Bolt Circle Calculator
Find the angle, chord spacing, and hole coordinates for a bolt pattern from the number of bolts and the bolt circle diameter.
🔩 What is a Bolt Circle Calculator?
A bolt circle calculator works out the layout of a circular bolt pattern, the angle between adjacent bolts, the straight-line chord distance between them, and the X,Y coordinate of every hole relative to the center. A bolt circle, also called a pitch circle, is the imaginary circle that passes through the center of every bolt hole in a circular flange, wheel, pump housing, or machine part, and its diameter (the BCD) is one of the most commonly quoted dimensions on a mechanical drawing.
Machinists, welders, and mechanics use this calculation constantly. Drilling a new flange to match an existing pump, laying out a custom wheel adapter, programming a CNC mill's hole pattern, or simply checking whether a replacement part will bolt up all start with the same geometry: how many bolts, on what diameter circle, and where exactly does each hole go. Getting the angle or spacing wrong by even a couple of degrees can mean holes that do not line up when the parts are mated.
A common point of confusion is treating the bolt circle diameter as the outer size of the part. It is not; the BCD is always measured hole-center to hole-center, well inside the outer edge of a flange or wheel. Another mix-up is assuming opposite bolts on any pattern sit exactly one BCD apart, which is only true for an even number of bolts, an odd bolt count like 5 has no two holes directly across from each other.
Enter the number of bolts, the bolt circle diameter, and a starting angle for where the first bolt sits, and this calculator returns the angle between bolts, the chord spacing you would measure with calipers, the radius, and a full coordinate table for every hole, alongside a scaled diagram of the layout.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A 6-Bolt Flange
6 bolts on a 6 inch bolt circle, starting at the top (90°)
Example 2 — An 8-Bolt Pump Cover
8 bolts on a 10 inch bolt circle, starting at the top (90°)
Example 3 — A 4-Bolt Wheel Adapter
4 bolts on a 4.5 inch bolt circle, starting at the top (90°)
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the angle between bolts on a bolt circle?
Divide 360 degrees by the number of bolts. A 6-bolt circle has 360 / 6 = 60 degrees between adjacent bolts, an 8-bolt circle has 360 / 8 = 45 degrees. This angle is the same regardless of the bolt circle diameter.
How do I find the chord distance between two adjacent bolt holes?
Multiply the bolt circle diameter by the sine of 180 divided by the number of bolts. For a 6-bolt circle with a 6 inch BCD, chord = 6 x sin(30 degrees) = 6 x 0.5 = 3 inches. This is the straight-line spacing you would measure with calipers between two neighboring holes.
What is a bolt circle diameter (BCD)?
The bolt circle diameter is the diameter of the imaginary circle that passes through the center of every bolt hole in a circular pattern, such as a wheel, flange, or pump housing. It is always measured hole-center to hole-center, never to the outer edge of the part.
How do I find the X and Y coordinates of each bolt hole?
For bolt number i (starting at 0), the angle is the starting angle plus i times 360/N. The X coordinate is the radius times cosine of that angle, and the Y coordinate is the radius times sine of that angle, where the radius is BCD divided by 2. This calculator lists the coordinates for every hole automatically.
Does the starting angle change the bolt spacing?
No. The starting angle only rotates where the first hole sits, for example at the top (90 degrees) or at 3 o'clock (0 degrees). The angle between bolts and the chord distance depend only on the bolt count and the bolt circle diameter, not the starting angle.
How do I lay out a bolt circle on a workpiece?
Mark the center point, scribe a circle at the bolt circle radius, then use a protractor or dividers to step off the angle between bolts around the circle, or use the X,Y coordinates from this calculator with a digital readout or CNC machine for precise center-punch locations.
What does a bolt pattern like 5x114.3 mean?
It means 5 bolts arranged on a bolt circle with a 114.3 mm diameter, a common automotive wheel pattern. The first number is the bolt count, the second is the bolt circle diameter, usually in millimeters for wheels and inches for flanges and machine parts.
Why do opposite bolts on a 5-bolt pattern not measure the full BCD apart?
With an odd number of bolts, no hole sits exactly opposite another, so no two holes are a full diameter apart. The measurable distance across a 5-bolt pattern is instead BCD times cosine of 36 degrees, about 0.809 times the BCD, which is why 5-lug wheel spacing is often quoted as this reduced figure.
Can I use this calculator for both inches and millimeters?
Yes. The formulas are unit-independent. Enter the bolt circle diameter in whichever unit your drawing uses, inches or millimeters, and the chord distance and coordinates come out in the same unit.
How accurate does bolt circle spacing need to be for machining?
For most bolted flanges and brackets, spacing within a few thousandths of an inch (or a tenth of a millimeter) is plenty, since bolt holes are typically drilled slightly oversized for clearance. Precision alignment work or press-fit dowel patterns need tighter tolerances, closer to the coordinates this calculator reports.