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Pulley Belt Length Calculator

Find the belt length needed for a two-pulley drive.

How it is calculated

The tool uses the standard approximation for an open belt on two pulleys: L = 2C + (π/2)(D + d) + (D − d)² / (4C). D and d are the two pulley diameters and C is the centre distance, all in the same length unit. The result is labelled in millimetres, so enter all three values in millimetres. The first term is the two straight spans, the second is the wrap around the pulleys, and the last corrects for the belt leaving the pulleys at a slight angle when the sizes differ. All three inputs must be above zero. The tool does not check that the pulleys physically fit at the distance you give, and it gives the length of a closed loop with no allowance for tensioner travel, belt stretch or standard belt sizes.

Worked example

A drive has a 200 mm pulley, a 100 mm pulley and a centre distance of 500 mm. Straight spans: 2 × 500 = 1,000. Wrap: (π/2) × (200 + 100) = 471.24. Correction: (200 − 100)² / (4 × 500) = 10,000 / 2,000 = 5. Sum: 1,000 + 471.24 + 5 = 1,476.24 mm. In practice you would choose the nearest standard belt length and use the motor mount adjustment to take up the difference.

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Common mistakes

  • Entering radii instead of diameters. The formula needs the full diameter of each pulley; using radii gives a belt far too short.
  • Measuring the centre distance to the pulley edges rather than between the shaft centres.
  • Using the wrong units. The output is in mm, so inches or centimetres typed into the fields give a length that is wrong by a factor of 25.4 or 10 when read as mm.
  • Using the result for a crossed belt or for a pulley layout with a third idler pulley. This is the open two-pulley case only.

About this calculator

This calculator finds the length of an open (crossed-free) belt running between two pulleys of different or equal diameter: L = 2C + π(D+d)/2 + (D−d)²/(4C), where D and d are the pulley diameters and C is the centre-to-centre distance. The formula accounts for the straight spans on each side plus the wrap around each pulley.

Mechanical engineers, machinists, and maintenance technicians use it when designing or replacing a belt drive on a conveyor, motor, lathe, or fan, so they order a belt of the correct length instead of guessing and re-measuring. Enter both pulley diameters and the centre distance to get the required belt length.

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