Circular Bolt Pattern Calculator: Measure PCD

This calculator works out the bolt pattern (Pitch Circle Diameter, or PCD) of a circular arrangement of bolts or holes. You enter the number of bolts and the distance between the centers of two adjacent bolts, and you get back the PCD in the same unit you measured. The PCD is the diameter of the imaginary circle that passes through the center of every bolt hole, and it is the key number for matching wheels, flanges, or any bolted circular component.

Formula

The formula for the Pitch Circle Diameter (PCD) from the center-to-center distance between two adjacent bolts is:

PCD = s / (2 × sin(180° / n))

Where:

• PCD = Pitch Circle Diameter, in millimeters (or inches, if you measure in inches)
• s = center-to-center distance between two adjacent bolts, same unit as PCD
• n = number of bolts (must be 3 or more)

The angle 180°/n comes from dividing the full circle into n equal segments. The sine function relates the chord length (the straight-line distance between two adjacent bolt centers) to the radius of the circle. For a 5-bolt pattern, the angle is 36°, and for a 4-bolt pattern, it is 45°.

Worked Example

Using the default values: 5 bolts, spacing = 100 mm.

1. Calculate the angle: 180° / 5 = 36°
2. Find the sine of 36°: sin(36°) ≈ 0.587785
3. Multiply by 2: 2 × 0.587785 = 1.17557
4. Divide spacing by that: 100 / 1.17557 ≈ 85.07 mm

So the PCD is approximately 85.07 mm. This matches the calculator output.

When to Use This Calculator

Use this calculator when you need to identify or verify the bolt pattern of a wheel, a flange, a brake rotor, a flywheel, or any circular part with holes arranged symmetrically. Common situations include:

• Buying new wheels for a car and needing to match the PCD (e.g., 5×114.3 mm, 4×100 mm).
• Replacing a flange or coupling where the bolt circle must match an existing pipe or mating part.
• Designing a custom adapter plate or spacer that must fit existing bolt holes.
• Verifying a part before machining, to avoid drilling misaligned holes.

You only need to measure the center-to-center distance between two adjacent bolts. That measurement is easy to take with a caliper or ruler, even if you cannot access the center of the circle.

How to Measure the Spacing

Measuring the center-to-center distance accurately is the most important step. Here is how to do it for common bolt counts:

• 4 bolts (square pattern): Measure from the center of one bolt to the center of the opposite bolt (diagonally). That distance equals the PCD directly. For adjacent bolts, use the formula.
• 5 bolts: Measure from the center of one bolt to the center of the farthest bolt (not adjacent). That distance is the PCD, but only if you measure correctly: on a 5-bolt pattern, the farthest bolt is not directly opposite; it is two bolts away. The formula above works with the adjacent distance.
• 6 bolts (hexagon): Measure from center of one bolt to the center of the opposite bolt. That is the PCD. Adjacent spacing also works with the formula.
• General method: Use a caliper to measure from the outer edge of one bolt hole to the outer edge of the adjacent hole, then subtract the diameter of one bolt hole. This gives the center-to-center distance. Alternatively, measure from the inner edge of one hole to the inner edge of the adjacent hole and add the hole diameter.

For odd numbers of bolts (5, 7, etc.), the adjacent measurement is always the safest because it does not rely on guessing which bolt is opposite.

Common Mistakes and Misconceptions

Several errors can lead to an incorrect PCD:

• Measuring between non-adjacent bolts on an odd pattern: On a 5-bolt pattern, the distance between two bolts that are not adjacent is not the PCD; it is a chord that is longer than the PCD. Only the adjacent distance gives the correct result with the formula.
• Mixing units: If you measure in inches, the PCD will be in inches. Do not mix millimeters and inches in the same calculation without converting (1 inch = 25.4 mm).
• Rounding too early: If you round the sine value to 0.588, you get 85.03 mm instead of 85.07 mm. Keep several decimal places until the final step.
• Using the diameter instead of the radius: The formula uses the chord length (spacing) and the number of sides. Do not substitute the diameter of the circle.
• Assuming the PCD equals the distance between opposite bolts for all patterns: That is only true for even numbers of bolts (4, 6, 8, etc.). For odd patterns, the opposite bolt does not exist.

A common misconception is that the PCD is the distance between the centers of two bolts that are directly across from each other. That is true only for even bolt counts. For a 5-bolt pattern, the correct PCD is actually about 1.7 times the adjacent spacing, not 2 times.

Limitations of the Formula

This formula assumes the bolts are evenly spaced on a perfect circle. In reality, manufacturing tolerances can cause small deviations. The formula gives the theoretical PCD based on your measurement, but if the part is worn or bent, the actual bolt circle may be slightly different. Also, the formula works for any number of bolts from 3 upward—it is not limited to common automotive patterns. For 3 bolts, the angle is 60°, and the PCD is s / (2 × sin(30°)) = s / 1.0 = s, which makes sense because an equilateral triangle’s circumscribed circle has a diameter equal to the side length divided by sin(60°), but here the side length is the chord, so it works out.

The calculator does not account for bolt hole size. The PCD is the circle through the centers of the holes, not the holes themselves. If you need to match a hub, you also need the center bore diameter and the number of lug nuts, but the PCD is the primary dimension for bolt circle compatibility.

Frequently Asked Questions

What is the difference between PCD and bolt pattern?

PCD (Pitch Circle Diameter) is the diameter of the circle that passes through the center of all bolt holes. The bolt pattern is usually expressed as the number of bolts multiplied by the PCD, for example “5×114.3 mm”. So PCD is the second number in that expression.

How do I measure a 5-bolt pattern if I only have a ruler?

Measure the center-to-center distance between two adjacent bolts. Use a caliper if possible; if using a ruler, measure from the outer edge of one hole to the outer edge of the adjacent hole, then subtract the diameter of one hole. Then use the calculator with n=5 and that spacing.

Does the bolt hole size affect the PCD?

No. The PCD is measured between the centers of the holes, regardless of the hole diameter. However, when measuring physically, you must account for the hole size to get the center-to-center distance correctly.

Can I use this calculator for a 4-bolt pattern?

Yes. Enter n=4 and the center-to-center distance between adjacent bolts. The formula will give the PCD. For a 4-bolt pattern, the PCD is also equal to the distance between opposite bolts, which is a simpler measurement.

What if my bolts are not evenly spaced?

This calculator assumes even spacing. If the bolts are not evenly spaced, the concept of a single PCD does not apply. You would need to measure each bolt’s position individually, which is beyond the scope of this simple calculation.

Why do some wheels have a PCD like 5×114.3 mm?

114.3 mm is a common PCD for many vehicles, often derived from imperial measurements (4.5 inches). The number of bolts (5) and the PCD together define the bolt pattern. Many manufacturers use the same PCD across different models, which is why it is a standard size.

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in n | Number of bolts | - | 5 | 3
in s | Center-to-center spacing | mm | 100 | 0
out pcd | Pitch Circle Diameter | mm | s / (2 * sind(180 / n)) | 2
out circum | Circumference of PCD | mm | pi * (s / (2 * sind(180 / n))) | 2