Bolt Circle Calculator
This bolt circle calculator gives the X and Y coordinates of every hole in a bolt pattern. Enter the bolt circle diameter, the number of holes, the start angle, the direction, and the center point, and the bolt circle calculator returns the angle between holes, the straight distance between neighboring holes, and a coordinate list you can use for layout, drilling, or a CNC program.
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The Bolt Circle Calculator is part of our Machinery collection. Browse more machinery to size, convert, and check your work alongside this tool.
What the bolt circle calculator does
A bolt circle, also called the pitch circle diameter or PCD, is the circle that runs through the centers of equally spaced holes on a flange, hub, wheel, or cover. Each hole sits at the same radius, separated by an equal angle of 360 degrees divided by the number of holes. The bolt circle calculator turns that pattern into Cartesian coordinates from the center you choose, so you can mark it out, set a drill press, or write the hole positions straight into a CNC program.
Bolt circle formula
With a bolt circle diameter D, n holes, and a first hole at angle θ0:
Each hole is then placed at X = Xc + R cos θk and Y = Yc + R sin θk. Clockwise patterns subtract the angle step instead of adding it. The hole spacing is the straight line between neighboring hole centers, useful for checking a pattern with calipers.
Bolt circle calculator example
An 8-hole flange on a 150 mm bolt circle, with the first hole at 22.5° so that no hole sits on the center lines:
The spacing between neighboring holes is 150 × sin 22.5° = 57.403 mm, and opposite holes sit 150 mm apart. Placing holes straddling the center lines, as here, is common on pipe flanges.
How to use the bolt hole circle calculator
Enter the bolt circle diameter and the number of holes. Set the start angle of the first hole, measured from the positive X axis; 0 places it at three o'clock, 90 at twelve o'clock. Choose counterclockwise or clockwise, and enter the center coordinates if the pattern is not at the origin. Use any length unit, as long as you use it throughout. Press Calculate to get the hole list.
Reading bolt hole coordinates
The coordinates are measured from the center you entered, along the same axes as your drawing or machine. Check the direction your machine counts angles: most CNC controls treat counterclockwise as positive, viewed from above the part. Round the values to the accuracy of your process; three decimal places in millimeters are more than enough for drilling. Measure two neighboring holes after drilling and compare with the hole spacing to catch a wrong angle early.
When to use a pcd calculator
- Drilling a flange or hub bolt pattern
- Writing hole positions into a CNC or milling program
- Laying out holes with a height gauge or scriber
- Checking a wheel or flange bolt circle diameter
- Designing covers, plates, and motor mounts
Common bolt circle calculator mistakes
- Entering the radius as the diameter. The bolt circle diameter is twice the radius.
- Measuring the start angle from the wrong axis. 0° is the positive X axis.
- Mixing clockwise and counterclockwise. Match your machine.
- Measuring hole edges as centers. Add half a hole on each side.
Tips for a bolt hole circle calculator layout
- Spot drill every hole before drilling to size.
- Check the spacing of the first two holes before drilling the rest.
- Straddle the center lines on pipe flanges.
Bolt pattern calculator for odd hole counts
With an even number of holes, opposite holes sit exactly one diameter apart, so a caliper across them gives the bolt circle directly. With 3, 5, or 7 holes, no two holes are opposite. For a 5-hole pattern, the widest distance between hole centers is D × sin 72° = 0.951 D, so a 5 × 100 mm wheel pattern measures about 95.1 mm across its widest pair. Once the holes are placed, select the drill for the thread with the tap drill size calculator.
Flange bolt circle and pitch circle diameter standards
Pipe flanges follow standard bolt circles: EN 1092-1 PN16 DN100, for example, uses 8 holes on a 180 mm circle, and ASME B16.5 Class 150 4-inch flanges use 8 holes on 7.5 inches. Holes straddle the center lines so that two flanges line up with the pipe axis level. After assembly, tighten the bolts in a star pattern to an even preload set with the bolt torque calculator, so the gasket compresses evenly around the circle.
Bolt circle chart: angle and hole spacing
Multiply the bolt circle diameter by the chord factor to get the straight distance between neighboring holes:
| Holes | Angle between holes | Chord factor | Hole spacing on 100 mm PCD |
|---|---|---|---|
| 3 | 120° | 0.86603 | 86.603 mm |
| 4 | 90° | 0.70711 | 70.711 mm |
| 5 | 72° | 0.58779 | 58.779 mm |
| 6 | 60° | 0.50000 | 50.000 mm |
| 8 | 45° | 0.38268 | 38.268 mm |
| 10 | 36° | 0.30902 | 30.902 mm |
| 12 | 30° | 0.25882 | 25.882 mm |
| 16 | 22.5° | 0.19509 | 19.509 mm |
Flange bolt circle example: 8 holes on 150 mm, start at 22.5°
| Hole | Angle | X | Y |
|---|---|---|---|
| 1 | 22.5° | 69.291 | 28.701 |
| 2 | 67.5° | 28.701 | 69.291 |
| 3 | 112.5° | -28.701 | 69.291 |
| 4 | 157.5° | -69.291 | 28.701 |
| 5 | 202.5° | -69.291 | -28.701 |
| 6 | 247.5° | -28.701 | -69.291 |
| 7 | 292.5° | 28.701 | -69.291 |
| 8 | 337.5° | 69.291 | -28.701 |
Bolt Circle Calculator FAQ
How do you calculate a bolt circle?
Divide 360° by the number of holes for the angle step, then place each hole at X = R cos θ and Y = R sin θ, where R is half the bolt circle diameter.
What is PCD?
Pitch circle diameter: the diameter of the circle through the centers of the bolt holes. It is the same as the bolt circle diameter.
How far apart are the holes on a bolt circle?
Hole spacing = D × sin(180° ÷ n). Six holes on a 100 mm circle are exactly 50 mm apart.
How do I measure the bolt circle of a 5-hole pattern?
Measure from the center of one hole to the far edge of the hole across, or measure the spacing between neighbors and divide by sin 36° (0.5878).