Equal-spacing coordinate geometry
Pitch circle / PCD layout
Inputs
Nominal diameter through equal-spacing hole centers.
Integer count of equally spaced nominal hole centers.
Angle of the first center from the positive X-axis in the displayed nominal coordinate frame.
Results
Pitch-circle radius
50
Equal angular pitch
60
Adjacent-center chord
50
First-hole nominal X
50
First-hole nominal Y
0
180° opposite nominal X
-50
180° opposite nominal Y
0
r = PCD/2; Δθ = 360°/n; chord = 2r sin(π/n); xi = r cos(θ₀+iΔθ); yi = r sin(θ₀+iΔθ)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Section geometry · Right-triangle frame · 3D coordinate span · Cylinder geometry
Method
Formula, when it applies, and when it does not
Calculate equal-spacing bolt-circle angle, chord, and nominal hole-center coordinates from PCD, hole count, and a start angle.
r = PCD/2; Δθ = 360°/n; chord = 2r sin(π/n); xi = r cos(θ₀+iΔθ); yi = r sin(θ₀+iΔθ)
When
- Equal angular spacing
- Nominal PCD geometry
- Cartesian XY coordinates
- No tolerance interpretation
Don’t
- This is equal-spacing nominal pitch-circle geometry only. It does not create CAD/CAM/G-code, select fasteners, calculate hole diameter or tolerance, interpret GD&T, establish datum references, assess positional accuracy, balance rotating components, determine manufacturability, or approve a drawing or part.
Elementary geometry — circular hole pattern