Torque measures how effectively a force rotates something around a pivot — think of loosening a bolt, opening a door, or pedaling a bicycle. This calculator computes physics torque using τ = rF sinθ, the formula taught in introductory mechanics, and lets you solve for force or lever-arm length when torque is the known quantity instead.
How the Torque Calculator works
The calculator applies τ = r × F × sin(θ) directly: it multiplies the lever-arm length (r, in meters) by the applied force (F, in newtons) and by the sine of the angle (θ, in degrees) between the force direction and the lever arm. The sine term is what makes angle matter — a force applied straight along the lever arm (θ = 0°) contributes nothing to rotation, while a force applied perpendicular to it (θ = 90°) contributes the full amount.
This is the same formula used across introductory and university-level mechanics courses (see, for example, Serway & Jewett's Physics for Scientists and Engineers). It assumes a rigid lever arm and a single applied force at a fixed distance from the pivot — real-world systems with distributed forces or flexible members need more advanced analysis, but τ = rF sinθ is the correct starting point for the vast majority of everyday torque questions.
Inputs and what they mean
Force (N): the magnitude of the applied force. Typical hand-applied forces range from a few newtons (light finger pressure) to a few hundred newtons (a firm push or pull); a car jack or torque wrench can involve much higher forces.
Lever-arm length (m): the distance from the pivot to where the force is applied. This is the input with the biggest leverage (literally) on the result — doubling the lever arm doubles the torque for the same force, which is why a longer wrench or handle makes a task easier.
Angle (°): the angle between the force direction and the lever arm, from 0° to 180°. Most people intuitively push or pull close to perpendicular (near 90°) without thinking about it, but pushing at a shallow angle can waste a large fraction of the applied force.
Limits and edge cases
When solving for force or lever-arm length on the Solve tab, the calculator cannot return an answer if sin(θ) is at or near zero (θ = 0° or 180°) — physically, no finite force applied exactly along the lever arm can produce a nonzero torque, so the equation has no solution at that angle. Enter an angle away from those extremes to solve for force or lever arm.
This calculator reports torque magnitude only; it does not track rotational direction (clockwise vs. counterclockwise) or handle multiple simultaneous forces and torques acting on the same object, which real mechanical systems (engines, gear trains, multi-force free-body diagrams) often require. For engine output specifically — not a lever-arm force — see the HP to Torque calculator instead, which converts between horsepower, torque, and RPM.