveys the design clearly. Even if you are going to transmit 3D CAD files as the product definition, you still need to consider how accurately the parts that you will eventually receive must match the model definition. Directly specifying tolerances in the model is one way to do this. You will learn more about tolerancing in Chapter 12.

Illustration of how dimensions could be automatically generated by CAD.

11.1 Automatically Generated Dimensions. Views and dimensions can be generated automatically from a solid model. (Courtesy of Robert Kincaid.)

Three Aspects of Good Dimensioning

Dimensions are given in the form of distances, angles, and notes regardless of the dimensioning units being used. For both CAD and hand drawing, the ability to create good dimensioned drawings requires the following:

1. Technique of dimensioning

The standards for the appearance of lines, spacing of dimensions, size of arrowheads, and so on, allow others to read your drawing. A typical dimensioned drawing is shown in Figure 11.2. Note the strong contrast between the visible lines of the object and the thin lines used for the dimensions. The dimensions are easily read because they follow the standards for dimensioning technique.

Illustration of the dimensions marked in millimeters.

11.2 A Drawing Dimensioned in Millimeters

2. Placement of dimensions

Use logical placement for dimensions according to standard practices so that they are legible, easy to find, and easy for the reader to interpret. Notice that when dimensions are placed between two views, it is easier to see how the dimension relates to the feature as shown in each view.

3. Choice of dimensions

The dimensions you show affect how your design is manufactured. Dimension first for function and then review the dimensioning to see if you can make improvements for ease of manufacturing without adversely affecting the final result. 3D CAD models can be transmitted as all or part of a digital product definition, but this method still requires a thorough understanding of the sizes and relationships between the part features.

A drawing released for production should show the object in its completed state and contain all necessary information for specifying the final part. As you select which dimensions to show, provide functional dimensions that can be interpreted to manufacture the part as you want it built. Keep in mind:

• The finished piece.

• The function of the part in the total assembly.

• How you will inspect the final part to determine its acceptability.

• Production processes.

Also, remember the following points:

• Give dimensions that are necessary and convenient for producing the part.

• Give sufficient dimensions so that none must be assumed.

• Avoid dimensioning to points or surfaces inaccessible to the worker.

• Do not provide unnecessary or duplicate dimensions.


When a finished part is measured, it will vary slightly from the exact dimension specified. Tolerance is the total amount that the feature on the actual part is allowed to vary from what is specified by the drawing or model dimension. You will learn a number of ways to specify tolerances in Chapter 12.

A good understanding of tolerance is important to understanding dimensioning, especially when choosing which dimensions to show. For now, keep in mind that tolerance can be specified generally by giving a note on the drawing such as


Another method of specifying tolerance is illustrated in the title block shown in Figure 11.3.

Image of the Title block showing tolerances.

11.3 A Title Block Specifying Tolerances (Courtesy of Dynojet Research, Inc.)

Geometric Breakdown

Engineering structures are composed largely of simple geometric shapes, such as the prism, cylinder, pyramid, cone, and sphere. They may be exterior (positive) or interior (negative) forms. For example, a steel shaft is a positive cylinder, and a round hole is a negative cylinder.

These shapes result directly from design necessity—keeping forms as simple as possible—and from the requirements of the fundamental manufacturing operations. Forms having plane surfaces are produced by planing, shaping, milling, and so forth; forms having cylindrical, conical, or spherical surfaces are produced by turning, drilling, reaming, boring, countersinking, and other rotary operations. One way to consider dimensioning of engineering structures involves two basic steps:

1. Give the dimensions showing the sizes of the simple geometric shapes, called size dimensions.

2. Give the dimensions locating these elements with respect to one another, called location dimensions. Note that a location dimension locates a 3D geometric element and not just a surface; otherwise, all dimensions would have to be classified as location dimensions.

This process of geometric analysis helps you determine the features of the object and the features’ relationships to one another, but it is not enough just to dimension geometry. You must also consider the function of the part in the assembly and the manufacturing requirements. This process is similar to that used when modeling designs in 3D CAD.

11.1 Lines Used in Dimensioning

A dimension line is a thin, dark, solid line terminated by an arrowhead, indicating the direction and extent of a dimension (Figure 11.4). In a machine drawing, the dimension line is usually broken near the middle to place the dimension value in the line. In structural and architectural drawing, the dimension figure is placed above an unbroken dimension line.

Illustration of Dimension Lines.

11.4 Dimension Line

As shown in Figure 11.5, the dimension line nearest the object outline should be spaced at least 10 mm (3/8″) away. All other parallel dimension lines should be at least 6 mm (1/4″) apart, and more if space is available. The spacing of dimension lines should be uniform throughout the drawing.

Illustration of Extension Lines.

11.5 Extension Lines

An extension line is a thin, dark, solid line that extends from a point on the drawing to which a dimension refers (Figure 11.5). The dimension line meets the extension lines at right angles, except in special cases. A gap of about 1.5 mm (1/16″) should be left where the extension line would join the object outline. The extension line should extend about 3 mm (1/8″) beyond the outermost arrowhead.

A centerline is a thin, dark line alternating long and short dashes. Centerlines are commonly used as extension lines in locating holes and other symmetrical features (Figure 11.6). When extended for dimensioning, centerlines cross over other lines of the drawing without gaps. Always end centerlines using a long dash. Refer to Figures 11.411.6 for examples of lines used in dimensioning.

Illustration of Centerlines.

11.6 Centerlines

11.2 Using Dimension and Extension Lines

Dimension lines and extension lines should follow the guidelines shown in Figure 11.7a. The shorter dimensions are nearest to the object outline. Dimension lines should not cross extension lines, as in Figure 11.7b, which results from placing the shorter dimensions outside. Note that it is perfectly satisfactory to cross extension lines (Figure 11.7a), but they should not be shortened (Figure 11.7c). A dimension line should never coincide with or extend from any line of the drawing (Figure 11.7d). Avoid crossing dimension lines wherever possible.

Examples of the best way to draw Dimension and Extension Lines.

11.7 Dimension and Extension Lines

Dimensions should be lined up and grouped together as much as possible, as in Figure 11.8a, and not as in Figure 11.8b.

Examples of the best way to draw Grouped Dimensions.

11.8 Grouped Dimensions

In many cases, extension lines and centerlines must cross visible lines of the object (Figure 11.9a). When this occurs, gaps should not be left in the lines (Figure 11.9b).

Examples of the best way to draw Crossing Lines.

11.9 Crossing Lines

Dimension lines are normally drawn at right angles to extension lines, but an exception may be made in the interest of clarity, as in Figure 11.10.

Examples of the best way to draw Oblique Extensions.

11.10 Oblique Extension

11.3 Arrowheads

Arrowheads, shown in Figure 11.11, indicate the extent of dimensions. They should be uniform in size and style throughout the drawing, not varied according to the size of the drawing or the length of dimensions. Sketch arrowheads freehand so that the length and width have a ratio of 3:1. The length of the arrowhead should be equal to the height of the dimension values (about 3 mm or 1/8″ long). For best appearance, fill in the arrowhead, as in Figure 11.11d. Figure 11.12 shows the preferred arrowhead styles for mechanical drawings. Most CAD systems allow you to select from a variety of styles.

Four arrowheads are displayed.

11.11 Arrowheads

Four arrowheads arranged in their order of preference.

11.12 Order of Preference for Arrow Styles


When you are drawing by hand and using the arrowhead method in which both strokes are directed toward the point, it is easier to make the strokes toward yourself.

11.4 Leaders

A leader is a thin, solid line directing attention to a note or dimension and starting with an arrowhead or dot.

A leader should be an inclined straight line drawn at a large angle, except for the short horizontal shoulder (about 3–6 mm or 1/8–1/4″) extending from the center of the first or last line of lettering for the note. A leader to a circle should be a radial line, which is a line that would pass through the center of the circle if extended. Figures 11.13ad show examples of leader lines; radial lines are shown in Section 11.22.

Examples of leader and radial lines.

11.13 Leaders

Use an arrowhead to start the leader when you can point to a particular line in the drawing, such as the edge of a hole. Use a dot to start the leader when locating something within the outline of the object, such as an entire surface (see Figures 11.13e and f).

