Bolt Circle Calculator

Flanges, wheels, sprockets and mounting plates share one geometry: holes arranged on a circle, located by coordinates a machinist can dial in. This calculator produces them: enter the bolt circle diameter, the number of holes and the starting angle, and it returns every hole’s X–Y position from the centre, plus the hole-to-hole chord distance for layout with dividers — the complete pattern, without a rotary table or a page of trigonometry.

Coordinates From a Centre, Angles From a Start

The whole pattern is one idea repeated: hole i sits at angle θ = start + i × (360°/N), at position (R·cos θ, R·sin θ) from the circle's centre. That pair of formulas is what a CNC mill executes, what a DRO (digital readout) operator dials hole by hole, and what this calculator tabulates so that neither has to be derived at the machine. The conventions matter more than the maths: coordinates are signed (holes in the third quadrant carry negative X and Y, as the worked example shows), angles run counterclockwise from the +X axis (the machinist's and mathematician's shared custom), and hole 1 lives wherever your start angle puts it — 0° places it on the +X axis (3 o'clock), 90° at top dead centre, and offset patterns (staggered flanges, wheel studs avoiding a valve stem) are just start angles with a reason. State the convention on the drawing, and the table this page prints is the pattern, unambiguous to anyone with a mill.

Worked Example: Six Holes on a Five-Inch Circle

The defaults are the classic flange: 6 holes on a 5-inch bolt circle diameter, hole 1 at 0°. Radius 2.5 in, angular spacing 60°, and the coordinates fall out as the hexagon's familiar figures: hole 1 at (2.500, 0.000); hole 2 at (1.250, 2.165); hole 3 at (−1.250, 2.165); hole 4 at (−2.500, 0.000); hole 5 at (−1.250, −2.165); hole 6 at (1.250, −2.165). The chord — neighbour-to-neighbour distance — is 2 × 2.5 × sin(30°) = 2.500 in, the hexagon's party trick: on a six-hole pattern the chord equals the radius, so dividers set to the radius step the whole pattern around the circle with no table at all. The calculator prints both languages (coordinates for machines, chord for hands) because patterns are still laid out both ways, sometimes on the same part.

The Chord Table and Hand Layout

Dividers and a surface plate predate the DRO by centuries and still earn their keep for one-offs and repairs: scribe the bolt circle, set dividers to the chord = 2R·sin(180°/N), and step around the circumference — each step lands on the next hole's centre, with the closure of the final step back onto hole 1 serving as the layout's built-in audit (a gap or overlap at closure is accumulated error announcing itself before any hole is drilled). Chord values for common counts at a 1-inch radius scale linearly with R: 4 holes, 1.414R; 5 holes, 1.176R; 6 holes, 1.000R; 8 holes, 0.765R; 12 holes, 0.518R. The calculator prints your pattern's chord beside its coordinates so both workflows start from the same verified page — and since the chord scales with the diameter, doubling the bolt circle doubles every number in the table, the pattern's geometry being indifferent to its size.

Patterns in the Wild: Wheels, Flanges, and the Odd Count

The applications share the geometry and differ in the conventions layered on it. Wheel bolt patterns are quoted as count × circle diameter (5 × 114.3 mm is five studs on a 114.3 mm circle) — with the trap that on even-count wheels the circle passes through opposite studs (measure centre-to-centre across), while on odd counts it doesn't (measure from one stud's centre to the far edge of the opposite hole and consult the maker's conversion). Pipe flanges standardise the whole pattern (count, circle, hole size by pressure class in ASME B16.5), so the calculator's job there is verification and repair layout rather than design. Odd and prime counts (5, 7) defeat diameter-tape shortcuts, which is why the coordinate method — this page's method — is the professional default: it never asks the pattern to be convenient. Whatever the part, the deliverable is identical: a centre, a radius, a start angle, and a table nobody has to derive twice.

