Torque from force and lever arm
Torque is the turning effect of a force. Pushing at right angles to a lever:
torque = force × lever arm
Pushing with 50 N on a wrench 0.3 m long gives 50 × 0.3 = 15 N·m. The same force on a longer wrench gives more torque, which is why a longer handle loosens a stuck bolt.
If the force is not at right angles, only the part across the lever counts: torque = force × lever arm × sin(angle).
Torque from power and speed
For a motor or engine:
torque (N·m) = power (kW) × 9,549 ÷ speed (RPM)
A 1.5 kW motor at 1,450 RPM delivers 1.5 × 9,549 ÷ 1,450 = 9.9 N·m. The same power at a lower speed means more torque.
In imperial units, torque (lbf·ft) = horsepower × 5,252 ÷ RPM.
How gears change torque
A gear train multiplies torque by its ratio and divides speed by the same ratio. A 3:1 reduction turns 9.9 N·m at 1,450 RPM into about 29.7 N·m at 483 RPM, less a few percent lost to friction in each stage.
Units
- 1 N·m = 0.7376 lbf·ft = 8.851 lbf·in
- 1 lbf·ft = 1.3558 N·m
- 1 kgf·m = 9.807 N·m
Tightening torque
Bolt tightening torques come from the maker's specification for the bolt size, grade and whether the threads are oiled. A torque wrench set to that value tightens the bolt correctly; guessing by feel easily over- or under-tightens it.
Calculators
The Torque Calculator works from force and lever arm or from power and speed, and converts the units. The Gear Ratio Calculator and Pulley Calculator show how speed and torque change through a drive.