For the Best Appearance, Make Leaders

• Near each other and parallel.

• Across as few lines as possible.

Don’t Make Leaders

• Parallel to nearby lines of the drawing.

• Through a corner of the view.

• Across each other.

• Longer than needed.

• Horizontal or vertical.

11.5 Drawing Scale and Dimensioning

Drawing scale is indicated in the title block, as described in Chapter 2. The scale is intended to help you visualize the object by giving an approximate idea of its size, but is not intended to communicate dimensions. Never scale measurements from drawings to find an unknown dimension. Many standard title blocks include a note such as DO NOT SCALE DRAWING FOR DIMENSIONS, as shown in Figure 11.14.

Image of the Title block showing the drawing scale.

11.14 Drawing scale is noted in the title block. The drawing should not be scaled for dimensions. (Courtesy of Dynojet Research, Inc.)

Draw a heavy straight line under any single dimension value that is not to scale (Figure 11.15). Before CAD was widely used, if a change made in a drawing was not important enough to justify correcting the drawing, the practice was simply to change the dimension value. If a dimension does not match the appearance in the drawing, the part is made as dimensioned, not as pictured. If there seems to be an error, many manufacturers check to confirm that the drawing is correct; however, it is your responsibility to specify exactly what you want built. If the entire drawing is not prepared to a standard scale, note NONE in the scale area of the title block. You may see the abbreviation NTS on older drawings, meaning “not to scale.”

Figure showing how dimension values that are not a scale are represented.

11.15 Draw a heavy line under any dimension value that is not to scale.

When you create a drawing using CAD, make sure to define dimensions according to the proper standards. Because it is easy to edit CAD drawings, you should generally fix the drawing geometry when making changes and not merely change dimension values. If you are using a digital model as the sole definition for the part, the model dimensions must be represented accurately.

Keeping Dimensions and Lettering Legible at Smaller Scales

The sizes for lettering height, dimension line spacing, and so on, are to be shown that size on the plotted sheet. If you are going to use reduced-size working prints, increase the lettering, dimension arrows, and other sizes by approximately 50% (depending on the amount of reduction) to maintain legibility on the smaller print.

11.6 Direction of Dimension Values and Notes

All dimension values and notes are lettered horizontally to be read from the bottom of the sheet, as oriented by the title block. Figure 11.16 shows the direction for reading dimension values.

Figure marked with Unidirectional Dimensions is displayed.

11.16 Unidirectional Dimension Figures

The exception is when dimensioning from a baseline as in coordinate dimensioning. Then dimension figures may be aligned with the dimension lines so that they may be read from the bottom or right side of the sheet as shown in Figure 11.17. In both systems, general notes on the sheet and dimensions and notes shown with leaders are always aligned horizontally to read from the bottom of the drawing.

Figure showing coordinate dimensioning.

11.17 Rectangular coordinate dimensioning may show values reading from the right. (Reprinted from ASME Y14.5M-1994 (R2004), by permission of The American Society of Mechanical Engineers. All rights reserved.)

11.7 Dimension Units

Dimension values are shown using metric or decimal-inch values. Millimeters and decimal inches can be added, subtracted, multiplied, and divided more easily than fractions. For inch–millimeter equivalents of decimal and common fractions, see the inside back cover of this book.

When a note stating ALL MEASUREMENTS IN MILLIMETERS or ALL MEASUREMENTS IN INCHES UNLESS OTHERWISE NOTED is used in the title block to indicate the measurement units, no units are needed with the dimension values. When indicating dimensions:

• Millimeters are indicated by the lowercase letters mm placed to the right of the numeral, as in 12.5 mm.

• Meters are indicated by the lowercase m, as in 50.6 m.

• Inches are indicated by the symbol ″ placed slightly above and to the right of the numeral.

• Feet are indicated by the symbol ′ similarly placed. It is customary in feet-inch expressions to omit the inch mark.

It is standard practice to omit millimeter designations and inch marks on drawings and note the units in the title block except when there is a possibility of misunderstanding. For example, 1 VALVE should be 1″ VALVE.

Either meters or feet and inches and fractional inches are used in architectural and structural work where precision in the thousandths of an inch is not necessary and the steel tape or framing square is used to make measurements. Commodities such as pipe and lumber are identified by standard nominal sizes that are close to the actual dimensions.

In some industries, all dimensions, regardless of size, are given in inches; in others, dimensions up to and including 72″ are given in inches, and dimensions greater than 72″ are given in feet and inches. In U.S. structural and architectural drafting, all dimensions of 1′ or more are usually expressed in feet and inches.

11.8 Millimeter Values

The millimeter is the commonly used unit for most metric engineering drawings. One-place millimeter decimals are used when tolerance limits permit. Two (or more)-place millimeter decimals are used when higher tolerances are required. One drawing can combine dimensions shown with more and fewer decimal places depending on the necessary tolerance. Keep in mind that 0.1 mm is approximately equal to .004 in. If you are used to working in U.S. customary units, don’t provide an unrealistic precision when specifying millimeter values.

Figure 11.18 shows various ways that millimeter values can be shown for dimensioning. Figure 11.19 shows an example drawing dimensioned in millimeters.

Examples of the ways millimeter values could be written for dimensioning.

11.18 Millimeter Dimension Values

Figure showing how dimension values can be written in millimeters.

11.19 Complete Millimeter Dimensioning

11.9 Decimal-Inch Values

Two-place inch decimals are typical when tolerance limits permit. Three or more decimal places are used for tolerance limits in the thousandths of an inch. In two-place decimals, the second place preferably should be an even digit (for example, .02, .04, and .06 are preferred to .01, .03, or .05) so that when the dimension is divided by 2 (for example, when determining the radius from a diameter), the result will still be a two-place decimal. However, odd two-place decimals are used when required for design purposes, such as in dimensioning points on a smooth curve or when strength or clearance is a factor. A typical example of the use of the complete decimal-inch system is shown in Figure 11.20.

Figure showing how dimension values can be written in decimals.

11.20 Complete Decimal Dimensioning

11.10 Rules for Dimension Values

Good hand-lettering is important for dimension values on sketches. The shop produces according to the directions on the drawing, so to save time and prevent costly mistakes, make all lettering perfectly legible.

Make all decimal points bold, allowing ample space. When the metric dimension is a whole number, do not show either a decimal point or a zero. When the metric dimension is less than 1 mm, a zero precedes the decimal point.

When the decimal-inch dimension is used on drawings, a zero is not used before the decimal point of values less than 1 in. Typical values are shown to two decimal places even when they represent a whole number (e.g., use 2.00 instead of 2). Correct decimal-inch dimension values are shown in Figures 11.21ae.

Examples of the ways decimal-inch values could be written for dimensioning.

11.21 Decimal-Inch Dimension Values

11.11 Rules for Rounding Decimal Dimension Values

It is difficult to maintain tolerances smaller than a few thousandths of an inch in manufacturing. To provide reasonable tolerances that can be achieved in manufacturing, calculated dimension values for drawings sometimes need to be rounded. Unlike rounding rules used for statistical values, it is preferred to round drawing values to an even number.

When rounding a decimal value to fewer places, regardless of whether the dimension is expressed in inches or metric units, follow these rules:

• If the number following the rounding position is less than 5, make no change.

• If the number following the rounding position is more than 5, round up.

• If the number following the rounding position is a 5, round to an even number. (To do this, note whether the number in the rounding position is even or odd. If the 5 follows an odd number in the rounding position, round up to an even number. If the 5 follows an even number in the rounding position, make no change.)

Examples of Rounded Decimal Values

• 3.4632 becomes 3.463 when rounded to three places. (Make no change, because the 2 following the rounding position is less than 5.)

• 3.4637 becomes 3.464 when rounded to three places. (Round up, because the 7 following the rounding position is more than 5.)

• 8.37652 becomes 8.376 when rounded to three places. (Make no change, because the 6 in the rounding position is even and the number following the rounding position is a 5.)

• 4.375 becomes 4.38 when rounded to two places. (Round up to an even number, because the 7 in the rounding position is odd and the number following the rounding position is a 5.)

