Circle radius
Half of the pitch-circle diameter.
Mechanics · Machining
Bolt circle / PCD hole coordinates
Define the circle diameter, hole count, first-hole angle and origin. Coordinates are calculated from the +X axis counter-clockwise.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Angular spacing
Constant angle between adjacent holes.
| # | θ | X | Y |
|---|
Relation and numerical substitution
xᵢ = x₀ + R cos θᵢ ; yᵢ = y₀ + R sin θᵢ—
Holes are equally spaced on one circle. N is a strictly positive integer. 0° points along +X and positive angles run counter-clockwise. Positional tolerances and CNC-specific conventions are not included.
01Formulas and symbols
Formulas used
R
PCD / 2Circle radiusΔθ
2π / NAngular spacingθᵢ
θ₀ + i · ΔθAngle of hole ixᵢ, yᵢ
x₀ + R cos θᵢ ; y₀ + R sin θᵢCartesian coordinates02Assumptions and limits
Scope of validity
- Holes are equally spaced on one circle.
- N is a strictly positive integer.
- 0° points along +X and positive angles run counter-clockwise.
- Positional tolerances and CNC-specific conventions are not included.
03Validation example
Reference numerical case
- PCD = 100 mm, N = 4, θ₀ = 0°, centre (0, 0).
- R = 50 mm, Δθ = 90°; holes (50,0), (0,50), (−50,0), (0,−50) mm.
04References
Technical references
- Polar-to-Cartesian conversion x = x₀ + R cos θ and y = y₀ + R sin θ.
- Convention on this page: 0° on +X, positive angles counter-clockwise.