Torque formula
Torque is the twisting effort produced by a force acting at a distance from an axis. It is what turns shafts, tightens bolts, and drives wheels, and it equals the force times the radius at which it acts.
Variables
| T | Torque | N·m or lb·ft |
| F | Applied force | N or lb |
| r | Radius (lever arm) | m or ft |
Rearranged
r = T / F
Worked example
A force of 150 N is applied at the end of a wrench 0.3 m long.
Multiply force by radius: 150 × 0.3 = 45.
Torque shares its formula with moment, force times distance, but describes twisting about an axis rather than bending about a point. A longer lever arm multiplies the torque from the same force, which is why a breaker bar loosens a stubborn bolt that a short wrench cannot.
Tightening fasteners or sizing power?
See the Bolt Torque Chart and the Horsepower Formula.
Torque in shafts and fasteners
On a rotating shaft, torque is what transmits power from a motor to a load, and it sets the shear stress the shaft must survive. On a fastener, the applied torque stretches the bolt to create clamping force, which is why tightening specs are given in torque. Both rely on the same force-times-radius relationship.
Torque and power
Torque and power are linked by rotational speed: power equals torque times angular velocity. A given torque delivers more power as the shaft spins faster, which is why engines are rated by both torque, the twisting force, and horsepower, the rate of doing work. One does not replace the other.
FAQ
What is the formula for torque?
Torque equals force times the radius at which it acts, T = F times r, in newton-metres or pound-feet.
What is the difference between torque and moment?
They are the same product of force and distance. Torque describes twisting about an axis; moment usually describes bending about a point.
How does a longer wrench help?
It increases the radius, so the same hand force produces more torque, making a tight bolt easier to turn.