🔩 Torque Calculator (τ = rF·sinθ)
Find the turning effect of a force (τ = r·F·sinθ), or solve for the lever arm, force or angle.
Torque τ
20 N·m
Torque τ = r·F·sin θ, where r is the lever arm, F the force and θ the angle between them. θ = 90° gives maximum torque. 🔒 Computed in your browser.
How the torque calculator (τ = rf·sinθ) works
Torque is the rotational analogue of force: τ = r·F·sin θ, where r is the distance from the pivot (lever arm), F the force and θ the angle between them. Enter any three of the four and the tool solves for the last. Torque is greatest when the force is perpendicular (θ = 90°). Force and torque are distinct quantities, force is measured in newtons, torque in newton-metres, and the same force gives more torque the farther from the pivot it acts.
The sin θ factor matters: a force pointing along the lever arm (θ = 0) produces no torque. Units are newton-metres (N·m).
Frequently asked questions
How do I calculate torque?
τ = r·F·sin θ, where r is the lever arm, F the force and θ the angle between them. A 40 N force at 0.5 m applied perpendicularly gives 20 N·m.
Why is torque maximum at 90°?
Because sin 90° = 1. A force perpendicular to the lever arm is fully effective at turning; a force along the arm (sin 0° = 0) produces no torque.
What is the lever arm?
The distance from the pivot (axis of rotation) to where the force is applied. A longer lever arm gives more torque for the same force, the principle of a wrench.
What are the units of torque?
Newton-metres (N·m). Though dimensionally like energy, torque is a distinct rotational quantity, not joules.
How does torque relate to rotation?
Net torque causes angular acceleration (τ = Iα, the rotational form of F = ma), where I is the moment of inertia.
Worked example: tightening a bolt
A 200 N force on the end of a 0.3 m wrench, applied at right angles, produces τ = r·F·sin 90° = 0.3 × 200 × 1 = 60 N·m of torque.
How can I get more torque from the same force?
Use a longer lever arm or apply the force perpendicular to it (θ = 90°, where sin θ = 1). That is why a longer wrench, or a pipe slipped over the handle, loosens a stubborn bolt more easily.
Why is torque in N·m if work is also N·m?
They are dimensionally similar but physically different: torque is a turning effect (force times a perpendicular lever arm) while work is energy (force times distance along the motion). Torque is quoted in newton-metres and work in joules to keep them apart.
How do balanced torques give equilibrium?
An object is in rotational equilibrium when the clockwise and anticlockwise torques about a pivot cancel. A seesaw balances when m₁gd₁ = m₂gd₂, so a lighter person farther out can balance a heavier one sitting closer in.