11.12 Dual Dimensioning

Dual dimensioning is used to show metric and decimal-inch dimensions on the same drawing. Two methods of displaying the dual dimensions are described next.

Position Method

In the position method of dual dimensioning, the millimeter dimension is placed above the inch dimension, and the two are separated by a dimension line, or by an added line when the unidirectional system of dimensioning is used. An alternative arrangement is the millimeter dimension to the left of the inch dimension, with the two separated by a slash line, or virgule. Placement of the inch dimension above or to the left of the millimeter dimension is also acceptable. Each drawing should illustrate the dimension identification as Image or MILLIMETER/INCH.

Bracket Method

In the bracket method of dual dimensioning, the millimeter dimension is enclosed in parentheses. The location of this dimension is optional but should be uniform on any drawing—that is, above or below or to the left or the right of the inch dimension. Each drawing should include a note to identify the dimension values, such as DIMENSIONS IN () ARE MILLIMETERS.

11.13 Combination Units

When more than one measurement system is used on the same drawing, the main units are indicated through a note in or near the title block. The alternative units are indicated with an abbreviation after the dimension value. Use mm after the dimension value if millimeters, or IN if inches, only when combining two measurement systems on one drawing. In the U.S. to facilitate the changeover to metric dimensions, some drawings are dual-dimensioned in millimeters and decimal inches, as shown in Figure 11.22. The second set of units shown in parentheses are for reference only.

Examples showing Dual-Dimensioning in millimeters.

11.22 Dual-Dimensioned Drawing in Millimeters. On drawing, inch values are given for reference only.

11.14 Dimensioning Symbols

A variety of dimensioning symbols are used to replace traditional terms or abbreviations (see Figure 11.23). The symbols are preferred because (1) they take less space in the drawing and (2) they are internationally recognized and therefore do not have translation issues if the part is manufactured in a country where a different language is spoken. Traditional terms and abbreviations found in Appendix 2 can be used if necessary.

Diagrammatic illustration of the various Dimension Symbols.

11.23 Form and Proportion of Dimensioning Symbols (Reprinted from ASME Y14.5M-1994 (R2004), by permission of The American Society of Mechanical Engineers. All rights reserved.)

11.15 Placing and Showing Dimensions Legibly

Rules for the placement of dimensions help you dimension your drawings so that they are clear and readable. They also help locate dimensions in standard places so that someone manufacturing the part doesn’t have to search a complicated drawing to find a dimension. You cannot always follow every placement rule to the letter, so keep in mind that the ultimate goal is to dimension the drawing clearly so that the parts are built to your specifications.

Rules for Placing Dimensions Properly

• Never letter a dimension value over any line on the drawing; if necessary, break the line.

• In a group of parallel dimension lines, the dimension values should be staggered, as in Figure 11.24a, and not stacked up one above the other, as in Figure 11.24b.

Figure shows the placement of dimension values.

11.24 Staggered Numerals, Metric

• Do not crowd dimension figures into limited spaces, making them illegible. There are techniques for showing dimension values outside extension lines or in combination with leaders (Figure 11.25). If necessary, add a removed partial view or detail to an enlarged scale to provide the space needed for clear dimensioning.

Figure shows the fitting of dimension values in small spaces.

11.25 Fitting Dimension Values in Limited Spaces (Metric Dimensions)

• Place dimensions between views when possible, but attached to only a single view. This way it is clear that the dimension relates to the feature, which can be seen in more than one view.

• When a dimension must be placed in a hatched area or on the view, leave an opening in the hatching or a break in the lines for the dimension values, as shown in Figure 11.26b.

Figure shows the proper usage of dimensions when section lines are used.

11.26 Dimensions and Section Lines

• Dimensions should not be placed on a view unless it promotes the clarity of the drawing, as shown in Figure 11.27. In complicated drawings such as Figure 11.27c, it is often necessary to place dimensions on a view.

Figure shows instances where dimensions are placed on and off a view.

11.27 Place dimensions on view only when clarity is enhanced.

• Avoid dimensioning to hidden lines (see Figure 11.28).

Figure shows the placement of dimensions.

11.28 Placement of Dimensions

• Do not attach dimensions to visible lines where the meaning is not clear, such as the dimension 20 in the top view shown in Figure 11.29b.

Figure shows the use of appropriate dimensions according to the view of an object.

11.29 Place dimensions where the contours of the object are defined.

• Notes for holes are usually placed where you see the circular shape of the hole, as in Figure 11.29a, but give the diameter of an external cylindrical shape where it appears rectangular. This way it is near the dimension for the length of the cylinder.

• Give dimensions where the shapes are shown—where the contours of the object are defined—as is shown in Figure 11.29.

• Locate holes in the view that shows the shape of the hole clearly.

Tip: Thinking of Dimensioning in Terms of Material Removal

There are many ways to dimension a drawing. If you are having trouble getting started, it may help to consider the overall block of material and what features are to be removed from it, similar to the way you visualize for a sketch. This is especially true when the part is to be manufactured using a process that removes material, such as milling.

Look for the largest portions to be removed and give dimensions for their sizes and locations first. Next, add dimensions for the smaller features.

Because the overall dimensions will be the largest, they will be placed farthest from the view. If you are using CAD, it is easy to move dimensions later if you need more space. When you are sketching, block the overall dimension in lightly and leave substantial space between it and the drawing view for placement of shorter dimensions.

Use the rules that you have learned to place dimensions on the view that best shows the shape and close to where the feature is shown. This makes the drawing easier to read.

Four representations placed adjacent to each other depict dimensioning in terms of material removal.

11.16 Superfluous Dimensions

All necessary dimensions must be shown, but do not give unnecessary or superfluous dimensions. Figure 11.30 shows examples of how to omit unnecessary dimensions. Do not repeat dimensions on the same view or on different views, or give the same information in two different ways.

Figure gives instances of unnecessary dimensioning.

11.30 Superfluous Dimensions

As Figure 11.30b shows, it can be impossible to determine how the designer intended to apply the tolerance when a dimension is given two different ways. In chained dimensions, one dimension of the chain should be left out if the overall dimension is given, so that the machinist will work from one surface only. This is particularly important where an accumulation of tolerances can cause problems with how parts fit or function.

Do not omit dimensions, thinking, for example, that a hole is symmetrical and will be understood to be centered. Note in Figure 11.30b that one of the two location dimensions should be given for the hole at the right side of the part, even though it is centered. As the creator of the drawing, you should specify exactly how the part is to be built and inspected.

As shown in Figure 11.30e, when one dimension clearly applies to several identical features, or a uniform thickness, it need not be repeated, but the number of places should be indicated. Dimensions for fillets and rounds and other noncritical features need not be repeated, nor need the number of places be specified.

11.17 Dimensioning Angles

Angles are dimensioned by specifying the angle in degrees and a linear dimension, as shown in Figure 11.31a. Coordinate dimensions can also be given for two legs of a right triangle, as shown in Figure 11.31b. The coordinate method is better when a high degree of accuracy is required. Variations in degrees of angle are hard to control because the amount of variation increases with the distance from the vertex of the angle. Methods of indicating angles are shown in Figure 11.31. The tolerancing of angles is discussed in Chapter 12.

Figure shows the technique to dimension angles.

11.31 Dimensioning Angles

In civil engineering drawings, slope represents the angle with the horizontal, whereas batter is the angle with the vertical. Both are expressed by making one member of the ratio equal to 1, as shown in Figure 11.32. Grade, as of a highway, is similar to slope but is expressed in percentage of rise per 100 feet of run. Thus a 20′ rise in a 100′ run is a grade of 20%. In structural drawings, angular measurements are made by giving the ratio of run to rise, with the larger size being 12″. These right triangles are referred to as bevels.

Figure shows the dimensioning of angles in civil engineering projects.

