About this tool
The Torque Calculator is a free, in-browser physics tool that applies τ = r·F·sinθ, the moment of a force about a pivot. Leave one of the four quantities — torque, radius (lever arm), force, or angle — blank and it is solved from the others, so you can find the torque a wrench delivers or the force needed to reach a target torque.
The calculation runs locally in your browser with nothing sent to a server, keeping your inputs private. Torque is reported in newton-metres with a pound-foot equivalent, and results recompute live as you change any field.
Radius is in metres (m), force in newtons (N), and the angle θ in degrees between the lever arm and the line of force, giving torque in newton-metres (N·m). The pound-foot conversion uses 1 lb·ft = 1.3558179483314 N·m. When solving for the angle, the ratio τ/(r·F) must lie between −1 and 1 for a real solution to exist.
Frequently asked questions
What units are used?
Radius in metres (m), force in newtons (N), and angle in degrees give torque in newton-metres (N·m). For example r = 0.5 m, F = 100 N at 90° gives τ = 0.5 × 100 × sin90° = 50 N·m. The result is also shown in lb·ft.
Why does the angle matter?
Only the force component perpendicular to the lever arm produces torque, which the sinθ factor captures. At 90° torque is maximal (sin90° = 1); at 0° or 180° the force is along the arm and torque is zero.
How is torque converted to pound-feet?
The N·m value is divided by 1.3558179483314, the number of newton-metres in one pound-foot, to give the imperial equivalent commonly used for fasteners and engines.
Why can't I always solve for the angle?
Solving for θ inverts sinθ = τ/(r·F). If that ratio is greater than 1 or less than −1 — meaning the requested torque exceeds r·F — no real angle exists and the calculator reports it instead of returning an error value.
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