Bolt Circle Calculator

The holes are spaced equally around a circle of radius R = PCD ÷ 2.

100% FreeRuns in your browserBasic

Enter Values

Pitch circle diameter PCD

Number of holes N

Start angle of first hole (deg)

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

Enter the pitch circle diameter (PCD) in mm — the diameter of the circle the hole centres sit on.
Enter the number of equally spaced holes N (2 or more).
Optionally set the start angle of the first hole (0° places it on the +X axis, to the right of centre). Read off the chord spacing, angular step and each hole's X/Y coordinate.

How it works

The holes are spaced equally around a circle of radius R = PCD ÷ 2. The angular step between neighbouring holes is 360° ÷ N. Each hole centre lies at X = R·cos(θ) and Y = R·sin(θ), where θ is the start angle plus a whole number of steps. This gives the exact XY position of every hole relative to the circle centre, ready to mark out or program into a CNC/DRO.

The straight-line centre-to-centre distance between two adjacent holes (the chord) is PCD × sin(180° ÷ N). The chord is what you would measure with callipers between neighbouring holes; it is always a little shorter than the arc length along the circle. All results are pure geometry — they assume perfectly placed hole centres and say nothing about hole size, edge distance or bolt strength.

Worked example

6 holes on a 100 mm PCD. A flange has 6 equally spaced holes on a 100 mm pitch circle diameter, first hole at 0°. Radius R = 50 mm. Angular step = 360 ÷ 6 = 60°. Chord spacing = 100 × sin(180 ÷ 6) = 100 × sin(30°) = 50.000 mm. Hole 1 sits at X = 50.000 mm, Y = 0.000 mm; hole 2 at 60° → X = 25.000 mm, Y = 43.301 mm, and so on around the circle.

Common mistakes

Confusing pitch circle diameter (PCD) with radius — the PCD is the full diameter across the circle of hole centres, so R is half of it.
Measuring the chord (straight callliper distance between adjacent holes) and assuming it equals the arc length — the chord is slightly shorter; use PCD × sin(180°/N) for the chord.
Treating this as a fastener-strength check: it is layout geometry only. Bolt torque, shear and tensile capacity are separate calculations.

Frequently asked questions

What is PCD (pitch circle diameter)?

PCD is the diameter of the imaginary circle that passes through the centre of every bolt hole. On a wheel or flange it is quoted as, for example, 5×114.3 — five holes on a 114.3 mm pitch circle diameter. The pitch circle radius used in the coordinate formulas is simply PCD ÷ 2.

How do I find the spacing between two adjacent holes?

Use the chord formula: chord = PCD × sin(180° ÷ N), where N is the number of holes. For 4 holes on a 100 mm PCD the chord is 100 × sin(45°) = 70.711 mm. This is the straight-line centre-to-centre distance you would measure with callipers, which is slightly less than the arc distance around the circle.

Where is the 0° start angle?

With a start angle of 0°, the first hole sits on the +X axis — directly to the right of the circle centre (X = R, Y = 0). Angles increase anticlockwise. Change the start angle to rotate the whole pattern, for example to place a hole straight up (90°) or to clock the pattern to match a mating part.

Tip: Enter any known values to calculate the remaining results.

All calculations run in your browser. Your inputs are never saved or transmitted.