Torque Calculator

Compute τ = r · F · sin θ for any force applied at an angle to a lever arm.

Formula

τ = r · F · sin θ
θ is the angle between the lever arm and the applied force.

Physics behind torque

Torque is what makes things rotate. It's the rotational analogue of force: where F = ma, the rotational version is τ = I·α (moment of inertia times angular acceleration). The magnitude of a torque depends on three things: how hard you push (F), how far from the axis you push (r), and at what angle you push (θ). Push at 90° and you get the most rotation per unit force; push along the lever arm and you get zero torque.

Worked example

F = 20 N, r = 0.5 m, θ = 90°

τ = 0.5 · 20 · sin 90° = 10 N·m

Related tools

Moment of Inertia Centripetal Force Angular Velocity Newton's 2nd Law

FAQs

What is torque?

The rotational equivalent of force.

Why does angle matter?

Only the perpendicular component of force produces torque.

What are the units?

Newton-metres (SI) or foot-pounds (imperial).