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Belt Length Calculator

Work out belt length instantly with clear inputs, formula shown and shareable results.

About Belt Length Calculator

Open belt length is 2C + (pi/2)(D + d) + (D - d)² / (4C): twice the centre distance for the straight spans, half a circumference of each pulley, and a small correction because the belt leaves the pulleys at an angle rather than tangentially opposite. Wrap angles follow from the same geometry and govern how much torque the belt can transmit before slipping.

Formulas

Belt length

L = 2C + (pi/2)(D + d) + (D - d)² / (4C)

Wrap angles

θ = 180 ± 2 arcsin[(D - d) / 2C] degrees

Worked example

With the default values below, Belt Length Calculator returns Belt pitch length of 50.262. Change any input above and every figure here is recalculated in your browser.

Inputs used

Large pulley pitch diameterminimum 0.1 in
6 in
Small pulley pitch diameterminimum 0.1 in
3 in
Centre distanceminimum 0.1 in
18 in

Results

Belt pitch length
50.262 in
Wrap angle on large pulley
189.6 °
Wrap angle on small pulley
170.4 °
Speed ratio
2.000

Step by step

  1. 1Values used
  2. 2Belt length
  3. 3Wrap angles
  4. 4Belt pitch length= 50.262 in
  5. 5Wrap angle on large pulley= 189.6 °
  6. 6Wrap angle on small pulley= 170.4 °
  7. 7Speed ratio= 2.000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Belt Length figure worked out?

L = 2C + (pi/2)(D + d) + (D - d)² / (4C). Open belt length is 2C + (pi/2)(D + d) + (D - d)² / (4C): twice the centre distance for the straight spans, half a circumference of each pulley, and a small correction because the belt leaves the pulleys at an angle rather than tangentially opposite.

Which pulley slips first?

The small one, because it has the least wrap angle and therefore the least friction available. Drive capacity is always calculated on the small pulley.

What values do I need to enter?

This calculator takes 3 inputs: Large pulley pitch diameter, Small pulley pitch diameter, Centre distance. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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