Bolt Circle Diameter Calculator | Free BCD Tool

What Is a Bolt Circle Diameter Calculator?

A bolt circle diameter (BCD) calculator finds the diameter of the circle that passes through the centers of a set of evenly spaced bolt holes. Engineers and mechanics use it to check that bolt patterns on parts such as wheels, flanges, and machine housings will line up correctly.

A bolt circle, also called a bolt pattern or pitch circle, is a ring of holes arranged around a center point at equal angles. The bolt circle diameter is the size of the circle that runs through the middle of every hole in that ring.

Bolt Circle Diameter Formula

The calculator needs two numbers: the number of bolt holes and the straight-line distance between two adjacent holes, measured center to center. The formula is:

BCD = distance between adjacent holes ÷ sin(π ÷ number of holes)

Here, π (pi) is about 3.14159. The value π ÷ number of holes is an angle in radians, and its sine is taken before dividing.

Why the Formula Works

Bolt holes spaced evenly around a circle sit at the corners of a regular polygon. In a circle of diameter d, the straight-line distance between two neighboring corners (a chord) follows this rule:

chord = d × sin(π ÷ n)

where n is the number of corners, or holes. Solving for the diameter gives:

d = chord ÷ sin(π ÷ n)

That is the formula the calculator uses.

How to Calculate Bolt Circle Diameter: Worked Example

Take a bolt pattern with 6 holes, spaced 15 mm apart from center to center.

1. Divide π by the number of holes: π ÷ 6 = 0.5236 radians, which is 30°.
2. Find the sine of that angle: sin(30°) = 0.5.
3. Divide the hole spacing by that value: 15 ÷ 0.5 = 30.

The bolt circle diameter is 30 mm.

This matches a known property of hexagons: in a regular six-sided shape, the distance between two adjacent corners equals the circle's radius. Since the radius here is 15 mm, the diameter is 30 mm.

Example: Automotive Wheel Bolt Pattern

Car wheels are often labeled with a bolt pattern such as "5x114.3," meaning 5 lug holes arranged on a 114.3 mm bolt circle. For 5 holes, the chord distance between adjacent holes on that circle is 114.3 × sin(π ÷ 5) ≈ 67.2 mm. Entering 5 holes and 67.2 mm into the calculator returns a bolt circle diameter of about 114.3 mm, confirming the pattern.

Where Bolt Circle Diameter Matters

• Automotive wheels: a replacement wheel must match the vehicle's number of lugs and bolt circle diameter, or the lug bolts will not line up with the hub.
• Pipe flanges: standards such as ASME B16.5 and ISO 7005 set bolt circle diameters for different pipe sizes and pressure ratings.
• Machine assembly: gears, pulleys, and bearing housings often use circular bolt patterns that must match a mating part exactly.
• Structural steel: column base plates use anchor bolts arranged on a bolt circle to attach the column to its foundation.

Limitations

The formula assumes every hole sits at an equal angle around the circle. It does not apply to patterns with irregular spacing. It also needs at least 3 holes, since fewer than three points cannot define a unique circle. As the number of holes grows, a small error in the measured hole spacing turns into a larger error in the calculated diameter, so careful measurement matters most on patterns with many holes.

Frequently Asked Questions

What is a bolt circle diameter?

It is the diameter of the circle that runs through the center of every bolt hole in an evenly spaced circular pattern. It is also called a pitch circle diameter (PCD).

What is the formula for bolt circle diameter?

BCD = distance between adjacent holes ÷ sin(π ÷ number of holes), with the angle measured in radians.

What is the minimum number of holes the calculator accepts?

Three. A circle cannot be uniquely defined by fewer than three points.

Is bolt circle diameter the same as pitch circle diameter?

Yes, they describe the same measurement. "Pitch circle diameter" is more common in gear design, while "bolt circle diameter" is more common for bolted connections.

Does the unit of measurement matter?

No. The formula works with any consistent unit. Entering the hole spacing in millimeters gives a result in millimeters; entering it in inches gives a result in inches.

Can this formula be used for unevenly spaced holes?

No. It assumes the holes sit at equal angles around the circle. Uneven spacing requires direct measurement or coordinate geometry instead.

References

1. Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. Machinery's Handbook (30th ed.). Industrial Press, 2016.
2. ASME B16.5: Pipe Flanges and Flanged Fittings. American Society of Mechanical Engineers, 2013.
3. ISO 7005-1: Pipe flanges — Part 1: Steel flanges. International Organization for Standardization, 2010.