Bolt Circle Calculator Template and Formula

A bolt circle calculator template computes the coordinates of equally spaced holes around a circle from the circle diameter, hole count, and starting angle. Enter those values in the calculator block to get the bolt-circle radius and the X and Y coordinates for each hole, ready to check or transfer to a drawing.

Formula

A bolt circle, also called a bolt pattern or pitch circle, places hole centers at equal angular intervals around a shared center. For a circle diameter d and n equally spaced holes, the angular spacing is:

Step angle = 360° / n

Number the holes from 0 through n − 1. If a is the angle of the first hole, the angle of hole i is:

θᵢ = a + i × (360° / n)

For coordinates measured from the bolt-circle center, convert the diameter to a radius and use:

r = d / 2
xᵢ = r × cos(θᵢ)
yᵢ = r × sin(θᵢ)

• d is the bolt-circle diameter, in millimeters in this template.
• n is the number of holes, a positive whole number.
• a is the starting angle, in degrees, measured counterclockwise from the positive X axis.
• i is the hole index, from 0 to n − 1.
• r, x, and y are lengths in the same unit as d.

The calculator block reports the radius and the coordinates of the first hole. Use the same equations with each successive angle to generate the complete pattern. A positive Y coordinate is above the center in the usual Cartesian drawing convention; a negative coordinate is below it.

Worked Example

Using the template defaults: diameter d = 100 mm, hole count n = 4, and starting angle a = 0°:

1. Radius: r = 100 / 2 = 50 mm.
2. Angular spacing: 360° / 4 = 90°.
3. First-hole X coordinate: x₀ = 50 × cos(0°) = 50.00 mm.
4. First-hole Y coordinate: y₀ = 50 × sin(0°) = 0.00 mm.

The first hole is therefore at (50.00 mm, 0.00 mm). The four center-relative coordinates are (50, 0), (0, 50), (−50, 0), and (0, −50) mm, before rounding. The calculator’s displayed radius is 50.00 mm.

What a Bolt Circle Template Is For

A bolt circle template is useful when laying out a flange, wheel, plate, cover, or other part with evenly distributed holes. Instead of measuring every hole-to-hole distance, the pattern is defined by its center, diameter, hole count, and angular orientation. A coordinate list is particularly helpful for CAD sketches, CNC programming, inspection, and transferring a pattern to a full-scale drawing.

The term can also mean a printable paper layout or a spreadsheet. The calculator block above is a compact calculation template; it does not create a scaled printable drawing or account for material thickness, fasteners, clearances, or machining tolerances. Those details depend on the part and its design requirements.

How to Use the Template

1. Enter the diameter through the centers of the holes, not the outside diameter of a flange.
2. Enter the number of holes as a whole number. For example, use 6 for six equally spaced holes.
3. Choose a starting angle that matches the drawing’s orientation. Zero degrees places the first hole on the positive X axis.
4. Calculate each remaining coordinate by adding 360° divided by the hole count to the preceding angle.
5. Keep the coordinate origin at the bolt-circle center, or add the part’s center coordinates if the drawing uses a different origin.

For six holes starting at 0°, the angles are 0°, 60°, 120°, 180°, 240°, and 300°. For a pattern rotated by 30°, add 30° to each of those angles. The diameter and spacing remain unchanged; only the orientation changes.

Units, Layout, and Measurement

The template uses millimeters, but the geometry works in any consistent length unit. For inches, enter a diameter in inches and interpret the resulting radius and coordinates in inches. To convert a measurement, 1 inch equals 25.4 mm. Do not enter a diameter in millimeters and then read the results as inches: the calculator does not infer or convert units.

In a physical layout, the bolt-circle diameter is a center-to-center measurement across opposite holes. It is not the gap between hole edges. If measuring a real part, account for the method and precision of the measuring tool; rounding a coordinate for display does not make the manufactured location more accurate.

Coordinate signs depend on the drawing convention. Some machine or CAD setups use a different axis direction or define angles clockwise. In that case, match the program’s convention by changing the sign or angle reference consistently, rather than mixing coordinate systems.

Common Errors and Limits

• Using the wrong diameter: The input is the diameter of the circle through the hole centers. A flange’s outside diameter is a different dimension.
• Confusing radius and diameter: Coordinates use the radius, which is half the entered diameter.
• Entering an invalid count: Hole count must be a positive whole number. A fractional count does not describe a bolt pattern.
• Mixing degrees and radians: The template’s starting angle is in degrees. The equations shown use degree-based trigonometry.
• Rounding too early: Keep unrounded values for intermediate coordinates and round only for display or according to the drawing’s required precision.

The equations assume identical angular spacing on a perfect circle. They do not calculate hole diameter, edge distance, thread engagement, fastener clearance, or a suitable manufacturing tolerance. They also do not verify that a pattern fits a particular component. Confirm those design details independently before making or modifying a part.

Frequently Asked Questions

How do I calculate a bolt-circle diameter from coordinates?
If a hole center has coordinates x and y relative to the circle center, its distance from that center is r = √(x² + y²). The bolt-circle diameter is d = 2r. Use consistent units and the correct center origin.

How do I find the distance between adjacent holes?
For n equally spaced holes on a circle of radius r, the straight-line center-to-center distance between neighbors is the chord length c = 2r sin(180° / n). This is not the same as the arc length along the circle.

Does the first-hole angle change the bolt-circle diameter?
No. The starting angle rotates the pattern around its center. It changes the coordinates and orientation, but not the radius, diameter, hole count, or angular spacing.

Can I use this for a pattern with unequal spacing?
Not directly. The template assumes equal angular spacing. For unequal spacing, enter or calculate each hole’s own angle, then use the coordinate equations separately for every hole.

What does PCD mean?
PCD commonly means pitch circle diameter: the diameter of the circle passing through the centers of the holes. It is the same geometric dimension called bolt-circle diameter in this calculation.

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in d | Bolt circle diameter | mm | 100 | 0
in n | Number of holes | - | 4 | 1
in a | Starting angle | deg | 0
out r | Bolt circle radius | mm | d / 2 | 2
out x | First hole X coordinate | mm | (d / 2) * cosd(a) | 2
out y | First hole Y coordinate | mm | (d / 2) * sind(a) | 2