11.32 Angles in Civil Engineering Projects

11.18 Dimensioning Arcs

A circular arc is dimensioned in the view where its true shape in seen by giving the value for its radius preceded by the abbreviation R (Figure 11.33). The centers is marked with small crosses to clarify the drawing, but not for small or unimportant radii or undimensioned arcs. When there is room enough, both the radius value and the arrowhead are placed inside the arc. If not, the arrowhead is left inside but the value is moved outside, or both the arrowhead and value are moved outside. When section lines or other lines are in the way, the value and leader can be placed outside the sectioned or crowded area. For a long radius, when the center falls outside the available space, the dimension line is drawn toward the actual center, but a false center may be indicated and the dimension line “jogged” to it (Figure 11.33f).

Figure shows the technique for dimensioning arcs.

11.33 Dimensioning Arcs

11.19 Fillets and Rounds

Individual fillets and rounds are dimensioned like other arcs. If there are only a few and they are obviously the same size, giving one typical radius is preferred. However, fillets and rounds are often numerous on a drawing, and they usually are some standard size, such as metric R3 and R6, or R.125 and R.250 when using decimal-inch dimensions. In this case, give a general note in the lower portion of the drawing, such as:






11.20 Size Dimensioning: Prisms

The right rectangular prism is probably the most common geometric shape. Front and top views are dimensioned as shown in Figures 11.34a and b. The height and width are usually given in the front view, and the depth in the top view. The vertical dimensions can be placed on the left or right, usually inline. Place the horizontal dimension between views as shown and not above the top or below the front view. Front and side views should be dimensioned as in Figures 11.34c and d. An example of size dimensions for a machine part made entirely of rectangular prisms is shown in Figure 11.35.

Figure shows the technique to dimension rectangular prisms.

11.34 Dimensioning Rectangular Prisms

Figure shows the dimensioning of a cutter block.

11.35 Dimensioning a Machine Part Composed of Prismatic Shapes

11.21 Size Dimensioning: Cylinders

The right circular cylinder is the next most common geometric shape and is commonly seen as a shaft or a hole. Cylinders are usually dimensioned by giving the diameter and length where the cylinder appears as a rectangle. If the cylinder is drawn vertically, give the length at the right or left, as in Figures 11.36a and b. If the cylinder is drawn horizontally, give the length above or below the rectangular view, as in Figures 11.36c and d.

Figure shows the technique to dimension cylinders.

11.36 Dimensioning Cylinders

Do not use a diagonal diameter inside the circular view, except when clarity is improved. Using several diagonal diameters on the same center becomes very confusing.

The radius of a cylinder should never be given, because measuring tools, such as the micrometer caliper, are designed to check diameters. Holes are usually dimensioned by means of notes specifying the diameter and the depth, as shown in Figure 11.37, with or without manufacturing operations.

Figure shows the use of the phi symbol in dimensioning cylinders.

11.37 Use of ∅ in Dimensioning Cylinders

Give the diameter symbol ∅ before all diameter dimensions, as in Figure 11.38a (ANSI/ASME Y14.5). In some cases, the symbol ∅ may be used to eliminate the circular view, as shown in Figure 11.38b. The abbreviation DIA following the numerical value was used on older decimal inch drawings.

Figure shows the dimensioning of a machine part that contains cylindrical shapes.

11.38 Dimensioning a Machine Part Composed of Cylindrical Shapes

When it is not clear that a hole goes all the way through the part, add the note THRU after the value.

11.22 Size Dimensioning: Holes

Figure 11.39 shows standard symbols used in dimensioning holes. The order of items in a note corresponds to the order of procedure in the shop in producing the hole. The leader of a note should point to the circular view of the hole, if possible.

Figure shows the technique for dimensioning holes.

11.39 Dimensioning Holes

When the circular view of the hole has two or more concentric circles, as for counterbored, countersunk, spotfaced or tapped holes, the arrowhead should touch the outer circle. Draw a radial leader line, that is, one that would pass through the center of the circle if it were extended. Figure 11.40 shows good and bad examples of radial leader lines.

Figure shows a good and a wrong technique of using a radial leader..

11.40 Good and Bad Examples of Radial Leader Lines

Countersunk, counterbored, spotfaced, and tapped holes are usually specified by standard symbols or abbreviations, as shown in Figure 11.41.

Figure shows the standard symbols for hole dimensions.

11.41 Standard Symbols for Hole Dimensions

Two or more holes can be dimensioned by a single note and by specifying the number of holes, as shown at the top of Figure 11.41. It is widely acceptable to use decimal fractions for both metric or inch drill sizes, as shown in Figure 11.41b. For numbered or letter-size drills (listed in Appendix 15), specify the decimal size or give the number or letter designation followed by the decimal size in parentheses—for example #28 (.1405) or “P” (.3230). Metric drills are all in decimal sizes and are not designated by number or letter.

Specify only the dimensions of the holes, without a note listing whether the holes are to be drilled, reamed, or punched, as shown in Figures 11.41c and d. The manufacturing technician or engineer is usually better suited to determine the least expensive process to use that will achieve the tolerance required.

11.23 Applying Standard Dimensioning Symbols

Use standard dimensioning symbols when possible to save space and communicate dimensions clearly. (Refer to Figure 11.23 for details on how to draw the symbols.) Most CAD software contains a palette of standard symbols. Figure 11.42 shows the application of a variety of standard symbols. Note that Figure 11.42a shows the basic dimension symbol used in geometric dimensioning and tolerancing (GD&T). In this case, “basic” does not mean “ordinary.” You will learn more about the use of this special symbol in Chapter 12.

Figure shows seven different dimensioning symbols.

11.42 Use of Dimensioning Symbols. (Reprinted from ASME Y14.5M-1994 (R2004), by permission of The American Society of Mechanical Engineers. All rights reserved.)

11.24 Dimensioning Counterbores and Spotfaces with Fillets

At times a fillet radius is specified for a counterbored or spot-faced hole. Figure 11.43 shows an example of counterbored hole with a fillet radius specified. Note that the fillet radius is to the inside of the counterbore diameter.

Figure shows a counterbore with fillet.

11.43 Counterbore with Fillet. A note specifying a counterbore fillet radius defines a radius to the inside of the counterbore diameter.

When a fillet radius is specified for a spotface dimension, the fillet radius is added to the outside of the spotface diameter, as shown in Figure 11.44.

Figure shows a spotface with a fillet.

11.44 Spotface with Fillet. A note specifying a spotface fillet radius defines a radius added to the outside of the spotface diameter.

11.25 Dimensioning Triangular Prisms, Pyramids, and Cones

To dimension a triangular prism, give the height, width, and displacement of the top edge in the front view, and the depth in the top view, as is shown in Figure 11.45a.

Figure shows the dimensioning of different shapes.

11.45 Dimensioning Various Shapes

For a rectangular pyramid, give the heights in the front view and the dimensions of the base and the centering of the vertex in the top view, as in Figure 11.45b. If the base is square, you need give dimensions for only one side of the base, preceded by the square symbol, as in Figure 11.45c (or on older drawings you may see it labeled SQ).

For cones, give the altitude and the diameter of the base in the triangular view (Figure 11.45d). For a frustum of a cone, give the vertical angle and the diameter of one of the bases (Figure 11.45e). Another method is to give the length and the diameters of both ends in the front view. Still another is to give the diameter at one end and the amount of taper per foot in a note.

Figure 11.45f shows a two-view drawing of a plastic knob. Overall, it is spherical and is dimensioned by giving its diameter preceded by the abbreviation and symbol for spherical diameter, S∅ (in older notations it may be followed by the abbreviation SPHER). The torus-shaped bead around the knob is dimensioned by giving the thickness of the ring and the outside diameter.

Figure 11.45g shows a spherical end dimensioned by a radius preceded by the abbreviation SR. Internal shapes corresponding to the external shapes in Figure 11.45 would be dimensioned similarly.

11.26 Dimensioning Curves

One way to dimension curves is to give a group of radii, as shown in Figure 11.46a. Note that in dimensioning the R126 arc, whose center is inaccessible, the center may be moved inward along a centerline and a jog made in the dimension line. Another method is to dimension the outline envelope of a curved shape so that the various radii are self-locating from “floating centers,” as shown in Figure 11.46b. Both circular and noncircular curves may be dimensioned by using coordinate dimensions, or datums, as in Figure 11.46c.

Figure shows the dimensioning of curves.

