A bolt circle calculator turns three numbers into exact positions for every hole in a circular pattern: the pitch circle diameter, the number of holes and the angle of the first hole. Instead of running sine and cosine for each hole by hand, you enter your values once and read a complete coordinate table. This free PCD calculator accepts a center offset, shows the formula with your own numbers, and checks its own results, so you can verify every line yourself.
Whether you are drilling a flange on a mill, drawing a mounting plate in CAD, laying out a 3D-printed part or checking a wheel pattern on paper, the geometry is identical. This guide explains how the tool works, the formulas behind it, how to measure a PCD when you only have the part in your hands, and the mistakes that most often put holes in the wrong place.
Quick answer: For N equally spaced holes on a circle of diameter PCD, the radius is R = PCD ÷ 2. Hole n sits at X = Xc + R × cos(θn) and Y = Yc + R × sin(θn), where θn = θ1 + (n − 1) × 360° ÷ N and (Xc, Yc) is the center of the circle.
| Hole | Angle (°) | X | Y |
|---|
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Table of Contents
What Is a Bolt Circle (Pitch Circle Diameter)?
A bolt circle, also called the pitch circle diameter (PCD) or bolt circle diameter, is the imaginary circle that passes through the centers of evenly spaced holes. It is not a feature you can see or machine. It is a construction circle drawn through hole centers, never through hole edges. As described in Wikipedia's article on the bolt circle, the idea is used for car wheels, steering wheel hubs, servomotor flanges, pipe flanges and bicycle chainrings, which is why the same maths appears in workshops, CAD offices and garages alike.
Bolt patterns are usually written as the number of holes followed by the circle diameter. A pattern written as 5×114.3 means five holes on a 114.3 mm circle. The calculator uses the same logic: tell it the circle and the hole count, and it returns where each hole center lands.
What You Get in This Bolt Circle Calculator
- Three ways to enter size: PCD, radius, or hole-to-hole spacing (chord).
- 2 to 360 holes, with a start angle, clockwise or counter-clockwise direction, and a center offset (Xc, Yc).
- Unit label (mm, cm, m, in, ft) and 0 to 6 decimals.
- Live preview with numbered holes. Hole 1 is highlighted.
- Step-by-step working that substitutes your numbers into the formulas for holes 1 and 2.
- Self-check: every hole must sit at distance R from the center, and the distance from hole 1 to hole 2 must equal the chord formula.
- Copy buttons for Excel or Google Sheets, CSV, and plain text.
- Light and dark themes, and a layout that adapts to phone, tablet and desktop.
The calculation runs in your browser using standard JavaScript double-precision numbers. Rounding is applied only to the displayed values, never to the intermediate maths.
How to Use the Bolt Circle Calculator
- Choose what you know. Select PCD (circle diameter), radius, or hole-to-hole spacing. Most drawings give the PCD.
- Enter the value and the number of holes (N). Any whole number from 2 to 360 works.
- Set the angle of hole 1. Angles are measured from the positive X axis (the 3 o'clock direction) and counter-clockwise is positive. An angle of 0° puts hole 1 on the right, and 90° puts it at the top.
- Pick the direction. Counter-clockwise is the usual convention. Choose clockwise if your drawing numbers holes the other way.
- Enter the center. Leave Xc and Yc at 0 for coordinates relative to the circle center. Enter your workpiece datum position to get coordinates in your own coordinate system.
- Choose unit label and decimals. The unit selector only labels the output. It does not convert numbers, so if you type inches you get inches.
- Read and copy the table. Check the preview, then copy the result in the format you need.
Five quick-fill presets (4×100, 5×100, 5×112, 5×114.3 and 6×139.7, all in mm) load common wheel-style patterns in one tap. They are only shortcuts for typing, not a fitment database.
Bolt Circle Formula Explained
Every result in the hole pattern coordinates table comes from five short formulas:
- R = PCD ÷ 2
- Step angle = 360° ÷ N
- θn = θ1 + (n − 1) × step angle (subtract instead of add for clockwise numbering)
- Xn = Xc + R × cos(θn)
- Yn = Yc + R × sin(θn)
The distance between two neighbouring holes, called the chord, follows from the same circle:
- Chord = 2 × R × sin(180° ÷ N) = PCD × sin(180° ÷ N)
The chord is useful because it is something you can measure directly on a real part. The table below lists the step angle and chord factor for common hole counts. Multiply the PCD by the chord factor to get the spacing, or multiply a measured chord by the last column to get the PCD.
