Bolt Circle Pattern Calculator: Formula & Examples

A bolt circle pattern calculator works out the X and Y coordinates for each bolt hole in a circular pattern, so you can drill or machine the holes accurately. You enter the number of bolts, the circle’s diameter (bolt circle diameter, BCD), and the angle of the first hole; the calculator returns the coordinates of every hole relative to the center. This is essential for wheel hubs, flange plates, gear covers, and any part where multiple fasteners must line up precisely.

Formula

The bolt circle is a circle of radius \( R = d/2 \), where \( d \) is the bolt circle diameter (the distance between two opposite holes, measured center-to-center). Each hole \( i \) (from 1 to \( n \)) is placed at an angle \( \theta_i \) measured from the positive X-axis:

\( \theta_i = a_0 + (i-1) \times \frac{360^\circ}{n} \)

Then the coordinates are:

\( x_i = R \cos(\theta_i) \)

\( y_i = R \sin(\theta_i) \)

Where \( a_0 \) is the angle of the first hole, \( n \) is the number of bolts, and angles are in degrees. The chord distance between adjacent holes (the straight-line distance from one hole center to the next) is:

\( \text{chord} = d \times \sin\left(\frac{180^\circ}{n}\right) \)

All coordinates are measured from the center of the bolt circle. If you need hole positions relative to a corner, add the center’s offset to each coordinate.

Worked Example

Using the default values: \( n = 5 \) bolts, \( d = 100 \) mm, and first hole at \( a_0 = 0^\circ \).

1. Radius \( R = 100/2 = 50 \) mm.
2. Angle step \( = 360/5 = 72^\circ \).
3. Hole 1: angle \( 0^\circ \), \( x = 50 \cos(0) = 50.00 \), \( y = 50 \sin(0) = 0.00 \).
4. Hole 2: angle \( 72^\circ \), \( x = 50 \cos(72^\circ) \approx 15.45 \), \( y = 50 \sin(72^\circ) \approx 47.55 \).
5. Hole 3: angle \( 144^\circ \), \( x \approx -40.45 \), \( y \approx 29.39 \).
6. Hole 4: angle \( 216^\circ \), \( x \approx -40.45 \), \( y \approx -29.39 \).
7. Hole 5: angle \( 288^\circ \), \( x \approx 15.45 \), \( y \approx -47.55 \).

The chord between adjacent holes is \( 100 \times \sin(36^\circ) \approx 58.78 \) mm. These coordinates match the calculator’s output (rounded to two decimals).

How to Use the Bolt Circle Calculator

Enter three values: the number of bolt holes, the bolt circle diameter, and the angle of the first hole. The calculator outputs the X and Y coordinates for each hole (starting from hole 1) and the chord distance between adjacent holes.

• Number of bolts: Must be an integer ≥ 3. For a 5-lug wheel, enter 5.
• Bolt circle diameter: Measure from the center of one hole to the center of the opposite hole. For an odd number of holes, measure from the center of one hole to the center of the hole directly across (not the nearest).
• First hole angle: Usually 0° (pointing to the right) unless you have a specific orientation, such as aligning with a keyway or a valve stem.

The coordinates are relative to the circle’s center. If you’re drilling on a mill with the part clamped at a known origin, add the center’s X and Y offsets to each coordinate.

When to Use a Bolt Circle Pattern

Bolt circles are everywhere in mechanical design:

• Wheel hubs (5-lug, 6-lug, etc.)
• Pipe flanges and bolted covers
• Gear and pulley mounting holes
• Rotary tables and indexing plates
• Loudspeaker mounting rings
• Any part where fasteners must be evenly spaced around a center

If the holes are not evenly spaced, you can’t use this calculator directly—you’d need to enter each hole’s angle individually.

Common Mistakes and How to Avoid Them

• Using the radius instead of the diameter: The bolt circle diameter is the full distance across the circle, not from center to a hole. If you measure from center to hole, double it.
• Mixing degrees and radians: The calculator uses degrees. If you’re doing the math by hand, make sure your calculator is in degree mode.
• Incorrect first hole angle: If your part has a reference mark (like a keyway), set the first hole angle to match that reference. Otherwise, the pattern will be rotated.
• Rounding too early: Round only the final coordinates, not intermediate values. Rounding each step can shift holes by fractions of a millimeter.
• Forgetting the center offset: If your coordinate system’s origin isn’t the center of the bolt circle, add the center’s coordinates to each result.

Limitations of the Formula

The formula assumes all holes lie exactly on a perfect circle and are equally spaced. Real parts may have tolerances, but the math gives the ideal positions. For a 3-bolt pattern, the chord is \( d \times \sin(60^\circ) \approx 0.866d \). For a 4-bolt pattern, the chord is \( d \times \sin(45^\circ) \approx 0.707d \). The calculator doesn’t account for hole size, thread depth, or material thickness—those are separate considerations.

Also, the calculator gives coordinates in the same unit you input. If you enter inches, the outputs are inches; if you enter millimeters, the outputs are millimeters. No conversion is done automatically.

Frequently Asked Questions

How do I measure the bolt circle diameter on a 5-lug wheel?

For an odd number of holes, measure from the center of one hole to the center of the hole directly opposite (not the nearest). On a 5-lug wheel, that’s from the center of one lug to the center of the lug that is two positions away. Alternatively, measure from the center of one hole to the outer edge of the hole directly opposite—but the standard method uses center-to-center.

What’s the difference between bolt circle and pitch circle?

They’re the same thing in this context. Pitch circle diameter (PCD) is the diameter of the circle that passes through the centers of the bolt holes. Bolt circle diameter (BCD) is the same measurement. The terms are used interchangeably.

Can I use this calculator for a 4-lug wheel?

Yes. Enter 4 for the number of bolts. The coordinates will be at 0°, 90°, 180°, and 270° (if the first hole is at 0°). The chord distance will be \( d \times \sin(45^\circ) \approx 0.707d \).

What if my holes are not evenly spaced?

This calculator only works for equally spaced holes. For uneven spacing, you need to enter each hole’s angle manually and compute coordinates individually. You can still use the same formula: \( x = R \cos(\theta) \), \( y = R \sin(\theta) \), but with different \( \theta \) values for each hole.

How do I convert bolt circle coordinates to hole positions on a CNC machine?

Set the machine’s origin at the center of the bolt circle. Then use the X and Y coordinates directly. If the origin is elsewhere, add the center’s coordinates to each X and Y. Most CNC controls can also use polar coordinates (radius and angle), which may be simpler: move to radius \( R \) and rotate to each angle.

Does the calculator work for inches and millimeters?

Yes, as long as you enter the diameter in one unit consistently. The outputs will be in the same unit. If you need to convert, do it before entering the value (e.g., 1 inch = 25.4 mm).

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in n | Number of bolts | - | 5 | 3
in d | Bolt circle diameter | mm | 100 | 10
in a0 | Angle of first hole | deg | 0 | 0
out x | X coordinate of each hole | mm | (d/2)*cosd(a0 + (i-1)*(360/n)) | 2
out y | Y coordinate of each hole | mm | (d/2)*sind(a0 + (i-1)*(360/n)) | 2
out chord | Chord between adjacent holes | mm | d*sin(180/n) | 2