MotionLab

Torque Calculator

The rotational equivalent of force — how effectively a push creates a twist.

Force (N)

Lever arm (m)

Angle (°)

Torque (N·m)

τ = F · r · sin(θ)

What you entered

Force (N): 20Lever arm (m): 0.3Angle (°): 90

1
τ = F × r × sin(θ)
20 × 0.3 × sin(90°)= 6 N·m

Result

Torque (N·m): 6

A 20N force at a 0.3m lever arm produces 6 N·m of torque.

Torque from force, radius and angle

Torque is force times radius times the sine of the angle between them. It is maximum at 90 degrees and zero when the force points along the arm.

Force (N)	Radius (m)	Angle (deg)	Torque (N m)
50	0.3	90	15.000
100	0.5	30	25.000
200	0.25	45	35.355
100	0.5	90	50.000
500	0.2	90	100.000

Rows two and four use the same force and radius and differ only in angle, halving the torque at 30 degrees because sin 30 is 0.5 - which is why you pull a spanner perpendicular to its handle rather than at a slant. Doubling the radius doubles the torque for the same force, which is the whole reason long breaker bars exist. Torque shares its units with energy but is not energy: a newton-metre of torque and a joule are dimensionally identical yet physically different, which is why torque is conventionally written N m rather than J.

Why angle matters

A force applied perpendicular to the lever arm (90°) produces maximum torque; a force applied along the lever arm's own direction (0°) produces zero torque, regardless of how strong it is — this is why door handles are placed far from the hinge.

Everyday torque

Wrenches, car engines, and door hinges are all governed by this formula — a longer wrench handle multiplies the torque you can apply with the same hand force, which is why breaker bars are longer than standard wrenches.

Frequently asked questions

I'm using a 0.3 m wrench with 50 N of force at 90°. What torque am I applying?

τ = F × r × sin(θ) = 50 × 0.3 × sin(90°) = 15 N·m. If you pull at 60° instead, τ = 50 × 0.3 × sin(60°) = 13 N·m — about 13% less. Always pull perpendicular for maximum torque.

Why are door handles placed far from the hinge?

Torque = force × distance from pivot. A handle 0.8 m from the hinge needs only 12.5 N to produce 10 N·m of torque. At 0.2 m, you'd need 50 N — four times the force. Placing the handle far from the hinge maximizes your mechanical advantage.

How is torque related to angular acceleration?

Just as F = ma for linear motion, τ = Iα for rotation — torque causes angular acceleration proportional to the moment of inertia. A larger moment of inertia (mass distributed far from the axis) requires more torque for the same spin-up rate. See the angular acceleration calculator.