Bolt Circle Calculator — BCD Hole Coordinates

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Walk-through

How to Use This Calculator

3 steps

1

Enter the bolt circle diameter (BCD)

Enter the bolt circle diameter — also called BCD or PCD (pitch circle diameter) — the diameter of the imaginary circle that passes through the center of every bolt hole. Pick inches or millimeters with the unit toggle.

2

Enter the number of holes and a starting angle

Enter how many holes sit on the circle (2 or more). Optionally set a starting angle — the angle of the first hole, measured counterclockwise from the positive X axis. Leave it at 0° for a hole due right of center, or use the 45°/90° presets to rotate the whole pattern.

3

Read the coordinate table

The Coordinates tab lists every hole's angle and its X/Y position relative to the circle center, updating instantly as you change any input. Switch to Angular Spacing or Arc Distance for the spacing between adjacent holes.

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Reference

Formula & Methodology

4 formulas

Hole angle

angle_i = startAngle + i × (360° / n)

For hole index i (0 through n-1), the angle is the starting angle plus i times the angular spacing (360° divided by the number of holes n).

Hole X/Y coordinates

x_i = (BCD / 2) × cos(angle_i) y_i = (BCD / 2) × sin(angle_i)

Each hole's position is the bolt circle radius (BCD / 2) times the cosine and sine of its angle, giving coordinates relative to the circle's center.

Angular spacing

spacing = 360° / n

The angle between any two adjacent holes, which is constant for evenly spaced holes.

Arc and chord distance between adjacent holes

arc = spacing(rad) × radius chord = 2 × radius × sin(180° / n)

Arc distance is the curved distance along the bolt circle between two adjacent hole centers. Chord distance is the straight-line distance between the same two points — the number you'd actually measure with calipers.

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Glossary

Key Terms Explained

7 terms

Bolt circle diameter (BCD) The diameter of the circle that passes through the center of every bolt hole in the pattern. Also called PCD.

PCD (pitch circle diameter) Another name for bolt circle diameter, common in flange, wheel, and machining contexts. BCD and PCD refer to the same measurement.

Angular spacing The angle between two adjacent holes on the bolt circle, equal to 360° divided by the number of holes.

Starting angle The angle of the first hole in the pattern, measured counterclockwise from the positive X axis. Rotating the starting angle rotates the entire hole pattern without changing hole spacing.

X/Y coordinates The position of each hole center relative to the bolt circle's center, expressed as a horizontal (X) and vertical (Y) distance — the values a CNC program or CAD drawing needs to place the hole.

Flange A disc- or ring-shaped fitting, typically bolted to a pipe or shaft, whose bolt holes are almost always laid out on a bolt circle.

Hole pattern The complete set of hole positions on a bolt circle, defined by the diameter, hole count, and starting angle.

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Scenarios

Real-World Examples

3 worked examples

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Flange fabricator

6-hole flange, 6 in BCD

Bolt circle diameter 6 in Number of holes 6 Starting angle 0°

With 6 holes on a 6 in BCD starting at 0°, the angular spacing is 60°. The six holes land at 0°, 60°, 120°, 180°, 240°, and 300° — for example, hole 1 sits at (3.000, 0.000) in and hole 2 at (1.500, 2.598) in. Doubling the hole count to 12 would halve the spacing to 30° without moving hole 1.

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Machinist

4-hole pattern, 45° start

Bolt circle diameter 4 in Number of holes 4 Starting angle 45°

4 holes with a 45° start angle land at 45°, 135°, 225°, and 315° — a square pattern rotated so its sides are parallel to the X and Y axes (holes at (1.414, 1.414), (-1.414, 1.414), (-1.414, -1.414), (1.414, -1.414) in). Using a 0° start instead rotates the same square 45°, moving the first hole to (2.000, 0.000) in.

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Quality inspector

Arc distance between adjacent holes

Bolt circle diameter 8 in Number of holes 8 Starting angle 0°

With 8 holes on an 8 in BCD, angular spacing is 45°. The arc length between adjacent holes (measured along the circle) is about 1.571 in, while the chord length — the straight-line distance a caliper would measure — is about 1.531 in. The two values converge as the hole count increases, since the arc between closely spaced holes approaches a straight line.

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Deep Dive

Understanding Bolt Circle Layout

3 chapters · 4 min read

A bolt circle (BCD) defines where a set of evenly spaced holes sit around a common center — on flanges, wheels, pump housings, and any machined part with a circular bolt pattern. This calculator turns three numbers (diameter, hole count, starting angle) into the X/Y coordinates a CNC program, CAD drawing, or layout scribe needs for every hole.

How the Bolt Circle Layout Calculator works

The calculator places n holes evenly around a circle of the entered bolt circle diameter (BCD). Each hole's angle is the starting angle plus a multiple of the angular spacing, 360° divided by n. Converting that angle to Cartesian coordinates — radius times cosine for X, radius times sine for Y — gives the position of every hole relative to the circle's center, using the standard math convention where angles increase counterclockwise from the positive X axis.

Inputs and what they mean

Bolt circle diameter (BCD or PCD) is the diameter of the circle through the hole centers, not the outer diameter of the part. Number of holes must be a whole number of 2 or more; odd hole counts (5, 7, and so on) are fully supported and simply produce an asymmetric-looking but still evenly spaced pattern. Starting angle defaults to 0°, which places the first hole due right of center; rotating it spins the whole pattern without changing the spacing between holes — useful for matching an existing part's orientation or avoiding interference with another feature.

Limits and edge cases

This calculator assumes perfectly even spacing — real-world bolt patterns with unequal gaps (common on some automotive lug patterns) aren't supported and need each hole entered individually. A hole count below 2 is rejected since a single point doesn't define spacing. Arc distance and chord distance are reported separately because they diverge more as the hole count drops and the gap between holes widens — for high hole counts they converge and either can be used as a close approximation of the other.

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Questions

Frequently Asked Questions

6 questions

What's the difference between BCD and PCD?+

None — they're the same measurement under two names. BCD (bolt circle diameter) is more common in North American machining and automotive contexts; PCD (pitch circle diameter) is more common internationally and in engineering drawings. This calculator's BCD input accepts either.

What's the formula for bolt hole coordinates?+

Each hole's angle is the starting angle plus its index times 360° divided by the number of holes. The X coordinate is the bolt circle radius times the cosine of that angle, and the Y coordinate is the radius times the sine of that angle, both measured from the circle's center.

What does the starting angle do?+

It rotates the entire hole pattern. At 0°, the first hole sits due right of center on the positive X axis; increasing the starting angle rotates every hole counterclockwise by that same amount, without changing the spacing between them.

What's the difference between arc distance and chord distance?+

Arc distance is the curved distance measured along the bolt circle between two adjacent hole centers. Chord distance is the straight-line distance between the same two points — the number you'd actually read off a set of calipers. They're close for large hole counts and diverge more as the hole count drops.

Does this calculator support odd numbers of holes?+

Yes. Any whole number of holes from 2 upward is supported, including odd counts like 3, 5, or 7. The math is identical — each hole still sits at startAngle plus a multiple of 360° divided by the hole count.

What units does the calculator use?+

Whatever unit you enter the bolt circle diameter in — inches or millimeters, toggled with the unit switch. All outputs (coordinates, radius, circumference, arc and chord distance) are reported in that same unit; angles are always in degrees.

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Bolt Circle Layout Calculator