Torque Calculator
Calculate torque (τ = F × r × sin θ), angular force, and mechanical advantage in rotational systems.
Results
What is it?
Torque (τ) is the rotational equivalent of force — it is the tendency of a force to rotate an object around an axis. Torque = Force × Lever Arm × sin(θ), where θ is the angle between the force vector and the lever arm. The SI unit is Newton-metre (N·m). In the US, torque is often quoted in pound-feet (lb-ft) — 1 lb-ft ≈ 1.356 N·m.
How to use
Enter the applied force, the lever arm length (distance from pivot to point of force application), and the angle between the force and the lever arm. A 90° angle produces maximum torque because sin(90°) = 1.
Example scenario
You tighten a bolt with a 0.5 m wrench, applying 100 N perpendicular to the handle (90°). Torque = 100 × 0.5 × sin(90°) = 50 N·m. If you apply the force at 30° instead, torque = 100 × 0.5 × sin(30°) = 25 N·m — half as effective.
Pro tip
Power in a rotating system equals torque times angular velocity: P = τ × ω (where ω is in rad/s). The right-hand rule determines the direction of the torque vector: curl your fingers in the direction of rotation, and your thumb points in the direction of the torque vector. In engineering, always apply force perpendicular to the lever arm to maximise efficiency.