Torque Calculator
Calculate torque with τ = r·F·sin θ. Solve for torque, force, radius, or angle, with torque shown in newton-metres (N·m).
Torque (τ = r·F·sin θ)
12 N·m
Torque: τ = r·F·sin θ in newton-metres (N·m). Torque is maximized at θ = 90°.
Frequently Asked Questions
What is the torque formula?
Torque is τ = r × F × sin θ, where r is the distance from the pivot (the lever arm) in metres, F is the applied force in newtons, and θ is the angle between the force and the lever arm. Torque is measured in newton-metres (N·m).
How do I calculate torque?
Multiply the lever-arm length, the force, and the sine of the angle between them. For example, 0.3 m, 40 N, and 90° gives 0.3 × 40 × sin 90° = 12 N·m.
Why does the angle matter?
Only the component of force perpendicular to the lever arm produces rotation. The sin θ factor captures that — torque is greatest at 90° (sin 90° = 1) and zero when the force is along the lever arm (sin 0° = 0).
How do I find the force needed for a given torque?
Rearrange to F = τ / (r × sin θ). Divide the desired torque by the lever arm times the sine of the angle.
What are the units of torque?
Torque uses newton-metres (N·m) in SI. Although dimensionally equivalent to joules, torque is kept in N·m to distinguish it from energy.