11.46 Dimensioning Curves

11.27 Dimensioning Curved Surfaces

When angular measurements are unsatisfactory, you may give chordal dimensions, as shown in Figure 11.47a, or linear dimensions on the curved surfaces, as shown in Figure 11.47b.

Figure shows the technique to dimension along curved surfaces.

11.47 Dimensioning Along Curved Surfaces

11.28 Dimensioning Rounded-End Shapes

The method for dimensioning rounded-end shapes depends on the degree of accuracy required. If precision is not necessary, use methods convenient for manufacturing, as in Figures 11.48ac. Figures 11.48dg show methods used when accuracy is required.

Figure shows the dimensioning technique for round-end shapes.

11.48 Dimensioning Rounded-End Shapes. For accuracy, in parts d–g, overall lengths of rounded-end shapes are given, and radii are indicated, but without specific values. The center-to-center distance may be required for accurate location of some holes. In part g, the hole location is more critical than the location of the radius, so the two are located.

The link to be cast (or cut from sheet metal or plate) in Figure 11.48a is dimensioned as it would be laid out for manufacture, giving the center-to-center distance and the radii of the ends. Note that only one radius dimension is necessary, and the number of places is included with the size dimension.

In Figure 11.47b, the pad on a casting with a milled slot is dimensioned from center to center to help the pattern maker and machinist in layout. This also gives the total travel of the milling cutter. The width dimension indicates the diameter of the milling cutter, so give the diameter of a machined slot. A cored slot, however, would be dimensioned by radius to conform with the pattern-making procedure.

The semicircular pad in Figure 11.48c is laid out like the pad in Figure 11.48b, except that angular dimensions are used. Angular tolerances can be used if necessary.

11.29 Dimensioning Threads

Local notes are used to specify dimensions of threads. For tapped holes, the notes should, if possible, be attached to the circular views of the holes, as shown in Figure 11.49. For external threads, the notes are usually placed in the longitudinal views, where the threads are more easily recognized, as in Figure 11.49b and c. For a detailed discussion of thread notes, see Chapter 13.

Figure shows the technique to dimension threads.

11.49 Dimensioning Threads

11.30 Dimensioning Tapers

A taper is a conical surface on a shaft or in a hole. The usual method of dimensioning a taper is to give the amount of taper in a note, such as TAPER 0.167 ON DIA (with TO GAGE often added), and then give the diameter at one end with the length or give the diameter at both ends and omit the length. Taper on diameter means the difference in diameter per unit of length.

Standard machine tapers are used on machine spindles, shanks of tools, or pins, and are described in “Machine Tapers” in ANSI/ASME B5.10. Such standard tapers are dimensioned on a drawing by giving the diameter (usually at the large end), the length, and a note, such as NO. 4 AMERICAN NATIONAL STANDARD TAPER as shown in Figure 11.50a.

Figure shows the technique to dimension tapers.

11.50 Dimensioning Tapers

For not-too-critical requirements, a taper may be dimensioned by giving the diameter at the large end, the length, and the included angle, all with proper tolerances, as shown in Figure 11.50b. Alternatively, the diameters of both ends, plus the length, may be given with necessary tolerances.

For close-fitting tapers, the amount of taper per unit on diameter is indicated as shown in Figures 11.50c and d. A gage line is selected and located by a comparatively generous tolerance, and other dimensions are given appropriate tolerances as required.

11.31 Dimensioning Chamfers

A chamfer is a beveled or sloping edge. It is dimensioned by giving the length of the offset and the angle, as in Figure 11.51a. A 45° chamfer also may be dimensioned in a manner similar to that shown in Figure 11.51a, but usually it is dimensioned by note, as in Figure 11.51b.

Figure shows the technique to dimension chamfers.

11.51 Dimensioning Chamfers

11.32 Shaft Centers

Shaft centers are required on shafts, spindles, and other conical or cylindrical parts for turning, grinding, and other operations. Such a center may be dimensioned, as shown in Figure 11.52. Normally the centers are produced by a combined drill and countersink.

Figure shows a shaft center.

11.52 Shaft Center

11.33 Dimensioning Keyways

The methods of dimensioning keyways for Woodruff keys and stock keys are shown in Figure 11.53. Note, in both cases, the use of a dimension to center the keyway in the shaft or collar. The preferred method of dimensioning the depth of a keyway is to give the dimension from the bottom of the keyway to the opposite side of the shaft or hole, as shown. The method of computing such a dimension is shown in Figure 11.53d. Values for A may be found in machinists’ handbooks.

Figure shows the dimensioning of keyways.

11.53 Dimensioning Keyways

For general information about keys and keyways see Appendix 20.

11.34 Dimensioning Knurls

A knurl is a roughened surface to provide a better handgrip or to be used for a press fit between two parts. For handgrip purposes, it is necessary only to give the pitch of the knurl, the type of knurling, and the length of the knurled area, as shown in Figures 11.54a and b. To dimension a knurl for a press fit, the toleranced diameter before knurling should be given, as shown in Figure 11.54c. A note should be added that gives the pitch and type of knurl and the minimum diameter after knurling (see ANSI/ASME B94.6.

Figure shows the dimensioning of knurls.

11.54 Dimensioning Knurls

11.35 Finish Marks

A finish mark is used to indicate that a surface is to be machined, or finished, as on a rough casting or forging. To the patternmaker or diemaker, a finish mark means that allowance of extra metal in the rough workpiece must be provided for the machining.

On drawings of parts to be machined from rolled stock, finish marks are generally unnecessary, because it is obvious that the surfaces are finished. Similarly, it is not necessary to show finish marks when the dimension implies a finished surface, such as ∅6.22–6.35 (metric) or ∅2.45–2.50 (decimal-inch).

As shown in Figure 11.55, three styles of finish marks, the general symbol Image, the new basic symbol Image, and the old symbolImage are used to indicate an ordinary smooth machined surface. The symbol is like a capital V, made about 3 mm high, in conformity with the height of dimensioning lettering. The extended symbol, preferred by ANSI, is like a larger capital with the right leg extended. The short leg is made about 5 mm high, and the height of the long leg is about 10 mm. The basic symbol may be altered for more elaborate surface texture specifications.

Figure shows the use of finish marks in different drawings.

11.55 Finish Marks

Figure 11.55c shows a simple casting having several finished surfaces. In Figure 11.55d, two views of the same casting show how the finish marks are indicated on a drawing. The finish mark is shown only on the edge view of a finished surface and is repeated in any other view in which the surface appears as a line, even if the line is a hidden line.

If a part is to be finished all over, finish marks should be omitted, and a general note, such as FINISH ALL OVER or FAO, should be lettered on the lower portion of the sheet.

The several kinds of finishes are detailed in machine shop practice manuals. The following terms are among the most commonly used: finish all over, rough finish, file finish, sand blast, pickle, scrape, lap, hone, grind, polish, burnish, buff, chip, spotface, countersink, counterbore, core, drill, ream, bore, tap, broach, and knurl. When it is necessary to control the surface texture of finished surfaces beyond that of an ordinary machine finish, the symbolImage is used as a base for the more elaborate surface quality symbols. Older drawings may contain the previous style of surface finish symbol shown in Figure 11.55e.

Finished surfaces can be measured more accurately, so provide dimensions from these when possible, as in Figure 11.56.

Figure shows the correct and incorrect ways of using finish marks on a drawing.

11.56 Correct and Incorrect Marks Showing Dimensions to Finished Surfaces. The point of the symbol should be directed inward toward the body of metal similar to a tool bit, not upside down, as is shown in part b.

11.36 Surface Roughness

The demands of automobiles, airplanes, and other machines that can stand heavy loads and high speeds with less friction and wear have increased the need for accurate control of surface quality by the designer, regardless of the size of the feature. Simple finish marks are not adequate to specify surface finish on such parts.

Surface finish is intimately related to the functioning of a surface, and proper specification of finish of surfaces such as bearings and seals is necessary. Surface quality specifications should be used only where needed, since the cost of producing a finished surface becomes greater as the quality of the surface called for is increased. Generally, the ideal surface finish is the roughest that will do the job satisfactorily.

