Bolt Circle Calculator: Find Hole Positions and Spacing

A bolt circle calculator finds the coordinates and spacing of equally spaced holes around a circular pattern. Enter the bolt circle diameter, number of holes, and a starting angle to get each hole’s position, plus the center-to-center spacing between neighboring holes.

Formula

For n equally spaced holes on a bolt circle of diameter d, the angle between adjacent holes is 360° / n. The straight-line distance between adjacent hole centers, called the chord spacing, is:

c = d × sin(180° / n)

The calculator uses the equivalent radian expression c = d × sin(π / n). Here, c is adjacent hole spacing and d is bolt circle diameter, both in millimeters; n is the number of holes, a positive whole number of at least 1. The radius is r = d / 2. The starting angle does not affect either distance; it sets the orientation of the pattern when calculating coordinates.

To find the center coordinates of hole k, if needed, use x_k = x₀ + r cos(θ₀ + 360°k/n) and y_k = y₀ + r sin(θ₀ + 360°k/n), for k from 0 to n − 1. The pattern center is (x₀, y₀), and θ₀ is the starting angle. This page’s compact calculator reports spacing and radius; the coordinate equations explain how the angle input is used in a full hole-layout calculation.

Worked Example

Using the defaults—100 mm bolt circle diameter and 6 holes—the angular interval is 360° / 6 = 60°. The half-angle is 30°, so the chord formula gives:

c = 100 × sin(π / 6) = 100 × 0.5 = 50 mm

The radius is r = 100 / 2 = 50 mm. Rounded to the calculator’s two decimal places, the outputs are an adjacent hole spacing of 50.00 mm and a radius of 50.00 mm. A starting angle of 0° places the first hole on the positive horizontal axis if coordinates are measured from the circle center.

What a Bolt Circle Calculator Is For

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 describes the layout used for many flanges, hubs, wheels, covers, and other parts that must align with matching components. The circle is a geometric reference, not a physical edge or necessarily the outside diameter of the part.

The calculator is useful when laying out a new pattern, checking dimensions from a drawing, or translating a diameter and hole count into a straight-line spacing. That spacing is helpful for checking adjacent hole locations with suitable measuring tools. It is not the distance measured along the circle’s curved circumference: chord spacing is a straight line between hole centers.

How to Use the Result and Choose Units

• Enter the diameter of the circle through the hole centers, not the part’s outside diameter or the radius.
• Enter the number of holes as a whole number. The displayed formula assumes the holes are evenly spaced.
• Use the starting angle to orient the pattern in a coordinate system or drawing. For example, 0° commonly puts the first hole to the right of the center, but coordinate conventions can differ.
• Keep all length measurements in one unit. This calculator reports millimeters; for inches, convert the entered diameter and interpret the spacing in the same unit, or multiply millimeters by 0.0393701.

For example, a 4-inch bolt circle with 8 equally spaced holes has adjacent chord spacing 4 × sin(22.5°), or about 1.5307 inches. The angular interval is 45°. If you need a metric drawing, convert the diameter to 101.6 mm first; the resulting spacing is about 38.88 mm. Avoid entering 4 as though it were 4 mm when the drawing says 4 inches.

Common Errors and Limits

A frequent misconception is that bolt circle diameter means the distance between opposite hole centers for any pattern. That is true for an even number of equally spaced holes when a pair lies directly opposite, but not generally for an odd number. The diameter is defined by the circle itself, so it remains meaningful regardless of whether a pair of holes is diametrically opposed.

Another common mix-up is using arc spacing instead of chord spacing. The arc length between neighboring holes is πd/n; the straight-line chord is d sin(π/n). They are close for many holes but not identical. For a 100 mm circle with 6 holes, the arc is about 52.36 mm while the chord is exactly 50 mm.

The calculation assumes a circular pattern with equal angular intervals and a known, accurate diameter. It does not account for hole diameter, tolerances, countersinks, slot shapes, material deformation, or manufacturing methods. Rounding the displayed spacing is suitable for a quick check, not a substitute for the tolerances and dimensions specified on an engineering drawing. For an actual part, verify the drawing’s datum, units, orientation, and fit requirements before marking or machining.

Frequently Asked Questions

How do I calculate bolt circle diameter from hole spacing?
For equally spaced holes with known adjacent chord spacing c and hole count n, rearrange the chord formula: d = c / sin(180° / n). Make sure the measured spacing is center-to-center and not an arc measurement or a gap between hole edges.

Is bolt circle diameter the same as pitch circle diameter?
In many mechanical drawings, bolt circle diameter and pitch circle diameter refer to the diameter of the circle through the centers of the mounting holes. Check the drawing’s terminology and dimension callouts, since conventions can vary between applications.

How do I find the angle between bolt holes?
For n equally spaced holes, divide 360° by n. Six holes have a 60° interval; eight holes have a 45° interval.

Can this calculation work in inches?
Yes. The formula works with any consistent length unit. If the diameter is entered in inches, the calculated radius and spacing are also in inches; this calculator’s output label is millimeters, so convert inch inputs to millimeters first for a correctly labeled result.

Does the starting angle change the hole spacing?
No. Rotating the whole pattern changes the hole coordinates relative to the chosen axes, but it does not change the circle diameter, angular interval, or distance between neighboring hole centers.

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