About Bolt Circle Calculator — Hole Coordinates & Chords
The bolt circle calculator turns a bolt circle diameter and hole count into the numbers a machinist or fabricator actually lays out with: the X-Y coordinate of every hole from the pattern center (or from your part zero, using the center offset), each hole's angle, and the chord — the straight-line distance between adjacent holes that a caliper can check directly. It is the digital version of the jig-boring coordinate tables in Machinery's Handbook, computed from the same trigonometry those tables tabulate.
Everything follows from two identities: hole i sits at angle start + (i−1)·360/N with coordinates (R·cos θ, R·sin θ), and adjacent holes are 2R·sin(π/N) apart. The classic Handbook chordal factors drop right out — five holes on any circle are 0.58779 × BCD apart, eight holes 0.38268 × BCD — and a six-hole pattern's chord equals the radius exactly, the old layout trick of walking a divider set to R around the circle. Despite the name, this tool is about hole geometry: bolt tightening lives in the bolt torque calculator and concrete anchors in the anchor bolt design tool.
How It Works
- Enter the bolt circle diameter (BCD) — the diameter through the hole centers, not across the holes' edges. Flanges, wheel hubs (a "5×114.3" wheel is 5 holes on a 114.3 mm BCD), motor mounts, and cover plates all specify it this way. The in ↔ mm toggle converts at the exact 25.4 and clamps to the caps.
- Set the hole count (2–60) and the start angle, measured counterclockwise from 3 o'clock (+X) — the standard math and jig-boring convention. Start at 90° to put the first hole at 12 o'clock, or at half the pitch to straddle a centerline (a 4-hole pattern started at 45° clears both axes).
- Add a center offset when your coordinate origin is the part corner or a fixture zero instead of the pattern center — every hole translates by exactly (X₀, Y₀).
- Read the table: hole number, angle, X, and Y at machinist display precision (0.0001 in or 0.001 mm), ready for a DRO, a CNC drill cycle, or manual layout. The chord lets you verify the pattern with calipers before cutting: measure adjacent holes center-to-center and compare.
- Sanity-check with the symmetries: opposite holes in an even pattern differ by exactly the BCD, a 6-hole chord equals the radius, and rotating the start angle changes coordinates but never chords or pitch.
Worked Example
A pump adapter plate needs 8 holes on a 10-inch bolt circle, first hole at 3 o'clock, coordinates from the pattern center. The pitch is 360/8 = 45°, so the holes land at 0°, 45°, 90°, … with hole 1 at (5.0000, 0.0000), hole 2 at (3.5355, 3.5355), hole 3 at (0.0000, 5.0000), and so on around. Adjacent holes sit 2 × 5 × sin(22.5°) = 3.8268 in apart — exactly the Handbook's 0.38268 chordal factor times the 10-inch diameter — which a caliper check across any neighboring pair confirms before the first drill touches metal.
Formulas
- Hole coordinates
θᵢ = θ₀ + (i−1)·360/N; xᵢ = X₀ + R·cos θᵢ; yᵢ = Y₀ + R·sin θᵢ- Chord and pitch
chord = 2R·sin(π/N) = BCD·sin(180°/N); pitch = 360°/N
Standards & References
- Plane trigonometry — coordinates and chords are arithmetic identities
- Machinery's Handbook, jig boring — hole-circle coordinate and chordal-distance tables; the printed unit-diameter chord factors (0.58779 for 5 holes, 0.38268 for 8) are reproduced by the 2R·sin(π/N) identity as verification anchors
Frequently Asked Questions
How do I calculate bolt circle hole coordinates?
Each hole sits at angle θ = start + (i−1)·360/N around the circle: X = R·cos θ, Y = R·sin θ, with R half the bolt circle diameter. An 8-hole pattern on a 10-in BCD starting at 3 o'clock puts hole 2 at (10/2 × cos 45°, 10/2 × sin 45°) = (3.5355, 3.5355). Add your pattern-center offset for coordinates from a part zero.
How do I measure a bolt circle diameter from an existing part?
For an even hole count, measure center-to-center across opposite holes — that IS the BCD. For odd counts (5-lug wheels, 5-hole flanges), measure the chord between adjacent holes and divide by sin(180/N): a 5-hole pattern's BCD is the adjacent spacing ÷ 0.58779. The calculator's chord output runs this check in reverse.
What is the distance between adjacent holes on a bolt circle?
Chord = BCD × sin(180°/N). Six holes are exactly one radius apart — the classic divider-walking layout trick. Five holes are 0.58779 × BCD apart, eight are 0.38268 × BCD; these are the chordal factors the Machinery's Handbook jig-boring tables print, and this calculator derives them from the identity rather than looking them up.
Which way are the angles measured, and how do I start at 12 o'clock?
Counterclockwise from +X (3 o'clock), the standard math and jig-boring convention. Enter a 90° start angle to put hole 1 at 12 o'clock, or start at half the angular pitch to straddle a centerline — a 4-hole pattern at 45° start keeps every hole off both axes, the usual flange orientation so bolts clear the vertical centerline.
Is this calculator for bolt torque or anchor bolts?
No — the name collision is exactly why this page says so up front. This tool computes hole-pattern GEOMETRY: coordinates, angles, and chords for laying out or inspecting a circular hole pattern. Tightening torque for a given preload is the bolt torque calculator; anchor bolts in concrete per ACI are the anchor bolt design tool; thread-making holes are the tap drill size calculator.