Bolt Circle Calculator
X/Y coordinates of holes spaced equally on a pitch circle or an arc, with a drawing.
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- Free preview: your inputs, the checks, the hole numbers of the table’s first rows and a watermarked drawing, with the coordinates, spacing and every figure hidden.
- Locked until you unlock it: download and copy.
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About the Bolt Circle Calculator
Work out where to drill a ring of equally spaced holes. Enter the number of holes, the pitch-circle diameter (PCD) and the angle of the first hole, and the calculator lists the X and Y coordinates of every hole about the centre you give, with the angle of each and the move from the hole before it. It works for a full circle or for an arc with a hole at each end, measures angles from +X (3 o’clock, the usual zero of CNC controls) or from +Y (12 o’clock, as many flange drawings do), and numbers the holes clockwise or counter-clockwise.
You also get the angle and the straight distance between neighbouring holes, the metal left between them for a given hole diameter (with a check that the holes do not overlap) and a drawing of the pattern with every hole numbered. With a Pro pass, copy the coordinates into a spreadsheet, or download them as a CSV, as a DXF drawing for CAD, or as a G-code drilling program with the G81 or G83 peck cycle (or every move written out, for controls without canned cycles).
Without a pass, the free preview shows your inputs, the checks, the hole numbers of the table’s first rows and a watermarked drawing of the pattern; the coordinates, the spacing, the working, Copy coordinates and the CSV, DXF and G-code files come with a Pro pass.
How to use it
- Choose millimetres or inches (switching converts what you have typed) and a Full circle or an Arc.
- Enter the number of holes, the pitch-circle diameter and the first hole’s angle; for an arc, the angle from the first hole to the last.
- Choose where angles are measured from and which way the holes are numbered, and the centre’s X and Y if the pattern is not at the origin. Add the hole diameter to check the spacing.
- Read the coordinates table, the drawing and the checks; the decimals setting rounds the table and the files alike.
- For a drilling program, set the depth, the R plane, the clearance height, the feed, the spindle speed and the pecks under Drilling program (G-code).
- Copy the coordinates or download the CSV, DXF or G-code — with a Pro pass, or after unlocking this result.
Examples
First hole at 0° from +X, counter-clockwise, centre at the origin
X 50, Y 0; X 25, Y 43.301; X −25, Y 43.301; X −50, Y 0; X −25, Y −43.301; X 25, Y −43.301. The holes are 60° and 50 mm apart
180 mm PCD, first hole at 22.5° (half the 45° pitch) from +X
Hole 1 at X 83.149, Y 34.442 and hole 2 at X 34.442, Y 83.149; neighbours are 68.883 mm apart, so 18 mm holes leave 50.883 mm of metal between them
Flange holes are usually placed off the centre lines like this, at half the pitch angle from them.
100 mm PCD, an arc of 120° starting at 30°
Holes every 30° from 30° to 150°: X 43.301, Y 25 … X −43.301, Y 25, with 25.882 mm between neighbours
Four holes on a 70 mm PCD, the first at 45° from +Y
X 24.749, Y 24.749; X 24.749, Y −24.749; X −24.749, Y −24.749; X −24.749, Y 24.749
Depth Z −0.5 in, R plane 0.1 in, feed 5 in/min, G81
G98 G81 X2.0000 Y0.0000 Z-0.5000 R0.1000 F5.0000, then X1.0000 Y1.7321 and one line per hole, G80 to end the cycle
Common uses
- Drilling flange, hub, wheel and cover-plate bolt patterns on a mill, a CNC machine or by marking out
- Setting a machine’s DRO to each hole of a pattern, from the X and Y list
- Putting a hole pattern into CAD from the DXF instead of drawing it by hand
- Checking that a ring of holes leaves enough metal between them
- Machining and technical-drawing coursework, with the working shown
Formulas
- Angle of hole i (from 0): θᵢ = θ₀ + i × 360° ÷ n round a full circle, or θ₀ + i × arc ÷ (n − 1) along an arc with a hole at each end
- Coordinates from +X, counter-clockwise: x = cx + r cos θ, y = cy + r sin θ, with r = PCD ÷ 2; clockwise, θ turns the other way
- From +Y (12 o’clock), clockwise: x = cx + r sin θ, y = cy + r cos θ
