Bolt Circle Calculator — Bolt Pattern PCD & Hole Coordinates
Enter the pitch circle diameter, the number of bolts and the starting angle to get the chord length between adjacent bolts, arc spacing, and bolt position diagram — everything needed to lay out a bolt pattern by hand or program a CNC.
mm
°
Straight-line distance between two adjacent bolt centres
- 1
Angle between bolts
360 ÷ 4 = 90 - 2
Half-angle in radians
π ÷ 4 = 0.785398 - 3
Chord length
100 × sin(π ÷ 4) = 70.711Straight-line distance between two adjacent bolt centres.
How does this calculator work?
A bolt circle places n holes equally spaced on a circle of diameter PCD. Hole i sits at angle θ₀ + i×360°/n, giving coordinates (PCD/2)·cos(θ) and (PCD/2)·sin(θ). The chord between adjacent bolt centres is PCD·sin(π/n) — the key measurement for calliper verification and CNC programming.
Formula
How this is calculated
A bolt circle (or bolt pattern) places n bolt holes at equal angular spacing around a circle of diameter PCD (Pitch Circle Diameter). The angular step between adjacent holes is 360°/n. Starting from a user-specified angle θ₀ (commonly 90° for the 12 o'clock position), hole i is placed at angle θ₀ + i × 360°/n measured from the positive x-axis (the 3 o'clock direction). The Cartesian coordinates are x = (PCD/2) × cos(θ) and y = (PCD/2) × sin(θ), with the bolt circle centre as the origin.
The chord length is the straight-line distance between two adjacent bolt centres and follows from the inscribed-chord formula: chord = PCD × sin(π/n). This is the measurement a machinist or inspector uses to verify the pattern with a steel rule or calliper — it is more practical than the PCD itself when direct measurement across the centre is not possible. The arc spacing (the curved path length between bolts along the circle) is π × PCD / n.
All distances are in the same units as the PCD input — millimetres in the default example. The calculator assumes all holes lie on a perfect circle with no runout. Real machining must also account for hole diameter, clearance and positional tolerance as specified in the engineering drawing.
Frequently asked questions
PCD (Pitch Circle Diameter) is the diameter of the imaginary circle on which the centre of each bolt hole falls. For a 4-lug wheel, measure the distance between the centres of two directly opposite holes — that distance is the PCD. For a 5-lug pattern, measure from the centre of one hole to the far edge of the hole directly across, or use the inverse formula: PCD = chord / sin(π/n) where chord is the measured centre-to-centre distance between adjacent holes.
Real bolt patterns are often drawn or machined with one hole at a specific position — typically at the top (90°, or the 12 o'clock position) or to the right (0°). The start angle θ₀ rotates the whole pattern to match your drawing convention or fixture orientation. It does not affect the chord length, arc spacing or any size metric — only the absolute X-Y coordinates of each hole.
Set the workpiece centre as the CNC origin (work offset G54). The X-Y coordinates from this calculator are the target positions for each hole centre. Cycle through the coordinates using a spot drill followed by a twist drill to the required diameter. Always verify the first hole before proceeding, and confirm that your units (mm vs inch) match the machine controller setting.
TG we-Calculate Editorial Team. (2026). Bolt Circle Calculator — Bolt Pattern PCD & Hole Coordinates [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bolt-circle-calculator
TG we-Calculate Editorial Team. "Bolt Circle Calculator — Bolt Pattern PCD & Hole Coordinates." TG we-Calculate. 2026. https://we-calculate.com/calculator/bolt-circle-calculator.
TG we-Calculate Editorial Team, "Bolt Circle Calculator — Bolt Pattern PCD & Hole Coordinates," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bolt-circle-calculator
@misc{wecalculate_bolt_circle_calculator, title = {Bolt Circle Calculator — Bolt Pattern PCD & Hole Coordinates}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bolt-circle-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?