The system of surface texture symbols recommended by ANSI/ASME (Y14.36M) for use on drawings, regardless of the system of measurement used, is now broadly accepted by U.S industry. These symbols are used to define surface texture, roughness, and lay. See Figure 11.57 for the meaning and construction details for these symbols. The basic surface texture symbol in Figure 11.57 a indicates a finished or machined surface by any method, just as does the general Image symbol. Modifications to the basic surface texture symbol, shown in Figures 11.57bd, define restrictions on material removal for the finished surface. Where surface texture values other than average roughness are specified, the symbol must be drawn with the horizontal extension, as shown in Figure 11.57e.

Figure shows the dimensions of two surface texture symbols.

11.57 Surface Texture Symbols and Construction (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)

Applications of Surface Roughness Symbols

Applications of the surface texture symbols are given in Figure 11.58a. Note that the symbols read from the bottom and/or the right side of the drawing and that they are not drawn at any angle or upside down. Measurements for roughness and waviness, unless otherwise specified, apply in the direction that gives the maximum reading, usually across the lay, as shown in Figure 11.58b.

Figure shows the application of surface texture symbols and surface characteristics.

11.58 Application of Surface Texture Symbols and Surface Characteristics (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)

Recommended Roughness and Waviness Values

Recommended roughness height values are given in Table 11.1. When it is necessary to indicate the roughness-width cutoff values, the standard values used are listed in Table 11.2. If no value is specified, the 0.80 value is assumed.

Table 11.1 Preferred Series Roughness Average Values* (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)





























































Table 11.2 Standard Roughness Sampling Length (Cutoff) Values (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)

Millimeters (mm)

Inches (″)













When maximum waviness height values are required, the recommended values are given in Table 11.3.

Table 11.3 Preferred Series Maximum Waviness Height Values (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)

Millimeters (mm)

Inches (″)































Lay Symbols and Surface Texture Symbols

Lay is the term for the dominant direction of the pattern formed by the cutting tool or grinding process used to manufacture a surface. When it is necessary to indicate lay, the lay symbols in Figure 11.59 are added to the surface texture symbols as shown in the given examples. Selected applications of the surface texture values to the symbols are given and explained in Figure 11.60.

Figure shows the various lay symbols.

11.59 Lay Symbols (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)

Figure shows the application of surface texture values to symbols.

11.60 Application of Surface Texture Values to Symbol (Reprinted from ASME Y14.36M-1996 (R2002), by permission of The American Society of Mechanical Engineers. All rights reserved.)

A typical range of surface roughness values that may be obtained from various production methods is included in Chapter 12.

11.37 Location Dimensions

After you have specified the sizes of the geometric shapes composing the structure, give location dimensions to show the relative positions of these geometric shapes. Figure 11.61a shows rectangular shapes located by their faces. In Figure 10.61b, cylindrical or conical holes or bosses, or other symmetrical shapes, are located by their centerlines. Location dimensions for holes are preferably given where the holes appear circular, as shown in Figures 11.62 and 11.63.

Figure shows location dimensions for two drawings.

11.61 Location Dimensions

Figure shows the correct and incorrect techniques for locating holes in a drawing.

11.62 Locating Holes

Figure shows the location of holes from the center of a drawing.

11.63 Locating Holes about a Center

In general, location dimensions should be built from a finished surface or from an important center or centerline. Location dimensions should lead to finished surfaces wherever possible, because rough castings and forgings vary in size, and unfinished surfaces cannot be relied on for accurate measurements. The starting dimension, used in locating the first machined surface on a rough casting or forging, must necessarily lead from a rough surface or from a center or a centerline of the rough piece.

Holes equally spaced about a common center may be dimensioned by giving the diameter of the circle of centers, or bolt circle. Use a note such as 3X to indicate repetitive features or dimensions, where the X means times, and the 3 indicates the number of repeated features. Put a space between the letter X and the dimension as shown in Figure 11.63. Unequally spaced holes are located by means of the bolt circle diameter plus angular measurements with reference to only one of the centerlines. Examples are shown in Figure 11.63.

Where greater accuracy is required, coordinate dimensions should be given, as shown in Figure 11.63c. In this case, the diameter of the bolt circle is enclosed in parentheses to indicate that it is to be used only as a reference dimension. Reference dimensions are given for information only. They are not intended to be measured and do not govern the manufacturing operations. They represent calculated dimensions and are often useful in showing the intended design sizes.

When several cylindrical surfaces have the same centerline (as in Figure 11.64b) you do not need location dimensions to show they are concentric; the centerline is enough.

Figure shows the location of holes in different drawings.

11.64 Locating Holes

When several nonprecision holes are located on a common arc, they are dimensioned by giving the radius and the angular measurements from a baseline, as shown in Figure 11.64a. In this case, the baseline is the horizontal centerline.

In Figure 11.64b, the three holes are on a common centerline. One dimension locates one small hole from the center; the other gives the distances between the small holes. Note that the dimension at X is left off. This method is used when the distance between the small holes is the important consideration. If the relation between the center hole and each of the small holes is more important, then include the distance at X and make the overall dimension a reference dimension.

Figure 11.64c shows another example of coordinate dimensioning. The three small holes are on a bolt circle whose diameter is given for reference purposes only. From the main center, the small holes are located in two mutually perpendicular directions.

Another example of locating holes by means of linear measurements is shown in Figure 11.64d. In this case, one measurement is made at an angle to the coordinate dimensions because of the direct functional relationship of the two holes.

In Figure 11.64e, the holes are located from two baselines, or datums. When all holes are located from a common datum, the sequence of measuring and machining operations is controlled, overall tolerance accumulations are avoided, and proper functioning of the finished part is assured. The datum surfaces selected must be more accurate than any measurement made from them, must be accessible during manufacture, and must be arranged to facilitate tool and fixture design. It may be necessary to specify accuracy of the datum surfaces in terms of straightness, roundness, flatness, and so on.

Figure 11.64f shows a method of giving, in a single line, all the dimensions from a common datum. Each dimension except the first has a single arrowhead and is accumulative in value. The overall dimension is separate.

These methods of locating holes are applicable to locating pins or other symmetrical features.

11.38 Mating Dimensions

In dimensioning a single part, its relation to mating parts must be taken into consideration. In Figure 11.65a, for example, a guide block must fit into a slot in a base. Those dimensions common to both parts, such as the distance between the holes, are mating dimensions. Other dimensions that do not control the accurate fitting together of two parts are not mating dimensions.

Figure shows the dimensioning of mating parts.

11.65 Mating Dimensions

These mating dimensions should be given on the multiview drawings in the corresponding locations, as shown in Figures 11.65b and c. The actual values of two corresponding mating dimensions may not be exactly the same. For example, the width of the slot in Figure 11.65b may be dimensioned 1/32″ (0.8 mm) or several thousandths of an inch larger than the width of the block in Figure 11.65c, but these are mating dimensions figured from a single basic width. Mating dimensions need to be specified in the corresponding locations on the two parts and toleranced to ensure proper fitting of the parts.

In Figure 11.66a, the dimension A is a necessary mating dimension and should appear on both the drawings of the bracket and of the frame. In Figure 11.66b, which shows a redesign of the bracket into two parts, dimension A is not used on either part because it is not necessary to closely control the distance between the cap screws. But dimensions F are now essential mating dimensions and should appear on the drawings of both parts. The remaining dimensions, E, D, B, and C, are not considered to be mating dimensions, since they do not directly affect the mating of the parts.

Figure shows single and double bracket assemblies.

11.66 Bracket Assembly

11.39 Coordinate Dimensioning

Coordinate dimensioning practices allow you to identify a corner of the part as the 0,0 location and dimension the remaining features relative to that position. This is very useful when numerically-controlled machines will be used in manufacturing the part, as the dimensions relate well to the manufacturing process. The lower-left corner on the part is often used as the 0,0 location (see Figure 11.67) as this is frequently the default for the numerically-controlled machine.

Figure shows a hole table.

11.67 Hole Table. A hole table is often used to dimension complicated patterns of holes. (Reprinted from ASME Y14.5M-1994 (R2004), by permission of The American Society of Mechanical Engineers. All rights reserved.)

Rectangular coordinate dimensioning without dimension lines is shown in Figure 11.68.

