Bolt Circle Diameter: Formula and Calculation

Calculate bolt circle diameter (BCD) by measuring the distance between the centers of two bolt holes and applying the formula for their angular spacing. Enter the number of equally spaced holes and the center-to-center chord distance; the calculator returns the diameter of the circle through the hole centers.

Formula

For n equally spaced holes, if c is the straight-line distance between the centers of adjacent holes, the bolt circle diameter is:

D = c / sin(180° / n)

• D is the bolt circle diameter, in the same unit as the measured distance.
• c is the chord length between the centers of adjacent holes, such as millimeters or inches.
• n is the total number of equally spaced holes around the circle.

The calculator uses the degree-based sine function. Its radius output is R = D / 2. The angle between adjacent holes is 360° / n; dividing that angle in half gives the right-triangle angle 180° / n used in the diameter formula. For measurements in inches, enter inches and the result will be in inches; for measurements in millimeters, enter millimeters and the result will be in millimeters.

Worked Example

Using the calculator’s defaults, there are n = 4 equally spaced holes and the center-to-center distance between adjacent holes is c = 50 mm.

1. Find half the angle between adjacent holes: 180° / 4 = 45°.
2. Evaluate the sine: sin(45°) ≈ 0.7071068.
3. Calculate the diameter: D = 50 mm / 0.7071068 ≈ 70.7107 mm.
4. Round to two decimal places: the bolt circle diameter is 70.71 mm. The radius is D / 2 = 35.36 mm, rounded to two decimal places.

The four holes form a square: the adjacent-hole spacing is one side, while the bolt circle is the square’s circumcircle. Its diameter is therefore the square’s diagonal, 50 × √2 ≈ 70.71 mm, an independent check of the calculation.

What Bolt Circle Diameter Means

Bolt circle diameter, commonly abbreviated BCD, is the diameter of an imaginary circle passing through the centers of the mounting holes. It is also called the pitch circle diameter (PCD) in many mechanical contexts. The circle describes the hole pattern, not the outside diameter of the part, the diameter of a hole, or the distance between the outer edges of two holes.

For a regularly spaced pattern, each hole lies at the same radius from the pattern’s center. The total number of holes and their angular spacing define the arrangement; the BCD tells you how large that arrangement is. The term is used for many circular mounting patterns, including flanges and wheels, but the method applies only when the holes really are distributed evenly around one center.

How to Measure the Hole Pattern

The calculator uses the straight-line distance between the centers of adjacent holes—not the arc along the circle. This straight-line distance is a chord. If you can reach the centers reliably, measure the chord with a suitable measuring tool, and record the hole count. Keep the measurement in one consistent unit.

Sometimes the centers are difficult to locate directly. For holes of equal diameter, measuring from the same edge of one hole to the matching edge of the adjacent hole gives the center-to-center distance, provided the measurement follows the straight line between their centers. Do not substitute a gap between the nearest edges: that is shorter by one hole diameter. If the hole diameters differ, edge-based measurements need an appropriate correction and are less reliable.

For a pattern with more than two holes, adjacent holes are not the only possible pair to measure. The angle between the selected holes changes the geometry. For two hole centers separated by a known central angle θ, the general relation is D = c / sin(θ / 2), where c is the chord between those centers. The calculator’s formula uses θ = 360° / n, so it expects adjacent holes in an equally spaced pattern.

Choosing a Measurement Method

• Adjacent-hole chord: Measure center to center between neighboring holes and use the calculator’s formula. This is straightforward when the hole centers are accessible.
• Opposite-hole span: If an even number of equally spaced holes includes a pair directly opposite each other, the center-to-center distance across that pair is the diameter itself. This can be convenient, but the selected centers must be exactly opposite.
• Coordinates or a drawing: If hole-center coordinates are available, calculate the distance between known centers and use the actual angular separation. A drawing may also state the BCD directly; check its units and whether the stated value refers to the hole-center circle.

With an odd number of holes, no pair of holes is directly opposite, so a measured center-to-center chord is not the diameter. For example, with five equally spaced holes, use the chord between neighboring holes with D = c / sin(36°), not D = c.

Common Errors and Accuracy Limits

The most common mistake is confusing a chord with the diameter. A chord is the straight-line distance between two points on the circle; it equals the diameter only when its endpoints are opposite. Another frequent mistake is using the wrong hole count or measuring between nonadjacent holes while still applying the adjacent-hole formula.

• Measure from center to center, not from the outside of one hole to the outside of another.
• Confirm the number of holes and whether they are evenly spaced.
• Use the same unit for the input and reported result. A result in millimeters is not inches; convert only after calculating or convert all measurements consistently.
• Keep enough measurement precision. Rounding a short chord can noticeably affect the calculated diameter, especially for patterns with many holes.
• Check the answer against the part’s approximate size or its drawing. A result far outside expectations often indicates a wrong hole count, unit, or measurement.

The formula assumes a perfect circular pattern and accurate measurements. Real parts have manufacturing tolerances, and hand measurements can be affected by access, worn holes, and difficulty locating centers. The calculator does not account for those uncertainties, unequal spacing, slotted holes, or a pattern whose centers do not share one circle. Reported decimal places are not proof that the original measurement is equally precise.

Frequently Asked Questions

How do I calculate bolt circle diameter from adjacent holes?
Measure the center-to-center chord between neighboring holes, count the equally spaced holes, then calculate D = c / sin(180° / n), with the angle in degrees.

Is bolt circle diameter the same as the distance between two holes?
Not usually. It equals the center-to-center distance only for two opposite points on the circle. Adjacent-hole spacing is a chord that must be converted using the hole count.

Can I calculate BCD from the distance between opposite holes?
Yes. If the centers are exactly opposite in a circular pattern, their center-to-center distance is the diameter. This requires an even-hole pattern with a pair positioned directly across the circle.

Does the formula work for an uneven bolt pattern?
No. The calculator assumes equally spaced holes on one circle. For an irregular pattern, you need coordinates or other measurements that identify the circle center and the actual geometry.

What is the difference between BCD and PCD?
Both terms commonly refer to the diameter of the circle passing through the centers of a mounting-hole pattern. Check a drawing’s definitions if it uses a special convention.

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in n | Number of equally spaced holes | - | 4 | 1
in c | Distance between adjacent hole centers | mm | 50 | 0
out d | Bolt circle diameter | mm | c / sind(180 / n) | 2
out r | Bolt circle radius | mm | d / 2 | 2