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Bolt Circle Calculator

Find the angle between bolt holes and the chord distance between adjacent holes on any bolt circle. Enter the radius and number of holes for instant results.

Result

7.071

4 holes on a 5 radius bolt circle are 90° apart, 7.071 apart in a straight line

Quick Answer

A bolt circle calculator gives the angular step between equally spaced holes and the chord distance between adjacent holes. For 6 holes on a 3-inch radius bolt circle, the angle step is 360 ÷ 6 = 60 degrees and the adjacent hole spacing is 2 × 3 × sin(π ÷ 6) = 3.000 inches.

Bolt Circle Calculator: Angle Step and Adjacent Spacing

This bolt circle calculator outputs two values: the angular step between consecutive holes and the straight-line (chord) distance between adjacent hole centers. The angle step is 360 degrees divided equally by the number of holes. The adjacent spacing is the chord length of the arc between two neighboring holes, calculated from the bolt circle radius and the angle step. This calculator reports angle and spacing only. It does not output full x/y coordinates for every hole position.

The Bolt Circle Formula for Step Angle and Spacing

Angle step (degrees) = 360 ÷ n Adjacent hole spacing = 2 × r × sin(π ÷ n)

  • Angle step (degrees) = 360 ÷ n
  • Angle step (radians) = 2π ÷ n
  • Adjacent hole spacing (in or mm) = 2 × r × sin(π ÷ n)

Using the Bolt Circle Calculator: Set Up and Read Results

Inputs

  • Bolt circle radius (in or mm): the distance from the center of the pattern to the center of any one hole
  • Number of holes: the count of equally spaced holes around the circle

Steps

  1. Identify the bolt circle diameter from the drawing and halve it to get the radius, or read the radius directly if specified.
  2. Count the number of holes from the drawing or pattern specification.
  3. Enter the radius and hole count into the calculator.
  4. Read the angle step (degrees) and adjacent hole spacing (same unit as the radius input).
  5. Use the angle step for angular indexing on a rotary table or dividing head; use the spacing for physical verification with a caliper.

Bolt Circle Worked Example: 8 Holes on a 50 mm Radius

An 8-hole bolt pattern on a 50 mm radius pitch circle.

  1. Calculate angle step: 360 ÷ 8 = 45.00 degrees.
  2. Calculate half-angle in radians: π ÷ 8 = 0.3927 rad.
  3. Calculate adjacent hole spacing: 2 × 50 × sin(0.3927) = 100 × 0.3827 = 38.27 mm.

Drill holes every 45 degrees of rotation. Adjacent hole centers are 38.27 mm apart.

When To Use a Bolt Circle Calculator On Any Project

Use this calculator when setting up a bolt hole pattern on a rotary table, mill, or CNC machine; when checking a drawing to verify hole spacing before cutting; or when ordering a bolt circle flange and confirming hole positions against a mating component. This calculator handles equally spaced holes on a single circle only. It does not calculate patterns with unequal angular spacing, staggered bolt circles, or slotted holes. For those configurations, lay out each hole individually using full x/y coordinates.

Assumptions

  • Holes are equally spaced at uniform angular intervals around a single circle.
  • Radius is measured center-to-center from the bolt circle axis to the hole center.
  • Adjacent spacing is the chord (straight-line) distance between neighboring hole centers, not the arc length.
  • All holes lie in a single plane; this is a 2D layout calculation.

Limitations

  • Does not output x/y Cartesian coordinates for each hole; calculate each as x = r cos(2πk/n), y = r sin(2πk/n) for k = 0 to n-1 if full coordinates are needed.
  • Does not handle non-uniform hole spacing or mixed-diameter patterns on the same circle.
  • Does not account for hole diameter; the spacing given is center-to-center.
  • Does not calculate the bolt circle diameter from hole positions measured on an existing part; use a three-point circle solver for reverse measurement.

In Practice

A common layout error is confusing bolt circle diameter with bolt circle radius. Many engineering drawings label the bolt circle by its diameter (for example, "4-inch BCD" meaning 4-inch bolt circle diameter), but the calculator input requires the radius, which is half that value. Entering the diameter directly instead of the radius doubles the spacing result and places the holes on the wrong circle. Always halve the BCD dimension before entry.

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Frequently Asked Questions: Bolt Circle Calculator

What is a bolt circle diameter?

Bolt circle diameter (BCD) is the diameter of the imaginary circle that passes through the center of each bolt hole in a circular pattern. It is the standard way to specify a bolt hole pattern on engineering drawings and flange specifications. The radius used in the bolt circle formula is half the BCD.

How do I find the bolt circle radius from a drawing?

Look for the BCD (bolt circle diameter) dimension on the flange or plate drawing, then divide by 2 to get the radius. If the drawing gives the radius directly, use that value. On some drawings the dimension is labeled PCD (pitch circle diameter), which means the same thing as BCD.

Does this calculator give the x/y position of each hole?

No. This calculator gives the angle step and adjacent chord spacing only. To get the full x/y coordinates for each hole, use the formulas x = r × cos(2πk/n) and y = r × sin(2πk/n), where k runs from 0 to n-1 and r is the bolt circle radius. Many CAD programs and CNC controllers have built-in bolt circle routines that compute these positions directly.

What does the adjacent hole spacing represent?

Adjacent hole spacing is the straight-line distance from the center of one hole to the center of the next hole clockwise or counterclockwise around the pattern. It is a chord length across the circle, not the arc length along the circle. This value is what you would measure with a caliper between two neighboring hole centers to verify a drilled pattern.

How accurate is the bolt circle calculation?

The formula is exact given exact inputs. Error comes from rounding the radius or from physical drilling tolerances. In practice, verify the first two drilled holes by measuring the chord distance before completing the pattern, particularly for precision flanges where misalignment causes leakage or misfit with mating components.

Sources

Last updated: . Reviewed for accuracy against the formula shown above.