Figure shows rectangular coordinate dimensioning of holes without dimension lines.

11.68 Rectangular Coordinate Dimensioning without Dimension Lines

Hole tables are often used in conjunction with coordinate dimensioning to save space when there are numerous holes of different sizes.

11.40 Tabular Dimensions

A series of objects having like features but varying in dimensions may be represented by one drawing, as shown in Figure 11.69. Letters are substituted for dimension figures on the drawing, and the varying dimensions are given in tabular form. The dimensions of many standard parts are given in this manner in catalogs and handbooks.

Figure shows an example of tabular dimensioning.

11.69 Tabular Dimensioning

11.41 Dimensioning for Numerically-Controlled Machining

When dimensioning for numerically-controlled machining, follow these basic guidelines.

A set of three mutually perpendicular datum or reference planes is usually required. These planes either must be obvious, as shown in Figure 11.70, or must be clearly identified. (See Chapter 12 for information on identifying datums.)

Figure shows the dimensioning for numerically-controlled machining.

11.70 Dimensioning for Numerically-Controlled Machining

The designer selects as origins for dimensions those surfaces or features most important to the function of the part. Enough of these features are selected to position the part in relation to the set of mutually perpendicular planes. All related dimensions are then made from these planes.

• All dimensions should be in decimals.

• Angles should be given, where possible, in degrees and decimal parts of degrees.

• Tools such as drills, reamers, and taps should be left up to the manufacturer unless a certain process is specifically required.

• All tolerances should be determined by the design requirements of the part, not by the capability of the manufacturing machine.

11.42 Machine, Pattern, and Forging Dimensions

The pattern maker is interested in the dimensions required to make the pattern, and the machinist is concerned only with the dimensions needed to machine the part. Frequently, a dimension that is convenient for the machinist is not convenient for the pattern maker, or vice versa. Because the pattern maker uses the drawing only once, while making the pattern, and the machinist refers to it continuously, the dimensions should be given primarily for the convenience of the machinist.

If the part is large and complicated, two separate drawings are sometimes made—one showing the pattern dimensions and the other the machine dimensions. The usual practice, however, is to prepare one drawing for both the pattern maker and the machinist.

For forgings, it is common practice to make separate forging drawings and machining drawings. A forging drawing of a connecting rod, showing only the dimensions needed in the forge shop, is shown in Figure 11.71. A machining drawing of the same part would contain only the dimensions needed in the machine shop.

Figure depicts the detailed drawing of the connecting rod with dimensions and the title box is shown at the bottom.

11.71 Forging Drawing of Connecting Rod (General Motors LLC. Used with permission. GM Media Archives.)

11.43 Sheet Metal Bends

In sheet metal dimensioning, allowance must be made for bends. The intersection of the plane surfaces adjacent to a bend is called the mold line, and this line, rather than the center of the arc, is used to determine dimensions, as shown in Figure 11.72. The following procedure for calculating bends is typical. If the two inner plane surfaces of an angle are extended, their line of intersection is called the inside mold line or IML, as shown in Figures 11.73ac. Similarly, if the two outer plane surfaces are extended, they produce the outside mold line or OML. The centerline of bend (B) refers primarily to the machine on which the bend is made and is at the center of the bend radius.

Figure shows the dimensioning done for a shape that includes bends.

11.72 Profile Dimensioning

The length, or stretchout, of the pattern equals the sum of the flat sides of the angle plus the distance around the bend measured along the neutral axis. The distance around the bend is called the bend allowance or BA. When metal bends, it compresses on the inside and stretches on the outside. At a certain zone in between, the metal is neither compressed nor stretched, and this is called the neutral axis, as shown in Figure 11.73d. The neutral axis is usually assumed to be 0.44 of the thickness from the inside surface of the metal.

Figure labels two different mold lines in a bend.

11.73 Bends

The developed length of material, or bend allowance, to make the bend is computed from the empirical formula

BA = (0.017453R + 0.0078T)N

where R = radius of bend, T = metal thickness, and N = number of degrees of bend, as in Figure 11.73c.

11.44 Notes

It is usually necessary to supplement the direct dimensions with notes. Notes should be brief and carefully worded to allow only one interpretation. Notes should always be lettered horizontally on the sheet and arranged systematically. They should not be crowded and should not be placed between views, if possible. Notes are classified as general notes when they apply to an entire drawing and as local notes when they apply to specific items.

General Notes

General notes should be lettered in the lower right-hand corner of the first sheet of a set of drawings, above or to the left of the title block or in a central position below the view to which they apply. If notes are continued onto a second sheet, that sheet number should be given in a note on the first sheet of the drawing set, as in NOTES CONTINUED ON PAGE 4.

Here are some examples of general notes:






In machine drawings, the title strip or title block will carry many general notes, including those for materials, general tolerances, heat treatments, and patterns.

Local Notes

Local notes apply to specific operations only and are connected by a leader to the point at which such operations are performed, as shown in Figure 11.74. The leader should be attached at the front of the first word of a note, or just after the last word, and not at any intermediate place.

Figure shows the use of local notes in several instances.

11.74 Local Notes

Use common abbreviations in notes (such as THD, DIA, MAX) only when they cannot be misunderstood. Avoid less common abbreviations. “When in doubt, spell it out” is a rule of thumb to avoid problems with misunderstood notes.

If a common symbol is available, it is preferred to the abbreviation because symbols are internationally recognized and not language dependent. All abbreviations should conform to ANSI Y14.38. See Appendix 2 for ANSI abbreviations.

In general, leaders and notes should not be placed on the drawing until the dimensioning is substantially completed. Notes and lettering should not touch lines of the drawing or title block. If notes are lettered first, they may be in the way of necessary dimensions and will have to be moved.

When using CAD to add text for drawing notes, keep in mind the final scale to which the drawing will be plotted. You may need to enlarge the text for it to be legible when plotted to a smaller scale.

11.45 Standards

Dimensions should be given, wherever possible, to make use of readily available materials, tools, parts, and gages. The dimensions for many commonly used machine elements—such as bolts, screws, nails, keys, tapers, wire, pipes, sheet metal, chains, belts, ropes, pins, and rolled metal shapes—have been standardized, and the drafter must obtain these sizes from company standards manuals, from published handbooks, from ANSI standards, or from manufacturers’ catalogs. Tables of some of the more common items are given in the appendices.

Such standard parts are not delineated on detail drawings unless they are to be altered for use; they are conventionally drawn on assembly drawings and are listed in parts lists. Common fractions are often used to indicate the nominal sizes of standard parts or tools. If the complete decimal-inch system is used, all such sizes are ordinarily expressed by decimals—for example, .250 DRILL instead of 1/4 DRILL. If the all-metric system of dimensioning is used, then the preferred metric drill of the approximate same size (.2480″) will be indicated as 6.30 DRILL.

11.46 Dos and Don’ts of Dimensioning

The following checklist summarizes briefly most of the situations in which a beginning designer is likely to make a mistake in dimensioning. Students should check the drawing with this list before submitting it to the instructor.

1. Each dimension should be given clearly so that it can be interpreted in only one way.

2. Dimensions should not be duplicated, nor should the same information be given in two different ways—except for dual dimensioning—and no dimensions should be given except those needed to produce or inspect the part.

3. Dimensions should be given between points or surfaces that have a functional relation to each other or that control the location of mating parts.

4. Dimensions should be given to finished surfaces or important centerlines, in preference to rough surfaces, wherever possible.

5. Dimensions should be given so that it will not be necessary for the machinist to calculate, scale, or assume any dimension.

6. Dimension features should be attached to the view where the feature’s shape is best shown.

7. Dimensions should be placed in the views where the features dimensioned are shown true shape.

8. Dimensioning to hidden lines should be avoided wherever possible.

9. Dimensions should not be placed on a view unless clarity is promoted and long extension lines are avoided.

10. Dimensions applying to two adjacent views should be placed between views, unless clarity is promoted by placing some of them outside.

11. The longer dimensions should be placed outside all intermediate dimensions so that dimension lines will not cross extension lines.

