About this calculator
Belt drives connect a motor to a machine such as a fan, pump, compressor or lathe. The ratio of the pulley diameters sets the speed of the driven machine. This calculator also gives the belt speed, which belt manufacturers limit, and an approximate belt length for an open (uncrossed) belt.
Formula
n2 = n1 × D1 ÷ D2 i = D2 ÷ D1
v = π × D1 × n1 ÷ 60
L ≈ 2C + π(D1 + D2) ÷ 2 + (D2 − D1)² ÷ 4C
D = pulley diameter, n = speed (rpm), v = belt speed (with D in m, gives m/s), C = centre distance, L = belt length (open belt).
Worked example
A motor at 1440 rpm with a 100 mm pulley drives a 200 mm pulley; centre distance 500 mm.
- Ratio = 200 ÷ 100 = 2 : 1
- Driven speed = 1440 × 100 ÷ 200 = 720 rpm
- Belt speed = π × 0.100 × 1440 ÷ 60 = 7.54 m/s
- Belt length ≈ 2 × 500 + π × 300 ÷ 2 + 100² ÷ 2000 = 1000 + 471.2 + 5 = 1476 mm
Assumptions and limitations
- Belt slip is ignored. Real V-belt and flat-belt drives run slightly slower (commonly around 1–3%).
- The belt length formula is the standard approximation for an open belt. Choose the nearest standard belt size from the manufacturer’s range and allow for tensioning adjustment.
- Power rating, number of belts, wrap angle and belt tension are not checked — use the belt manufacturer’s selection procedure.
References
- Standard belt-drive kinematics and the open-belt length approximation, as given in machine design texts.