Bolt Circle Calculator: Pitch Circle Diameter

This bolt circle calculator determines the pitch circle diameter (PCD) and the chordal distance between adjacent holes for a given number of holes and their spacing. You enter the number of bolts and the center-to-center distance between two adjacent holes, and the calculator returns the diameter of the circle on which the hole centers lie, plus the angular spacing between holes. This is the fundamental geometry used for wheel rims, flanges, and any circular bolt pattern.

Formula

The pitch circle diameter (PCD) is the diameter of the imaginary circle that passes through the center of every bolt hole. For a regular polygon formed by the hole centers, the chord length between adjacent holes is related to the radius by:

s = 2 × r × sin(180° / n)

Since the diameter is twice the radius, the formula becomes:

PCD = s / sin(180° / n)

Where:

• s = center-to-center distance between two adjacent holes (any linear unit, e.g., mm, inches)
• n = number of bolt holes (must be an integer ≥ 3)
• PCD = pitch circle diameter (same unit as s)

The angle between adjacent holes is simply 360° / n, which is the central angle of the regular polygon.

Worked Example

Using the default values from the calculator (n = 5 bolts, s = 100 mm):

1. Calculate the angle: 180° / 5 = 36°
2. Find sin(36°) ≈ 0.587785
3. Divide the spacing by that: 100 / 0.587785 ≈ 170.13 mm

So the pitch circle diameter is approximately 170.13 mm, and the angle between holes is 72° (360° / 5). This matches the calculator’s output.

When to Use a Bolt Circle Calculator

You need this calculation whenever you are drilling or measuring a circular pattern of holes. Common situations include:

• Replacing a wheel hub or measuring a bolt pattern on a vehicle.
• Machining a flange or a plate with a circular array of holes.
• Designing a custom adapter, spacer, or mounting plate.
• Verifying the bolt circle of an existing part before ordering a replacement.

In automotive contexts, wheel bolt patterns are often described as “5×114.3� meaning 5 holes on a 114.3 mm diameter circle. This calculator helps you derive that diameter when you only know the hole spacing.

How to Choose the Right Measurement Method

To use the calculator, you need the center-to-center distance between two adjacent holes. Here’s how to get it:

• If you have a drawing or CAD model, read the dimension directly.
• If measuring a physical part, use calipers to measure from the center of one hole to the center of the next. For holes with chamfers, measure from the same side of each hole (e.g., left edge to left edge) to avoid errors.
• For an odd number of holes, you cannot measure directly across the diameter; the spacing method is the most reliable.
• For an even number of holes, you can measure the distance between opposite holes, which is the diameter itself. But the spacing method still works.

Always measure in the same unit system (metric or imperial) and enter the value accordingly. The calculator does not convert units, so be consistent.

Common Mistakes and Misconceptions

One frequent error is confusing the chordal distance (straight line between hole centers) with the arc length (distance along the circle). The formula uses the chord, not the arc. If you measure along the surface of the flange, you may get the arc length, which will be slightly larger.

Another mistake is using the wrong number of holes. For a 5-bolt pattern, n = 5, not 4 or 6. Also, the formula assumes the holes are evenly spaced. If they are not, the calculator will not give a meaningful PCD.

Unit mix-ups are common. If you measure spacing in inches but expect the diameter in millimeters, you must convert first. The calculator returns the same unit you entered.

Finally, rounding too early can cause small errors. For a 5-bolt pattern with 100 mm spacing, rounding sin(36°) to 0.59 gives 169.49 mm, which is off by about 0.6 mm. Keep at least 4 decimal places in intermediate steps.

Limitations and Real-World Considerations

The formula assumes ideal geometry: perfectly round holes, exact center locations, and a flat plane. In practice, manufacturing tolerances, wear, and deformation can affect measurements. For critical applications, always verify with a physical fit test or a coordinate measuring machine.

Also, the calculator only gives the PCD and the angle. It does not account for hole diameter, bolt size, or clearance. Those are separate specifications.

For wheel bolt patterns, the PCD is often stamped on the wheel or listed in the vehicle manual. If you are unsure, consult a reliable source for your specific vehicle model.

Alternative Methods

If you have the diameter of the circle directly (e.g., from a drawing), you do not need this calculator. You can also use a bolt circle template or a digital caliper with a PCD function. For odd-numbered patterns, some machinists use a dividing head or a rotary table to index the holes, which avoids measurement altogether.

When you only know the diameter and need the hole spacing, you can rearrange the formula: s = PCD × sin(180° / n). This calculator can be used in reverse by entering the diameter as the spacing? No, that would be incorrect. Instead, set the spacing to the known diameter and adjust the number of holes until the output matches the desired PCD? That is not practical. The simplest is to use the formula directly.

Frequently Asked Questions

How do I measure a 5-bolt pattern?

For a 5-bolt pattern, measure from the center of one bolt hole to the center of the farthest hole? That is not correct. The standard method is to measure from the center of one hole to the center of the hole directly opposite? For odd numbers, there is no opposite hole. Instead, measure the center-to-center distance between two adjacent holes, then use this calculator with n=5 to find the PCD.

What does 5×114.3 mean?

It means the wheel has 5 bolt holes arranged on a circle with a diameter of 114.3 mm (which is 4.5 inches). The “5� is the number of bolts, and “114.3� is the PCD in millimeters.

Can I use this calculator for 4-bolt patterns?

Yes. Enter n=4 and the center-to-center distance between adjacent holes. The calculator will give the PCD. For a 4-bolt pattern, you can also measure directly across from one hole to the opposite hole, which is the diameter itself.

What is the difference between PCD and bolt pattern?

PCD (pitch circle diameter) is the diameter of the circle that passes through the centers of the bolt holes. The bolt pattern is usually expressed as the number of bolts and the PCD (e.g., 5×114.3). So the PCD is a key part of the bolt pattern.

Why do I get a different result if I measure from the edge of the holes?

Measuring from the edge of a hole to the edge of another hole gives the center-to-center distance only if you measure from the same relative point on each hole (e.g., left edge to left edge). If you measure from the left edge of one to the right edge of the other, you are adding the hole diameters, which will give a larger value. Always measure center to center, or use the same edge on both holes.

Is the PCD the same as the bolt circle radius?

No. The radius is half the diameter. If you know the radius, double it to get the PCD. This calculator gives the diameter directly.

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in n | Number of bolts | - | 5 | 3
in s | Adjacent hole spacing | mm | 100 | 0
out pcd | Pitch circle diameter | mm | s / sind(180 / n) | 2
out angle | Angle between holes | deg | 360 / n | 1