Worked example
Six holes on a Ø80 mm circle, first hole on the +X axis. The radius is 40. The holes sit at 0°, 60°, 120°, 180°, 240° and 300°: (40, 0), (20, 34.6410), (−20, 34.6410), (−40, 0), (−20, −34.6410) and (20, −34.6410). Neighbouring holes are 80 × sin 30° = 40 mm apart – for six holes the spacing always equals the radius.
Using the coordinates
- CNC milling or drilling: program the holes as a point list in G90 absolute mode, or use a bolt-hole-circle cycle if your control has one. The table gives each position once, so nothing accumulates.
- Manual mill with a DRO: use the X/Y values from the table, moving to each in absolute mode. Add the centre offset if the circle is not at the part zero.
- Inspection: measure the hole positions from the datum centre and compare with this table; for position tolerance see the true position calculator.
- Odd numbers of holes have no hole opposite another, so you cannot measure the circle diameter directly across; measure over the pins or use the spacing.
Frequently asked questions
How do I calculate bolt circle coordinates?
For hole i of n on a circle of diameter D: X = cx + (D/2) × cos θ and Y = cy + (D/2) × sin θ, with θ = start angle + i × 360° / n.
How do I find the distance between holes on a bolt circle?
The chord between neighbouring holes is D × sin(180° / n). Six holes on Ø80 are 80 × sin 30° = 40 mm apart.
What is a PCD?
PCD stands for pitch circle diameter – the diameter of the circle through the centres of the holes. It is the same as the bolt circle diameter.
Which direction do the angles run?
Counter-clockwise from the +X axis, the usual mathematical convention. A first hole at 90° is on the +Y axis.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- RPM and feed – Calculate spindle RPM from surface speed and diameter, surface speed from RPM, and feed rate from chip load – metric and imperial, with formulas.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- TPI to pitch – Convert a thread pitch in millimetres to threads per inch (TPI) and back, for matching metric and inch threads.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Tolerance stack-up – Add up the tolerances of a chain of parts: closing gap, worst case and statistical RSS for up to eight dimensions. Free, in your browser.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
- Spur gear – Pitch and outside diameter, centre distance, ratio and circular pitch of a pair of external spur gears from the module and the tooth numbers.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.