Bolt Circle Calculator: Hole Coordinates on a Pitch Circle Diameter

Get the position of every hole on a bolt circle.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the pitch circle diameter, the number of holes, the angle of the first hole and the position of the centre.

The calculator finds the radius, the angle between holes 360 over n, the chord distance between neighbours and the x and y coordinates of every hole.

Use the coordinates directly in a CAD drawing or on a machine.

Formulas used

  • x_i = c_x + r\cos(\alpha_0 + i\,360^\circ/n)
  • y_i = c_y + r\sin(\alpha_0 + i\,360^\circ/n)
  • c = D\sin(180^\circ/n)

Worked example

With the default numbers in the calculator above:

  1. Radius of the bolt circle and the angle between holes: 50.00 mm and 60.00 degrees
  2. Distance between neighbouring holes (the chord): 50.00 mm
  3. Coordinates of each hole (x, y): 1: (50.000, 0.000) 2: (25.000, 43.301) 3: (-25.000, 43.301) 4: (-50.000, 0.000) 5: (-25.000, -43.301) 6: (25.000, -43.301)

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is PCD?

The pitch circle diameter, which is the diameter of the circle that passes through the centres of the holes.

How is the chord found?

The distance between two neighbouring holes is D times the sine of 180 degrees over the number of holes.

Which way is the angle measured?

Anticlockwise from the positive horizontal axis, as in most CAD systems.

Does it work for flanges?

Yes. The flange standards give the PCD and the number of holes for each size.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS 4087 Metallic flanges for waterworks purposes; AS 2129 Flanges for pipes, valves and fittings.

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