Bolt Circle Calculator
A bolt circle calculator divides 360° by the bolt count and finds chord spacing as diameter × sin(180° ÷ bolts): 6 bolts on an 8 in circle sit 4.00 in apart.
How do you lay out a bolt circle?
A bolt circle calculator needs two numbers: the diameter of the circle through the hole centers, and how many bolts sit on it. Divide 360° by the bolt count to get the angle between neighbors. Then multiply the diameter by the sine of half that angle to get the straight-line chord spacing you can check with calipers. Six bolts on an 8 in circle are 60° apart and 4.00 in center to center.
Enter the circle diameter in inches and the number of bolts. The calculator returns both the angle and the chord.
The formula in plain words
- Angle between bolts = 360° ÷ number of bolts
- Chord spacing = bolt circle diameter × sin(180° ÷ number of bolts)
Draw lines from the center to two neighboring holes and you get a narrow triangle. Split it down the middle and each half is a right triangle whose short side is half the chord. That side equals the radius × sin(half the angle). Double it and the radius becomes the diameter.
The chord is shorter than the arc along the curve. A ruler or calipers can only measure the chord, so it is the number you use.
Worked examples
These results match the calculator.
- Six bolts on an 8 in circle**
- Angle: 360 ÷ 6 = 60.0°
- Chord: 8 × sin(30°) = 8 × 0.5 = 4.00 in
With six bolts the chord always equals the radius, so you can step the pattern off with a compass set to the radius.
- Eight bolts on a 7.5 in circle**
- Angle: 360 ÷ 8 = 45.0°
- Chord: 7.5 × sin(22.5°) = 7.5 × 0.3827 = 2.87 in
- Checking a 5-lug wheel pattern of 5 × 4.5 in**
- Angle: 360 ÷ 5 = 72.0°
- Chord: 4.5 × sin(36°) = 4.5 × 0.5878 = 2.65 in
Chord factors by bolt count
Multiply the bolt circle diameter by the factor to get the adjacent spacing. Divide a measured spacing by the factor to recover the diameter.
| Bolts | Angle apart | Chord factor sin(180°/n) | Chord on a 10 in circle |
|---|---|---|---|
| 3 | 120° | 0.8660 | 8.66 in |
| 4 | 90° | 0.7071 | 7.07 in |
| 5 | 72° | 0.5878 | 5.88 in |
| 6 | 60° | 0.5000 | 5.00 in |
| 8 | 45° | 0.3827 | 3.83 in |
| 10 | 36° | 0.3090 | 3.09 in |
| 12 | 30° | 0.2588 | 2.59 in |
| 16 | 22.5° | 0.1951 | 1.95 in |
Common patterns you may meet
| Application | Pattern | Adjacent spacing |
|---|---|---|
| Passenger car wheel | 5 × 4.5 in (114.3 mm) | 2.65 in |
| Light truck wheel | 6 × 5.5 in (139.7 mm) | 2.75 in |
| Small car wheel | 4 × 100 mm | 70.7 mm |
| Pipe flange | 8 bolts on a 7.5 in circle | 2.87 in |
Pipe flange bolt circles are set by the flange standard and pressure class. Confirm the exact circle and hole size against the standard or the mating part, not a table.
How to measure an existing pattern
- For an even bolt count, measure from the center of one hole straight across to the center of the opposite hole. That is the diameter.
- Shortcut for even counts: measure from the far edge of one hole to the near edge of the opposite hole. The hole sizes cancel out.
- For an odd bolt count, measure between two adjacent hole centers and divide by the chord factor from the table.
- Use calipers, not a tape, when the pattern must mate with another part. A tenth of an inch is enough to stop bolts from lining up.
Common mistakes
- Using the radius as the diameter. The formula uses the full diameter. Entering the radius halves the spacing.
- Measuring the arc with a flexible tape. The arc is always longer than the chord, so holes drilled to it will drift.
- Rounding the angle. On 7, 9, or 11 bolts the angle is not a whole number. Lay out from the exact value, or errors stack up around the circle.
- Laying out from one hole only. Step around from the center and check the last gap. If it differs, the layout has crept.
Related calculators
Once the pattern is set, size the fastener tightening with the bolt torque calculator and check load with the bolt shear calculator. For the circle itself, the circumference calculator gives the full distance around. For load-bearing or pressure connections, have a licensed engineer confirm the design.
Frequently asked questions
What is a bolt circle diameter?
It is the diameter of the imaginary circle that runs through the center of every hole in an evenly spaced pattern. Flanges, wheel hubs, and pipe fittings are described by it. A 5 × 4.5 in wheel pattern, for example, means 5 lugs whose centers sit on a 4.5 in circle.
How do I find the chord spacing between bolts?
Multiply the bolt circle diameter by the sine of 180° divided by the number of bolts. For 8 bolts on a 7.5 in circle, 180 ÷ 8 = 22.5°, sin 22.5° = 0.3827, and 7.5 × 0.3827 = 2.87 in between adjacent bolt centers.
How do I measure a 5-bolt pattern when no hole sits opposite another?
With an odd number of bolts you cannot measure straight across the center. Measure center to center between two adjacent holes, then divide by sin(180° ÷ 5) = 0.5878. A 2.65 in adjacent spacing gives 2.65 ÷ 0.5878 = 4.51 in, so it is a 4.5 in bolt circle.
How do I get X and Y coordinates for each hole?
With the center at 0,0 and radius r (half the bolt circle), hole k sits at X = r × cos(angle × k) and Y = r × sin(angle × k), where angle is 360° ÷ bolts and k runs from 0. On an 8 in circle with 6 bolts, r = 4, so the holes are at (4, 0), (2, 3.464), (−2, 3.464), (−4, 0), (−2, −3.464), and (2, −3.464).
Does this work for any number of bolts?
Yes, as long as the holes are evenly spaced around the full circle. It works the same for a 3-hole pattern, a 4-bolt flange, or a 24-bolt ring. It does not cover patterns with uneven spacing, such as some flanges with a skipped hole, where each gap must be laid out separately.
Estimates only. Verify quantities with your supplier before purchasing.