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Energy, electricity and mechanics

Pulleys and gears

Transmission ratio, output rpm and output torque in a pair of pulleys or gears.

mm
mm
rpm

Revolutions per minute of the driving shaft.

N·m

Optional: torque on the driving shaft, if you know it.

%

Friction losses. Typical: belt 95-98 %, gears 90-98 % depending on type and condition.

Result

Transmission ratio (driven ÷ driving)
—
Output speed
— rpm
Output torque
— N·m
Belt linear speed
— m/s

How it is calculated

Transmission ratio: i = driven ÷ driving (diameters for pulleys, number of teeth for gears). Output speed: rpm_output = rpm_input ÷ i.

Output torque, if the input torque is known: torque_output = torque_input × i × efficiency (power is conserved minus friction losses; as speed drops, torque rises, and vice versa).

Belt linear speed (the same on both pulleys if there is no slip): v = π × driving_diameter × rpm_input ÷ 60, with the diameter in metres.

Keep in mind

  • In a pair of gears in direct contact, the driven gear turns opposite to the driving one; with a belt, in the same direction (unless the belt is crossed).
  • This calculator is for a single stage. For several stages in series, multiply the ratios of each one.
  • Always guard moving pulleys, belts and gears with housings: they are a common entanglement hazard.

See also

More tools in “Energy, electricity and mechanics”