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Two-Pulley Belt Length Calculator

Enter the center distance and both pulley diameters to size your belt.

How it is calculated

The tool uses the common approximation for an open belt: L = 2C + π(D + d)/2 + (D − d)² / (4C). C is the centre distance between the two shafts, D the large pulley diameter and d the small pulley diameter, all in millimetres (the tool labels results in mm, so convert inches first). The first term is the two straight runs, the second is the belt wrapped around the average pulley circumference, and the third adds the extra length caused by the size difference. The length is shown to one decimal in mm and also in inches (mm ÷ 25.4). All three values must be above zero. The tool does not check that the pulleys fit, and swapping D and d gives the same length, because the difference is squared. It is a pitch-length estimate: it ignores belt thickness and standard belt sizes.

Worked example

Centre distance C = 500 mm, large pulley D = 200 mm, small pulley d = 100 mm. Straight runs: 2 × 500 = 1000 mm. Wrap: π × (200 + 100) / 2 = π × 150 = 471.2 mm. Size correction: (200 − 100)² / (4 × 500) = 10000 / 2000 = 5.0 mm. Total 1,476.2 mm, which is 58.12 in. In practice you would then pick the nearest standard belt length and adjust the centre distance slightly to suit it.

Try this example →

Common mistakes

  • Entering the pulley radius instead of the diameter. The formula needs diameters; radii give a belt far too short.
  • Entering inches or centimetres while the result is labelled in millimetres. Convert everything to mm first.
  • Using the outside diameter of a V-belt pulley instead of the pitch diameter, where the belt actually rides.
  • Treating the answer as a catalogue size. Belts come in standard lengths, so round to the nearest available one and allow for adjusting the shaft spacing for tension.
  • Using this for crossed belts or more than two pulleys. The formula is for an open belt over exactly two pulleys.

About this calculator

Sizing a flat or V-belt for a two-pulley drive means finding the belt length that lets it wrap both pulleys and run taut across the center distance between them, without being so tight it strains the bearings or so loose it slips. The standard formula is L = 2C + π(D + d)/2 + (D − d)²/(4C), where C is the center distance, D is the large pulley diameter, and d is the small pulley diameter — the π(D+d)/2 term accounts for the belt wrapped around both pulleys, and the last term corrects for the extra length needed when the pulleys are different sizes.

Mechanical designers and machinists use this formula (or its close variants) when specifying a belt for conveyors, compressors, motors, and other belt-driven machinery, since ordering the wrong belt length means either a drive that can’t be tensioned properly or one that won’t fit the pulleys at all. Measure the center distance and both pulley diameters; the open-belt formula then gives the belt length to order.

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