Solve torque, force, lever arm or angle from τ = F × r × sin θ, with newton-metre, pound-foot and kilogram-force conversions.
Only the component of force perpendicular to the lever arm creates torque — that is why the angle matters. At 90° you get the full F × r; at 0° or 180° (pushing straight along the arm) you get zero.
torque (τ)
How to use this tool
Choose what to solve for: torque, force, lever arm, or angle. The other three fields become your inputs.
Type the known values and pick their units — newtons, pound-force or kilogram-force for force; metres, centimetres, millimetres, inches or feet for length.
Set the angle between the force and the lever arm (90° for a straight perpendicular push, the usual wrench case).
Read the torque in N·m, lb·ft and kgf·m, plus the perpendicular force component and the maximum torque possible at 90°. Use the angle note when two angles give the same torque.
Formula & worked example
Push with 50 N at the end of a 0.4 m wrench, at 90° to the handle: τ = 50 × 0.4 × sin 90° = 20 N·m, which is 14.751 lb·ft. Push at 30° instead and the same force and wrench give only 10 N·m, because only the perpendicular part of the force twists.
Limitations — read this before you rely on it
This calculator treats the lever arm as a rigid, straight arm and the force as a single force at one point — real wrenches flex slightly, and distributed loads (like wind on a door) need integration, not one force value. It assumes static torque; it does not cover rotational dynamics (angular acceleration needs the moment of inertia) or friction in the pivot, which always reduces the torque that actually reaches the bolt. Angle results are for 0°–180° only.
Frequently asked questions
Torque (τ) is the twisting effect of a force applied at a distance from a pivot — what tightens a bolt, opens a door, or turns a wheel. It is force times lever arm times the sine of the angle between them: τ = F × r × sin θ.
Because only the part of the force perpendicular to the lever arm causes rotation. At 90° the full force twists; at 0° or 180° you are pushing straight along the arm, so nothing twists and torque is zero.
The newton-metre (N·m) in metric, and the pound-foot (lb·ft) in imperial. 1 N·m = 0.738 lb·ft, and 1 lb·ft = 1.356 N·m. This calculator converts between them automatically.
Enter the torque you need and switch the solver to “Force”, “Lever arm” or “Angle”: it rearranges τ = F × r × sin θ for the unknown. Note the angle solve has two answers (θ and 180° − θ) because sin θ = sin (180° − θ).
No, not quite. Work is force times distance in the direction of motion (joules), while torque is force times distance from a pivot (newton-metres). The units look alike but the quantities describe different things.