| Holes (N) | Step angle | Chord ÷ PCD | PCD ÷ chord |
|---|---|---|---|
| 3 | 120° | 0.8660 | 1.1547 |
| 4 | 90° | 0.7071 | 1.4142 |
| 5 | 72° | 0.5878 | 1.7013 |
| 6 | 60° | 0.5000 | 2.0000 |
| 7 | 51.4286° | 0.4339 | 2.3048 |
| 8 | 45° | 0.3827 | 2.6131 |
| 9 | 40° | 0.3420 | 2.9238 |
| 10 | 36° | 0.3090 | 3.2361 |
| 11 | 32.7273° | 0.2817 | 3.5495 |
| 12 | 30° | 0.2588 | 3.8637 |
Factors are rounded to four decimals. The calculator uses the unrounded values.
Worked Example: 5 Holes on a 114.3 mm PCD
Take a 5×114.3 pattern with hole 1 at 0°, counter-clockwise, and the center at (0, 0).
- R = 114.3 ÷ 2 = 57.15
- Step angle = 360° ÷ 5 = 72°
- Hole 2: X = 57.15 × cos 72° = 17.660 and Y = 57.15 × sin 72° = 54.353
| Hole | Angle | X | Y |
|---|---|---|---|
| 1 | 0° | 57.150 | 0.000 |
| 2 | 72° | 17.660 | 54.353 |
| 3 | 144° | −46.235 | 33.592 |
| 4 | 216° | −46.235 | −33.592 |
| 5 | 288° | 17.660 | −54.353 |
You can confirm the chord with the table above: 114.3 × 0.5878 gives about 67.18, which matches the 67.184 the calculator reports between neighbouring holes.
Hole Pattern Coordinates With a Center Offset
Real parts rarely have the pattern centered on the origin. Suppose you need six holes on an 80 mm circle whose center sits at X = 25 and Y = 40, with hole 1 at 0°. The radius is 40, and the center offset is simply added to each result.
| Hole | Angle | X | Y |
|---|---|---|---|
| 1 | 0° | 65.000 | 40.000 |
| 2 | 60° | 45.000 | 74.641 |
| 3 | 120° | 5.000 | 74.641 |
| 4 | 180° | −15.000 | 40.000 |
| 5 | 240° | 5.000 | 5.359 |
| 6 | 300° | 45.000 | 5.359 |
The start angle matters just as much. Rotating the same three-hole pattern so that hole 1 points straight up (90°) on a 60 mm PCD gives (0, 30), (−25.981, −15) and (25.981, −15) instead of a hole on the right-hand side. Always match the start angle to how your drawing orients the pattern.
How to Measure PCD on a Real Part
You can only apply the bolt circle formula if the PCD is known. When you have the part but not the drawing, the method depends on the hole count:
- Even number of holes (4, 6, 8…): measure the center-to-center distance between two holes directly opposite each other. That distance is the PCD.
- Odd number of holes (3, 5, 7…): no hole sits directly opposite another. Measure the center-to-center distance between two adjacent holes (the chord), then switch the calculator to hole-to-hole spacing mode or multiply by the last column of the table above. For example, 5 holes spaced 67.2 mm apart give a PCD of about 114.3 mm.
- Calipers on hole edges: for holes of equal size, center-to-center equals the inner edge-to-edge distance plus one hole diameter, or the outer edge-to-outer edge distance minus one hole diameter.
- Square four-hole patterns: the PCD is the side length multiplied by 1.4142. A 70 mm square gives a PCD of about 99.0 mm.
Because the PCD is calculated from your measurement, any measuring error is multiplied by the factor in the table. Measure twice and compare the result with standard sizes before trusting it.
Common Bolt Patterns and Their Geometry
The table shows the geometry of five familiar wheel-style patterns. Inch values are exact conversions of the millimetre size divided by 25.4.
| Pattern | PCD (mm) | PCD (in) | Radius (mm) | Neighbour spacing (mm) |
|---|---|---|---|---|
| 4×100 | 100 | 3.937 | 50.00 | 70.711 |
| 5×100 | 100 | 3.937 | 50.00 | 58.779 |
| 5×112 | 112 | 4.409 | 56.00 | 65.832 |
| 5×114.3 | 114.3 | 4.500 | 57.15 | 67.184 |
| 6×139.7 | 139.7 | 5.500 | 69.85 | 69.850 |
A 5×114.3 pattern is the same circle as 5×4.5 in, since 4.5 × 25.4 = 114.3. Keep in mind that PCD is only one wheel-fitment factor. Offset, center bore and other dimensions also decide whether a wheel fits, so this table describes circle geometry and is not a vehicle fitment guide.
