Bolt Hole Circle Calculator: Coordinates, Centers

This calculator works out the X and Y coordinates of each hole in a bolt hole circle (also called a PCD, pitch circle diameter) when you enter the circle diameter, the number of holes, and the angle of the first hole. You get the coordinates for every hole, measured from the center of the circle, which you can then use directly in CNC work, drilling, or layout. The first output is the X coordinate of the first hole, followed by a full list of all coordinates.

Formula

The coordinates of each hole on a bolt hole circle are found using basic trigonometry. For hole i (starting at 1), the angle from the positive X-axis is:

θ_i = a + (i − 1) × (360° / n)

Then the coordinates are:

X_i = (d / 2) × cos(θ_i)
Y_i = (d / 2) × sin(θ_i)

• d – the pitch circle diameter (PCD), in mm (or any unit you use consistently).
• n – number of holes (must be an integer ≥ 2).
• a – angle of the first hole, in degrees, measured counterclockwise from the positive X-axis (3 o’clock position).
• θ_i – angle for hole i, in degrees.
• X_i, Y_i – coordinates of hole i relative to the circle center.

All angles are in degrees. The origin (0,0) is the center of the bolt circle. The positive X-axis points to the right (3 o’clock), and the positive Y-axis points up (12 o’clock).

Worked Example

Using the default values: circle diameter = 100 mm, number of holes = 8, first hole angle = 0°.

1. Radius = 100 / 2 = 50 mm.
2. Angle step = 360° / 8 = 45°.
3. Hole 1: θ = 0°, X = 50 × cos(0°) = 50.00, Y = 50 × sin(0°) = 0.00.
4. Hole 2: θ = 45°, X = 50 × cos(45°) ≈ 35.36, Y = 50 × sin(45°) ≈ 35.36.
5. Hole 3: θ = 90°, X = 50 × cos(90°) = 0.00, Y = 50 × sin(90°) = 50.00.
6. Hole 4: θ = 135°, X ≈ −35.36, Y ≈ 35.36.
7. Hole 5: θ = 180°, X = −50.00, Y = 0.00.
8. Hole 6: θ = 225°, X ≈ −35.36, Y ≈ −35.36.
9. Hole 7: θ = 270°, X = 0.00, Y = −50.00.
10. Hole 8: θ = 315°, X ≈ 35.36, Y ≈ −35.36.

The calculator’s first output (X of hole 1) is 50.00 mm, matching step 3. The other outputs show the coordinates for holes 2 and 3; you can extend the pattern for the rest.

When to Use a Bolt Hole Circle Calculator

You need this whenever you have to drill or machine holes that lie evenly spaced on a circle. Common situations include:

• Flanges and pipe connections – bolt holes around a central bore.
• Wheel hubs and rims – lug nut patterns.
• Gear or sprocket mounting holes.
• CNC milling or drilling – you can directly enter the coordinates into your program.
• Layout on a manual mill or drill press using a digital readout (DRO).

The calculator gives you Cartesian (X/Y) coordinates from the center. If your machine uses polar coordinates (radius and angle), you already have those: radius = d/2, and the angles are the ones shown above.

How to Choose the Angle of the First Hole

The angle of the first hole is a reference point. In most drawings, the first hole is at 0° (3 o’clock) unless otherwise specified. But sometimes the drawing shows a hole at the top (12 o’clock), which is 90° in this system. If you need a hole at the top, set the first hole angle to 90°. If you need a hole at the left (9 o’clock), set it to 180°.

Also consider the direction: this calculator uses counterclockwise (CCW) positive angles, which is the standard mathematical convention. If your drawing uses clockwise (CW) angles, you can either negate the angles or mirror the Y coordinates (multiply Y by −1).

Common Mistakes and How to Avoid Them

• Using diameter instead of radius in the formula. The formula uses radius (d/2), not the full diameter. Always divide by 2 first.
• Mixing degrees and radians. This calculator uses degrees. If you’re doing the math manually in a spreadsheet, make sure the trig functions are set to degrees, or convert: radians = degrees × Ï€/180.
• Counting holes incorrectly. The angle step is 360° divided by the number of holes. For 5 holes, the step is 72°, not 60°.
• Forgetting the first hole angle. If you set the first hole angle to 0° but the drawing shows the first hole at 30°, all your coordinates will be rotated by 30°.
• Unit inconsistency. If you enter the diameter in inches, your coordinates come out in inches. Don’t mix mm and inches in the same calculation.
• Rounding too early. Round only at the final step. If you round each coordinate to 2 decimals and then use them for further calculations, errors can accumulate.

Limitations and Practical Notes

This calculator assumes the holes are evenly spaced around the full 360° circle. If you have an arc of holes (not a full circle), you need a different approach – this tool won’t handle that. Also, it gives you coordinates relative to the circle center. If your workpiece origin is elsewhere, you must add an offset to every coordinate.

For machining, always double-check your first hole location physically before drilling all holes. A small error in angle or radius becomes a larger error in hole position as the diameter grows. For example, on a 200 mm diameter circle, a 1° angular error shifts the hole position by about 1.75 mm at the rim.

The formula is exact for any number of holes ≥ 2. For very small numbers (2 or 3 holes), the coordinates are still correct, but the “circle� is trivial – two holes are just opposite each other, three holes form an equilateral triangle.

Frequently Asked Questions

What is a bolt hole circle (PCD)?

A bolt hole circle is the imaginary circle that passes through the centers of all the bolt holes in a pattern. The PCD (pitch circle diameter) is the diameter of that circle. It’s the standard way to describe a bolt pattern, e.g., “5 × 100 mm� means 5 holes on a 100 mm diameter circle.

How do I measure the PCD of an existing part?

For an even number of holes, measure the distance between the centers of two opposite holes – that’s the PCD. For an odd number of holes, measure from the center of one hole to the center of the hole across from it (not exactly opposite), then use a formula: PCD = measured distance / sin(180°/n), where n is the number of holes. Or use a caliper to measure from the edge of one hole to the edge of the opposite hole and adjust by the hole radii.

Can I use this for a 5-hole pattern?

Yes, absolutely. Enter 5 as the number of holes. The angle step will be 72°. The coordinates will be correct for any odd or even number of holes.

What if my first hole is at the top (12 o’clock)?

Set the first hole angle to 90°. Then the first hole will be at (0, d/2) – directly above the center. The rest will follow counterclockwise.

Do I need to convert mm to inches?

No, the calculator works with any unit. Just be consistent. If you enter the diameter in inches, the coordinates come out in inches. If you enter mm, you get mm.

Why does the calculator only show the first three holes?

To keep the output readable, the calculator displays the first three holes’ coordinates. For more holes, you can either use the pattern (each hole is rotated by 360/n from the previous) or use a full table generator. The first three are enough to verify your setup; the rest follow the same spacing.

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in d | Circle diameter (PCD) | mm | 100 | 0
in n | Number of holes | - | 8 | 3
in a | Angle of first hole | deg | 0 | 0
out x1 | X coordinate of hole 1 | mm | (d/2) * cosd(a) | 2
out y1 | Y coordinate of hole 1 | mm | (d/2) * sind(a) | 2
out x2 | X coordinate of hole 2 | mm | (d/2) * cosd(a + 360/n) | 2
out y2 | Y coordinate of hole 2 | mm | (d/2) * sind(a + 360/n) | 2
out x3 | X coordinate of hole 3 | mm | (d/2) * cosd(a + 2*360/n) | 2
out y3 | Y coordinate of hole 3 | mm | (d/2) * sind(a + 2*360/n) | 2