The Five-Lug Problem, Solved by the Chord

The odd-count measurement trap from the applications section has a clean exit through this page's chord formula, worth working once in full. A 5-lug wheel's pattern cannot be measured across (no opposite stud), but adjacent studs are easy caliper work — and the chord between neighbours is D × sin(180°/N). For the ubiquitous 5 × 114.3 mm pattern: chord = 114.3 × sin(36°) = 114.3 × 0.5878 ≈ 67.2 mm between adjacent stud centres. Measure 67.2 mm on an unknown wheel and the pattern announces itself as 114.3 — divide your measured chord by sin(180°/N) for the suspected count and the diameter falls out. It is the calculator run backwards, and it identifies more wheels in more car parks than any other formula on this hub.

PCD: The Metric Dialect

Metric practice names the same geometry PCD — pitch circle diameter — and quotes patterns identically (4 × 100, 5 × 112), the count and the millimetres of the circle. The coordinate and chord formulas are unit-blind, and one metric rehearsal fixes them: a 4 × 100 pattern's adjacent-stud chord is 100 × sin(45°) = 70.7 mm, its coordinates the square's (±35.36, ±35.36) at 45° clocking or (±50, 0), (0, ±50) at the cardinal points, depending on the start angle's convention. Enter millimetres in this calculator and read millimetres out; the circle does not know which empire measured it.

A Note on Tolerances and Truth

The coordinates are exact; the world is not. A scribed layout holds perhaps ±0.010 in, a careful DRO workflow ±0.001, and a CNC rather better — and the pattern's fitness is judged against the clearance of the holes drilled at those coordinates, which is why bolt circles and clearance tables (the sibling page) are designed together: the pattern's tolerance budget and the holes' forgiveness are one budget, spent in two currencies.

Related Tools

More from the Construction Calculators hub: the Arch Calculator — the same circle, struck in masonry — and the Clearance Hole Calculator for the drill sizes these holes usually need.

Frequently Asked Questions

How do I measure an existing bolt circle diameter?

On even hole counts, measure centre-to-centre between two opposite holes — that distance is the diameter. On odd counts, no hole sits opposite another: measure from one hole's centre to the far inside edge of a non-adjacent hole and add roughly half that hole's diameter (the standard field approximation), or measure the chord between neighbours and invert this page's formula — diameter = chord ÷ sin(180°/N). The coordinate mindset converts any two honest measurements of the pattern into the circle.

What starting angle should I use?

Whatever your datum demands: 0° puts hole 1 on the +X axis (3 o'clock), 90° at top dead centre — the commonest drawing convention for flanges that must clock a feature (a keyway, a valve stem, a drain) to a specific hole. Patterns are often rotated so that no hole sits exactly on a centreline (a "straddled" pattern: start at half the spacing, e.g. 30° for six holes), which the start-angle input handles directly — enter half of 360/N and the whole pattern rotates by that half-step.

How accurate do the coordinates need to be?

The calculator prints three decimals (thousandths of an inch), the ordinary currency of machining layout; the pattern's real tolerance is set by the joint's design — clearance holes forgive hundredths, dowel and locating patterns demand the tenths-of-thousandths that only machined datums hold. Match the table's precision to the process: scribed layouts live comfortably at the printed precision, CNC programs will take all the decimals the formulas offer.

Can I use this for equally spaced points that aren't bolts?

Yes — the geometry is the division of a circle into N equal parts, and it serves gear teeth layouts, clock numerals, sprinkler heads on a circular bed, rivet rings and decorative rosettes identically. Anywhere a design says "N of these, evenly around a circle of diameter D", this page's table is the layout, and the chord is the spacing whatever the points turn out to be.

Why do my stepped divider holes not close the pattern?

Accumulated error: each step carries the divider setting's error plus the scribe's, and N steps multiply them — the classic symptom is the last step landing a hair short of or past hole 1. Defences: verify the divider setting against the calculator's chord with calipers (not against the scribed circle), prick each centre lightly and audit closure before centre-punching hard, and for counts where it matters, fall back to the coordinate table and a height gauge or DRO, where errors don't compound around the ring.

What about a bolt rectangle or other non-circular patterns?

Different layout, different arithmetic (rectangular grids are just X and Y pitches — the province of the mill's own hole-pattern cycles). This page's commitment is the circle: the pattern that flanges, wheels and rotating machinery overwhelmingly use, priced completely. Mixing a circular flange pattern with a rectangular one on the same part is common in real assemblies; each half is computed in its own geometry and joined at the shared centre datum, which is why both conventions anchor everything to the centre.