12. In machine drawing, all unit marks should be omitted, except when necessary for clarity; for example, 1″ VALVE or 1 mm DRILL.

13. Don’t expect production personnel to assume that a feature is centered (as a hole on a plate), but give a location dimension from one side. However, if a hole is to be centered on a symmetrical rough casting, mark the centerline and omit the locating dimension from the centerline.

14. A dimension should be attached to only one view, not to extension lines connecting two views.

15. Detail dimensions should line up in chain fashion.

16. A complete chain of detail dimensions should be avoided; it is better to omit one. Otherwise add a reference to the overall dimension by enclosing it within parentheses.

17. A dimension line should never be drawn through a dimension figure. A figure should never be lettered over any line of the drawing. The line can be broken if necessary.

18. Dimension lines should be spaced uniformly throughout the drawing. They should be at least 10 mm (.38″) from the object outline and 6 mm (.25″) apart.

19. No line of the drawing should be used as a dimension line or coincide with a dimension line.

20. A dimension line should never be joined end to end with any line of the drawing.

21. Dimension lines should not cross, if avoidable.

22. Dimension lines and extension lines should not cross, if avoidable. (Extension lines may cross each other.)

23. When extension lines cross extension lines or visible lines, no break in either line should be made.

24. A centerline may be extended and used as an extension line, in which case it is still drawn like a centerline.

25. Centerlines should not extend from view to view.

26. Leaders for notes should be straight, not curved, and point to the center of circular views of holes wherever possible.

27. Leaders should slope at 45°, 30°, or 60° with horizontal, but may be made at any convenient angle except vertical or horizontal.

28. Leaders should extend from the beginning or the end of a note, with the horizontal “shoulder” extending from mid-height of the lettering.

29. Dimension figures should be approximately centered between the arrowheads, except in a stack of dimensions, where they should be staggered.

30. Dimension figures should be about 3 mm (.13″) high for whole numbers and 6 mm (.25″) high for fractions.

31. Dimension figures should never be crowded or in any way made difficult to read.

32. Dimension figures should not be lettered over lines or sectioned areas unless necessary, in which case a clear space should be reserved for the dimension figures.

33. Dimension figures for angles should generally be lettered horizontally.

34. Fraction bars should never be inclined except in confined areas, such as in tables.

35. The numerator and denominator of a fraction should never touch the fraction bar.

36. Notes should always be lettered horizontally on the sheet.

37. Notes should be brief and clear, and the wording should be standard in form.

38. Finish marks should be placed on the edge views of all finished surfaces, including hidden edges and the contour and circular views of cylindrical surfaces.

39. Finish marks should be omitted on holes or other features where a note specifies a machining operation.

40. Finish marks should be omitted on parts made from rolled stock.

41. If a part is finished all over, all finish marks should be omitted and the general note FINISH ALL OVER or FAO should be used.

42. A cylinder is dimensioned by giving both its diameter and length in the rectangular view, except when notes are used for holes. A diagonal diameter in the circular view may be used in cases where it increases clarity.

43. Manufacturing processes are generally determined by the tolerances specified, rather than specifically noted in the drawing. When the manufacturing process must be noted for some reason—such as for dimension holes to be bored, drilled, and reamed—use leaders that preferably point toward the center of the circular views of the holes. Give the manufacturing processes in the order they would be performed.

44. Drill sizes should be expressed in decimals, giving the diameter. For drills designated by number or letter, the decimal size must also be given.

45. In general, a circle is dimensioned by its diameter, an arc by its radius.

46. Diagonal diameters should be avoided, except for very large holes and for circles of centers. They may be used on positive cylinders for clarity.

47. A diameter dimension value should always be preceded by the symbol ∅.

48. A radius dimension should always be preceded by the letter R. The radial dimension line should have only one arrowhead, and it should pass through or point through the arc center and touch the arc.

49. Cylinders should be located by their centerlines.

50. Cylinders should be located in the circular views, if possible.

51. Cylinders should be located by coordinate dimensions in preference to angular dimensions where accuracy is important.

52. When there are several rough, noncritical features obviously the same size (fillets, rounds, ribs, etc.), it is necessary to give only typical (abbreviation TYP) dimensions or to use a note.

53. When a dimension is not to scale, it should be underscored with a heavy straight line or marked NTS or NOT TO SCALE.

54. Mating dimensions should be given correspondingly on both drawings of mating parts.

55. Pattern dimensions should be given in two-place decimals or in common whole numbers and fractions to the nearest 1/16″.

56. Decimal dimensions should be used for all machining dimensions.

57. Cumulative tolerances should be avoided where they affect the fit of mating parts.


Drawings show the different views of an oscillator cover.

This drawing for a small part shows dimensions in millimeters with the inch values given [in brackets] for reference. (Courtesy of Big Sky Laser.)

Drawings show the different views of a switch mounting bracket is shown.

Dimensioned Drawing for a Sheet Metal Part (Courtesy of Wood’s Power-Grip Co., Inc.)

Plan and profile drawing for a dam site are shown.

Plan and Profile for Dam Site (Courtesy of Schnabel Engineering.)

An architectural drawing depicts detailed dimensions.

Portion of a Drawing Showing Dimensioned Architectural Details (Courtesy of Locati Architects.)

Key Words




Bracket Method


Chordal Dimensions

Coordinate Dimensions

Dimension Line


Dual Dimensioning

Extension Line

Finish Mark

General Notes



Local Notes

Location Dimensions

Mating Dimensions

Position Method

Radial Leader Line

Size Dimensions


Superfluous Dimensions

Surface Texture Symbols



Chapter Summary

• To increase clarity, dimensions and notes are added to a drawing to describe size, location, and manufacturing process precisely.

• Drawings are scaled to fit on a standard sheet of paper. Drawings created by hand are drawn to scale. CAD drawings are drawn full size and scaled when they are printed.

• Dimensions and notes are placed on drawings according to prescribed standards.

• Good placement practices are essential to making drawings easy to read.

• It is important to learn to dimension basic shapes. Complex drawings are usually made of many simpler features.

• Finish symbols and notes are a part of describing how the part is to be manufactured. They should be shown on the drawing as needed.

• The CAD database can serve as the design documentation, in which case drawings may not be necessary.

• Dimensioning dos and don’ts can provide guidelines for dimensioning practices, but overall, the dimensions that are necessary for the part to be manufactured and function in the assembly as intended must be shown.

• Special dimensioning techniques are used for surfaces that have been machined by one of the manufacturing processes.

Review Questions

1. What are the different units used when a drawing is created using a metric scale? Using an architects’ scale?

2. Explain the concept of contour dimensioning.

3. Which type of line is never crossed by any other line when dimensioning an object?

4. How is geometric analysis used in dimensioning?

5. What is the difference between a size dimension and a location dimension?

6. Which dimension system allows dimensions to be read from the bottom and from the right? When can a dimension be read from the left?

7. Draw an example of dimensioning an angle.

8. When are finish marks used? Draw two types.

9. How are negative and positive cylinders dimensioned? Draw examples.

10. How are holes and arcs dimensioned? Draw examples.

11. What are notes and leaders used for?

12. How does a counterbore dimension that specifies a fillet radius differ from a fillet radius specified as part of a spot-face dimension?

13. Why is it important to avoid superfluous dimensions?

Chapter Exercises

Most of your practice in dimensioning will be in connection with working drawings assigned from other chapters. However, some dimensioning problems are available here. The following problems are designed for 8.50″ × 11″ size sheets and are to be drawn and dimensioned to a full-size scale. Size 297 mm × 420 mm sheets may be used with appropriate adjustments in the title strip layout.

Eight drawings are present in the figure.

Exercise 11.1 To obtain sizes, use the views on this page and transfer them to the scale at the side to obtain values. Dimension drawings completely in one-place millimeters or two-place inches as assigned, full size. See the inside back cover for decimal-inch and millimeter equivalents.

Top and frontal views of eight objects are present along with inches to millimeter conversion scale.

Exercise 11.2 To obtain sizes, use the views on this page and transfer them to the scale at the side to obtain values. Dimension drawings completely in one-place millimeters or two-place inches as assigned, full size. See the inside back cover for decimal-inch and millimeter equivalents.

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