How Many Decimals Do You Need?
Rounding a coordinate to a given number of decimals can move it by at most half of the last digit. The table shows that limit for each axis and an approximate worst-case position error, which is that limit multiplied by about 1.414 when both axes round in the worst direction.
| Decimals | Max error per axis | Worst-case position error (approx.) |
|---|---|---|
| 0 | 0.5 | 0.707 |
| 1 | 0.05 | 0.0707 |
| 2 | 0.005 | 0.00707 |
| 3 | 0.0005 | 0.000707 |
| 4 | 0.00005 | 0.0000707 |
The values are in whatever unit you entered. How much precision you actually need depends on your drawing tolerance, your machine and your process, so treat the table as an estimate of rounding only. It does not include measurement, machine or tool error.
Common Mistakes When Calculating Bolt Hole Circle X Y Positions
- Mixing up diameter and radius. The formulas use the radius. Entering a PCD as a radius doubles the whole pattern.
- Using the wrong start angle. A pattern that is correct but rotated by 90° will not match the mating part.
- Forgetting the direction. Clockwise and counter-clockwise numbering gives the same hole positions in a different order, which matters when holes are numbered on the drawing.
- Measuring to hole edges. The PCD runs through hole centers. Edge measurements need the hole-diameter correction shown above.
- Mixing units. Do not enter a metric PCD and an inch offset in the same run.
- Forgetting the center offset. Coordinates relative to the circle center are not the same as coordinates relative to your workpiece datum.
- Rounding too early. Round only the final numbers. The tool does this by calculating with full precision and rounding the display.
Who Uses a PCD Calculator?
Machinists and CNC programmers use the coordinates as drilling positions. CAD users place holes or construction points from the table. Fabricators and makers lay out flanges, covers, pulleys, hubs and mounting plates. Students use the worked steps to learn polar-to-Cartesian conversion. Anyone comparing a measured pattern with a known size, such as 5×114.3, can switch to the chord mode and check it in seconds.
Frequently Asked Questions
How do you calculate a bolt circle?
Divide the PCD by 2 to get the radius, divide 360° by the number of holes to get the step angle, then place each hole at X = Xc + R × cos(θ) and Y = Yc + R × sin(θ). The calculator does all of this and shows the working.
What is the formula for bolt hole circle X Y coordinates?
X = Xc + (PCD ÷ 2) × cos(θ) and Y = Yc + (PCD ÷ 2) × sin(θ), where θ is the angle of the hole measured counter-clockwise from the positive X axis.
How do I find the PCD from the distance between two holes?
For equally spaced holes, PCD = chord ÷ sin(180° ÷ N), where the chord is the center-to-center distance between adjacent holes. In the calculator, choose hole-to-hole spacing as the known value.
Is 5×114.3 the same as 5×4.5?
Yes. 4.5 inches multiplied by 25.4 equals exactly 114.3 mm, so both describe the same five-hole circle.
Which angle does hole 1 start from?
Whatever you enter. Zero degrees is the positive X axis, and positive angles run counter-clockwise unless you select clockwise.
How many holes can the calculator handle?
Any whole number from 2 to 360.
Does the calculator work in inches?
Yes, as long as every value you enter is in inches. The unit selector labels the output and does not convert between units.
Can I use the coordinates in CAD or on a CNC machine?
You can copy the coordinates into a spreadsheet or use them as reference points in a CAD sketch or program. The calculator does not generate machine code, so check the numbers against your drawing and your machine's coordinate system before cutting.
Quick Summary
A bolt circle is the imaginary circle through the centers of evenly spaced holes. With the PCD, the hole count and the start angle, each hole follows from X = Xc + R × cos(θ) and Y = Yc + R × sin(θ). This bolt circle calculator does that instantly, shows your numbers inside the formulas, checks itself, and lets you copy the table. Measure PCD at hole centers, match the start angle to your drawing, and round only at the end.
Disclaimer
This calculator and article are provided for general information and planning only. Results come from the standard geometry formulas shown above and are displayed rounded to the number of decimals you choose. They have not been checked against your specific drawing, material, machine, standard or application.
Always compare the output with your drawing or specification, and confirm on a test piece before cutting, drilling or ordering parts. For safety-critical uses such as wheels, pressure flanges, lifting or structural joints, follow the applicable standard and consult a qualified engineer. Wheel fitment also depends on factors beyond PCD, and the example patterns here are not a fitment guide. The tool and content are provided as is, without warranty of any kind, and you use them at your own risk.