Free Engineering Calculator
Bolt Circle Calculator: Hole Positions and Spacing
Hole coordinates, angles and spacing for holes evenly spaced on a bolt circle. 6 holes on a 100 mm circle are 60° and 50 mm apart.
Bolt Circle Calculator
Enter the number of holes, the bolt circle diameter and the angle of the first hole. The calculator lists every hole’s angle and X, Y coordinates, the spacing between neighboring holes, and draws the pattern.
Bolt Circle Calculator
Hole positions, angles and spacing for holes evenly spaced on a bolt circle.
| Hole | Angle | X | Y |
|---|
Angles are measured counterclockwise from the positive X axis, hole 1 at the first hole angle. X = Xc + R cos θ, Y = Yc + R sin θ, with R = diameter / 2. Chord = D x sin(180° / N).
How to Use the Bolt Circle Calculator
- Enter the number of equally spaced holes (2 to 72).
- Enter the bolt circle diameter (also called the pitch circle diameter, PCD) and choose mm or inches.
- Enter the angle of the first hole, measured counterclockwise from the positive X axis. Use 0 for a hole on the X axis, or half the hole spacing (for example 45° for 4 holes) to straddle the axes.
- Enter the center coordinates if the circle is not at the origin, then copy the coordinates into your drawing or CNC program.
Formula and Worked Examples
For hole i (counting from 0): θ = θ0 + 360° x i / N, X = Xc + R cos θ, Y = Yc + R sin θ, where R is half the bolt circle diameter. The straight-line spacing between neighboring holes is chord = D x sin(180° / N).
Example 1: 6 holes on a 100 mm bolt circle, first hole at 0°. The holes are 60° apart and 50.000 mm apart center to center:
| Hole | Angle | X (mm) | Y (mm) |
|---|---|---|---|
| 1 | 0° | 50.000 | 0.000 |
| 2 | 60° | 25.000 | 43.301 |
| 3 | 120° | -25.000 | 43.301 |
| 4 | 180° | -50.000 | 0.000 |
| 5 | 240° | -25.000 | -43.301 |
| 6 | 300° | 25.000 | -43.301 |
Example 2: 4 holes on a 4.000 in bolt circle starting at 45° sit at X, Y = ±1.4142 in, 2.8284 in apart. Example 3: 8 holes on a 150 mm circle are 45° and 57.403 mm apart.
Frequently Asked Questions
What is a bolt circle?
The circle that passes through the centers of a ring of equally spaced bolt holes, as on a flange, wheel hub or motor mount. Its diameter is the bolt circle diameter or pitch circle diameter (PCD).
How do you calculate bolt hole spacing on a circle?
Center-to-center spacing between neighboring holes = bolt circle diameter x sin(180° / number of holes). For 6 holes on 100 mm that is 100 x sin 30° = 50 mm.
How do I measure the bolt circle of a 4-hole pattern?
Measure center to center between two opposite holes; that distance is the bolt circle diameter. On a 5-hole pattern, measure from one hole center to the far edge of the hole opposite and correct with the formula, or divide the neighbor spacing by sin 36°.
Which direction are the angles measured?
Counterclockwise from the positive X axis, the usual convention in CAD and CNC. For a clockwise sequence, enter the start angle as a negative value or number the holes in reverse order; the coordinates are the same points.
Related Charts and Calculators
Next checks: Tap Drill Size Calculator for the tapped holes, Bolt Size and Strength Calculator, Bolt Torque and Preload Calculator and all calculators and charts.
Specifying a Safety-Critical Joint?
These charts are reference values drawn from published standards. Send us your drawing or specification and our team will review the fastener choice with you.