Bolt Circle Calculator: Find Hole Coordinates and Spacing

A bolt circle calculator finds the coordinates of equally spaced holes on a circular pitch diameter, along with the angle between holes and, when needed, the straight-line distance between neighboring hole centers. Enter the bolt-circle diameter, number of holes, and a starting angle; the results describe a layout you can transfer to a drawing or machine setup.

Formula

For a circle with diameter D and N equally spaced holes, the radius is R = D / 2. The angular increment is Δθ = 360° / N. If the first hole is at starting angle θ₀, hole i is at θᵢ = θ₀ + iΔθ, where i runs from 0 through N − 1. Its Cartesian coordinates, relative to the circle center, are xᵢ = R cos(θᵢ) and yᵢ = R sin(θᵢ). The straight-line distance between adjacent hole centers is c = D sin(π / N).

• D is the bolt-circle diameter, in millimeters here (or inches if you consistently use inches).
• N is the number of holes, a whole-number count of at least one.
• R is the bolt-circle radius, in the same length unit as D.
• θ₀ and θᵢ are angles in degrees; Δθ is the angle step in degrees.
• xᵢ and yᵢ are hole-center coordinates in the same length unit as D.
• c is the adjacent center-to-center chord distance, in the same length unit as D.

The calculator reports the angle step, radius, and chord spacing as well as the coordinates implied by the formula. Its first result is the adjacent hole spacing. For N = 1, the formula returns zero spacing because there is no distinct neighboring hole; a useful bolt pattern normally has two or more holes.

Worked Example

Using the calculator defaults, D = 100 mm, N = 6, and θ₀ = 0°:

1. Radius: R = 100 / 2 = 50 mm.
2. Angle increment: Δθ = 360° / 6 = 60°.
3. Adjacent center spacing: c = 100 × sin(π / 6) = 100 × 0.5 = 50.00 mm.
4. Coordinates use x = 50 cos θ and y = 50 sin θ. For angles 0°, 60°, 120°, 180°, 240°, and 300°, the centers are (50.00, 0.00), (25.00, 43.30), (−25.00, 43.30), (−50.00, 0.00), (−25.00, −43.30), and (25.00, −43.30) mm.

The listed coordinates are relative to the center of the pattern. Add the actual center coordinates of your part to each x and y value to place the pattern on a drawing or machine coordinate system.

Using a Bolt Circle for a Machine Layout

A bolt circle, also called a bolt pattern or pitch circle, is an imaginary circle passing through the centers of a group of holes. It is used to specify patterns for mounting flanges, covers, hubs, wheels, and other parts. The circle is not the outside edge of the part, nor is its diameter the distance across the outside edges of two holes. It is the diameter through the hole centers.

For example, a six-hole pattern divides a full turn into six equal 60° steps. The first hole’s angle sets the orientation of the entire pattern, not its size. Rotating θ₀ changes where the holes sit but leaves the diameter, equal spacing, and symmetry unchanged. A zero-degree starting angle places the first hole on the positive x-axis under the usual mathematical convention, where positive y points upward.

To lay out a pattern on a manual mill or rotary table, establish the part center and the circle radius, then index by the angular increment. Depending on the machine setup, you may instead position the tool from the calculated x-y coordinates. Check how the control defines its axes and angle direction: some shop drawings or machine controls use a different zero direction or clockwise-positive convention.

When to Use the Results

Use the diameter and hole count to check a known pattern, generate coordinates for a new one, or compare a drawing with a mating component. The adjacent spacing result is a chord: it measures directly from one hole center to the next. It is not the distance traveled along the curved circumference between those holes.

For a 100 mm circle with six holes, the chord is 50 mm. The arc length between adjacent holes is different: the circumference is πD, so one sixth of it is about 52.36 mm. Do not use arc spacing as the straight-line distance between hole centers. Also, the chord result is not the clear gap between the edges of drilled holes. For equal hole diameters H, the edge-to-edge gap along the chord direction is c − H, provided the holes do not overlap.

The calculation gives ideal geometric center positions only. It does not choose a drill size, provide a thread specification, account for clearances, or establish whether the part has enough material around the holes. Those depend on the design, fasteners, material, and application.

Common Errors and Practical Limits

• Mixing units: If the diameter is in inches, coordinates and chord spacing are in inches. Convert all lengths consistently before combining them; 1 inch equals 25.4 mm.
• Using the wrong diameter: Enter the pitch-circle diameter, not the part diameter, hole diameter, or radius. If a drawing gives radius, double it for the diameter input.
• Rounding too early: Keep full precision while generating coordinates and round only for the drawing or machine’s required resolution. Rounded values may not sum to a perfect circle.
• Misreading the angle: An angle step is 360° divided by the hole count. A six-hole pattern uses 60° increments; it does not start every hole 60° from the circle’s centerline in a separate direction.
• Ignoring the datum: Coordinates here are relative to the circle center. A machine needs the correct work origin, offsets, and orientation as well.

Real machining also involves tool diameter, workholding, runout, backlash, and measurement uncertainty. A calculator cannot compensate for those automatically. Verify the drawing’s datum and tolerances, confirm the machine’s units and coordinate convention, and check the setup before cutting. For high-precision or safety-critical parts, use the approved drawing and process requirements rather than treating rounded calculator output as a tolerance specification.

Frequently Asked Questions

How do I calculate a bolt circle?
Divide the full 360° turn by the number of holes to get the angular step. Use half the bolt-circle diameter as the radius, then calculate each center with x = R cos θ and y = R sin θ. The calculator applies these relationships.

Is bolt circle diameter the same as bolt circle radius?
No. Diameter spans the circle through its center; radius runs from the center to the hole-center circle. The radius is half the diameter.

How do I find the distance between adjacent holes?
For diameter D and N equal-spaced holes, the straight-line center distance is D sin(π/N). This is the chord length, not the arc length around the circle.

Does the starting angle change the bolt-circle spacing?
No. It rotates the pattern around its center. The diameter, angular increment, and adjacent chord spacing remain the same.

Can I enter inches instead of millimeters?
Yes, if the diameter is in inches, interpret all length outputs and coordinates as inches. Keep the units consistent when adding offsets or comparing measurements.

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in diameter | Bolt circle diameter | mm | 100 | 0
in holes | Number of holes | - | 6 | 1
in angle | Starting angle | deg | 0
out spacing | Adjacent hole spacing | mm | diameter * sin(pi / holes) | 2
out increment | Angle between holes | deg | 360 / holes | 2
out radius | Bolt circle radius | mm | diameter / 2 | 2