Belt Length Calculator

How is belt length calculated?

A belt around two pulleys consists of two straight spans and two arcs wrapped on the pulleys. For an open belt the exact equation is L = 2 × C × cos β + π × (d₁ + d₂) / 2 + β × (d₂ − d₁), where C is the centre distance and β is the angle between a belt span and the line of centres, β = asin((d₂ − d₁) / (2 × C)).

Hand calculations usually use the approximate form L ≈ 2 × C + π × (d₁ + d₂) / 2 + (d₂ − d₁)² / (4 × C). When the centre distance is large compared with the diameter difference the two results differ by less than a millimetre.

Wrap angle

The wrap angle is the arc of contact between belt and pulley. For an open belt it is θ = 180° − 2 × β on the small pulley and θ = 180° + 2 × β on the large one. A smaller wrap angle on the small pulley means less power can be transmitted, so it deserves a check on drives with a high ratio and a short centre distance.

Example

Take pulleys of 100 mm and 300 mm at a centre distance of 500 mm. Then β = asin(200 / 1000) = 11.54 degrees and the belt length is 979.8 + 628.3 + 40.3 = 1648.4 mm. The wrap angle on the small pulley is 156.9 degrees.

Limits

The calculated length is theoretical. Belts come in standard lengths: choose the nearest one and recalculate the centre distance for it, which is what the second mode of this tool does. Power capacity and tensioning force are determined from the manufacturer's catalogue.