- Distance between neighbours (chord): c = 2r sin(Δθ ÷ 2), so a full circle of n holes has c = PCD × sin(180° ÷ n)
- Metal between holes (ligament): c − hole diameter; at zero or less the holes touch or overlap
The files
- CSV: hole number, angle, X, Y and the moves ΔX and ΔY, with the pattern described in the first lines; the copy is the same table as tab-separated text, which pastes into a spreadsheet as columns
- DXF: an AutoCAD R12 drawing with the pitch circle on layer PCD, the centre on CENTER, each hole as a circle (or a point when no diameter is given) on HOLES and its number on NUMBERS. R12 files carry no unit, so open it in the unit you chose here
- G-code: absolute coordinates with Z0 on the top face, the work offset you choose (G54 to G59), the spindle started with M03, a tool change (T… M06) with its length offset (G43 H…) if you give a tool number, and the G81 drilling cycle — or G83 with pecks — with G98, so the drill returns to the clearance height between holes. For controls without canned cycles, such as classic GRBL, choose the written-out moves: G00 and G01 for every hole and every peck; for GRBL choose no tool change as well, as it has no M06 or G43 H
Check every program in a simulator and dry-run it above the part before cutting: the feed, the speed, the depth (allow for the drill’s point) and the safe heights are yours to set for your machine and drill.
Sources
- Plane trigonometry: the polar-to-cartesian relations x = r cos θ and y = r sin θ, and the chord 2r sin(θ ÷ 2)
- Machinery’s Handbook: hole-circle coordinate tables, the classic way the same coordinates were looked up
- ISO 6983-1: numerical control of machines, program format and the G and M word addresses
Limitations
- One pitch circle of equally spaced holes per calculation. Patterns with unequal spacing or several circles need a calculation each.
- The table and the files are rounded to the decimals you choose.
- The DXF is a flat 2D drawing; the G-code drills straight down at each hole with a canned cycle or simple moves, without cutter compensation or helical boring.
- A G-code program has to suit your control and machine: check it in a simulator and dry-run it before cutting.
Privacy
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Frequently asked questions
What do I get without a pass?
Without a pass, Bolt Circle Calculator shows your inputs, the checks, the hole numbers of the table’s first rows and a watermarked drawing, with the coordinates, spacing and every figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the coordinates of a bolt circle?
Halve the PCD to get the radius r, find each hole’s angle θ (the first hole’s angle plus 360° ÷ n for each step) and use x = r cos θ, y = r sin θ, adding the centre’s coordinates. For six holes on a 100 mm PCD starting at 0°, hole 2 is at 60°: x = 50 cos 60° = 25, y = 50 sin 60° = 43.301.
What is the PCD?
The pitch-circle diameter is the diameter of the circle through the centres of the holes, also called the bolt-circle diameter (BCD). It is not the outside diameter of the part or of the holes.
How far apart are the holes?
Along the circle they are 360° ÷ n apart; in a straight line the distance is PCD × sin(180° ÷ n). Six holes on a 100 mm PCD are 50 mm apart, eight holes on 180 mm are 68.883 mm apart.
Where should the first hole go?
Wherever the drawing puts it. Flange patterns usually straddle the centre lines, so the first hole sits at half the pitch angle from them: 45° for four holes, 22.5° for eight. Enter that angle as the first hole’s angle.
Will the G-code run on my machine?
The canned-cycle program uses G81 or G83 with G98, which Fanuc-style controls, LinuxCNC and Mach run; controls without canned cycles, such as classic GRBL, need the written-out moves (and, for GRBL, no tool change: it has no M06 or G43 H). Either way, Z0 is the top face and the coordinates are absolute (G90). Set your own feed, speed and depth, then check the program in a simulator and dry-run it before cutting.
Which way are the angles measured?
You choose. From +X (3 o’clock) counter-clockwise is the mathematical convention most CNC controls use; from +Y (12 o’clock) clockwise is how many flange drawings dimension the holes. The table lists each hole’s angle in the convention you choose, and the drawing shows the zero line and the numbering direction.