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Torque is the rotational equivalent of force — the twisting effect a force has about a pivot. It is τ = F × r × sin(θ), where F is the applied force, r is the lever arm (distance from the pivot) and θ is the angle between the force and the arm. Only the component of force perpendicular to the lever produces rotation, so torque is greatest when the force is applied at a right angle (θ = 90°), reducing to the familiar τ = F × r. The SI unit is the newton-metre (N·m); this calculator also converts to pound-feet (1 N·m ≈ 0.7376 lb·ft).

As a worked example, pushing with 100 N at the end of a 0.5 m wrench, perpendicular to the handle, produces τ = 100 × 0.5 × sin(90°) = 50 N·m. Angle the same push at 30° to the handle and it drops to 100 × 0.5 × 0.5 = 25 N·m, because only half the force now acts crossways. This is why a longer wrench or a straight-on pull loosens a stubborn bolt more easily — you multiply either the lever arm or the effective force.

If you enter a rotational speed, the calculator also returns the mechanical power, P = τ × ω, where the angular speed ω = rpm × 2π / 60 in radians per second. The same torque delivers more power the faster it turns, which is the link between an engine’s torque and its horsepower. Torque calculations are essential for tightening fasteners to spec, sizing motors and gearboxes, designing levers and wrenches, and analysing any rotating machinery.