Math
Torque Calculator
Compute torque from force, lever arm, and angle (tau = F * r * sin theta). Solves for any variable, plus mechanical power from torque and RPM.
Torque Calculator
Given force, lever arm, and angle, compute torque. tau = F * r * sin(theta).
Magnitude of the applied force.
Distance from the pivot to where the force is applied.
Angle between force vector and lever arm. Use 90 for perpendicular force.
Torque
5 N·m
Torque (N·m)
5 N·m
Torque (lb·ft)
3.687811 lb·ft
Torque (lb·in)
44.253729 lb·in
Torque (kgf·m)
0.509858 kgf·m
Force (N)
10 N
Lever arm (m)
0.5 m
Angle (deg)
90 deg
Angle (rad)
1.570796 rad
Frequently Asked Questions about the Torque Calculator
How do I calculate torque?
Multiply force by lever arm length by the sine of the angle between them: tau = F x r x sin(theta). For a wrench held perpendicular (90 degrees) to the bolt, sin(theta) equals 1, so torque is simply force times lever arm. If you push 100 N on a 0.3 m wrench at 90 degrees, you generate 30 N m of torque.
What is the difference between N m, lb ft, and lb in?
These are all torque units, just in different systems. 1 N m equals about 0.7376 lb ft or 8.8507 lb in. Mechanics in the US typically use lb ft for engine and chassis torque, while engineers and scientists use N m. The calculator shows all four units (N m, lb ft, lb in, kgf m) for every result.
Why does the angle matter for torque?
Torque depends on the perpendicular component of the force. Only the part of the force at right angles to the lever arm contributes to rotation. At 90 degrees you get maximum torque; at 0 or 180 degrees the force is parallel to the lever arm and produces zero torque, no matter how hard you push.
How do I convert torque to horsepower?
Power equals torque times angular velocity: P = tau x omega. Convert RPM to radians per second with omega = 2 x pi x RPM / 60, then divide watts by 745.7 to get horsepower. For example, 100 N m at 3000 RPM equals about 314.16 rad/s, or 31,416 W, which is about 42.1 hp.
When is solving for the angle impossible?
Torque cannot exceed F x r, because sin(theta) tops out at 1. If you ask the calculator to solve for the angle when the requested torque is larger than F x r, no real angle satisfies the equation and the calculator returns no result. Reduce the target torque, increase the force, or increase the lever arm.