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.
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
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).