Bolt Circle Calculator
Find the hole-to-hole spacing and X-Y coordinates for any bolt circle, from its diameter and hole count.
Reviewed by the ToolNestr Editorial Team — July 2026
How the bolt circle calculator works
A bolt circle is a set of holes spaced evenly around an imaginary circle — on a wheel hub, a pipe flange, or a machined plate. The bolt circle diameter (BCD) is the diameter of that circle through the hole centers. Two things follow from the BCD and the number of holes: the straight-line spacing between neighboring holes, and the exact position of each hole.
The spacing between adjacent holes is the chord of the arc between them. It equals the BCD times the sine of 180 divided by the number of holes. For a 5-inch circle with six holes, that is 5 × sin(30°) = 2.5 inches. This chord is what you would measure with calipers straight across from one hole center to the next, and it is a quick way to check a pattern.
To lay the pattern out precisely, work in coordinates from the circle's center. Each hole's angle steps by 360 ÷ number of holes, starting from whatever start angle you choose, and its position is X = radius × cos(angle), Y = radius × sin(angle). Plotting coordinates from one origin avoids the error that builds up when you step a divider around the circle hole by hole, which is why machinists prefer it on a coordinate table.
Bolt pattern and hole-spacing conventions follow SAE J1063 and common ANSI flange bolt-circle layout practice.
Enter the circle
Bolt circle diameter and number of holes.
Set a start angle
Where the first hole sits, often 0°.
Read spacing & XY
Chord distance plus each hole's coordinates.
The formula explained
Chord spacing
= BCD × sin(180 ÷ N). A 5 in circle, 6 holes: 5 × sin(30°) = 2.5 in.
Angle step
= 360 ÷ N = 360 ÷ 6 = 60° between holes.
Coordinates
X = r cosθ, Y = r sinθ with r = BCD ÷ 2 and θ stepping from the start angle.
Worked example
A 4-hole flange on a 4 in bolt circle, first hole at 45°.
Tips for laying out a bolt circle
Verify the BCD before ordering hardware
Bolt circle diameter is measured center-to-center through the hole pattern, not edge-to-edge. On an odd number of holes it cannot be measured directly across the circle, so it is easier to measure one chord and back-calculate the BCD, or use a bolt pattern gauge.
Center-punch before drilling
Plot each hole's X-Y coordinate from the center, then center-punch every location before drilling. A punch mark keeps the drill bit from wandering, which matters most on the outer holes where a small angular error translates into a larger position error.
Double-check the start angle on asymmetric parts
Most patterns are symmetric and the start angle does not matter, but on brackets or flanges that must clear an obstruction, get the start angle right the first time — rotating a finished hole pattern after drilling is not an option.
Real-world context
Automotive wheels are the most common bolt circle in everyday life. A typical 5-lug passenger car wheel uses a 4.5 in (114.3 mm) bolt circle diameter. Plugging that into the chord formula gives 4.5 × sin(180 ÷ 5) = 4.5 × sin(36°) = 2.645 in between adjacent lug centers — the number a mechanic checks with calipers before assuming a wheel is a straight bolt-pattern match, since two different vehicles can share a bolt count but use a different BCD.
Pipe flanges push the hole count higher. An 8-hole ANSI flange on a 13.5 in bolt circle gives a step angle of 360 ÷ 8 = 45° between holes, and a chord of 13.5 × sin(180 ÷ 8) = 13.5 × sin(22.5°) = 5.166 in. Because flange bolts must line up with a mating flange on the other side of a joint, machinists lay these holes out by X-Y coordinate rather than by walking a divider around the circle, since accumulated error at hole eight would misalign the gasket seal.
Small fabrication jobs use the same math at a smaller scale. A 3-hole mounting plate on a 2 in bolt circle needs a chord of 2 × sin(180 ÷ 3) = 2 × sin(60°) = 1.732 in between holes, spaced 120° apart. At just three holes, the coordinate method and the chord-stepping method agree closely enough that either works, but the calculator's coordinate table still saves a step of trigonometry on the shop floor.
Common misconceptions
"Two wheels with the same number of lug holes will always bolt up." Not necessarily. Hole count alone says nothing about the bolt circle diameter. A 5-lug wheel on a 4.5 in BCD and a 5-lug wheel on a 5.5 in BCD both have five holes, but the hole spacing is completely different and the wheels are not interchangeable.
"Measuring the chord between two adjacent holes is the same as measuring the bolt circle diameter." It is not. The chord is always smaller than the diameter — it only equals the diameter's straight-line span between two points on the circle that are one hole-spacing apart, not the full diameter across the center. Confusing the two leads to ordering the wrong hardware.
Related calculators
Frequently asked questions
How do I calculate bolt circle hole spacing?
The straight-line distance between two adjacent holes (the chord) equals the bolt circle diameter times the sine of 180 divided by the number of holes. For a 5-inch circle with 6 holes: 5 × sin(30°) = 2.5 inches between holes.
How do I find the coordinates of each hole?
Place the center at the origin. Each hole sits at X = radius × cos(angle) and Y = radius × sin(angle), where the angle steps by 360 ÷ number of holes around the circle. This calculator lists the coordinates for every hole.
What is a bolt circle diameter?
The bolt circle diameter (BCD) is the diameter of the imaginary circle that passes through the center of every bolt hole in a pattern — on a wheel, flange, or hub. It sets where the holes are placed, independent of the bolt size.
Why lay out holes by coordinates instead of measuring around the circle?
Marking X-Y coordinates from a common origin avoids the compounding error of stepping a divider hole-to-hole around a circle. On a mill or drill press with a coordinate table, plotting each hole position gives a far more accurate pattern.
Sources & references
This tool uses standard formulas and reference values from:
- • American Concrete Institute — ACI 318, Building Code Requirements for Structural Concrete. concrete.org
- • ICC — International Residential Code (IRC), span, footing and framing tables. codes.iccsafe.org
- • APA – The Engineered Wood Association, allowable span and load guidance.
Estimates for planning only. Span, load and code values vary by jurisdiction — verify against your local adopted code and a licensed engineer before building.