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Torque is the twisting force that turns things — a wrench on a bolt, a pedal on a crank. It depends not just on how hard you push but on how far from the pivot you push, and at what angle: τ = F × r × sin(θ).
Choose what you're solving for, enter the values, and get the torque in newton-metres.
How is it calculated?
The torque relation
| Solve for | Formula |
|---|---|
| Torque τ (N·m) | force × lever arm × sin(θ) |
| Force F (N) | torque ÷ (lever arm × sin θ) |
| Lever arm r (m) | torque ÷ (force × sin θ) |
θ is the angle between the force and the lever arm. When you push perpendicular to the arm — the most effective way — sin(90°) = 1 and torque is simply force × distance.
Why a longer lever arm helps
Torque grows with the distance from the pivot, which is why a longer wrench loosens a stubborn bolt with less effort: doubling the lever arm doubles the torque for the same push. It's the mechanical advantage behind levers, door handles far from the hinge, and breaker bars.
The angle matters
Only the component of force perpendicular to the lever arm produces torque, and that's what sin(θ) captures. Pushing straight along the arm (0° or 180°) produces no turning at all; pushing at 90° gives the maximum. At 30°, you get only half the torque of a perpendicular push.
Where it helps
Tightening bolts to spec, engineering and statics problems, engine and motor specs, and understanding gears and levers. Note that torque (N·m) and energy (joules) share units dimensionally but are different quantities — torque is a twisting effect, not energy.
Worked example
You push with 20 N on a wrench 0.5 m long, perpendicular to it. The torque is 20 × 0.5 × sin(90°) = 20 × 0.5 × 1 = 10 N·m. Push at 30° instead and only half is useful: 20 × 0.5 × sin(30°) = 20 × 0.5 × 0.5 = 5 N·m — the same effort, half the turning force.
FAQ
How do I calculate torque?+
Multiply the force by the lever-arm length and by the sine of the angle between them: τ = F × r × sin(θ). A 20 N force on a 0.5 m arm, perpendicular, gives 10 N·m.
What are the units of torque?+
The newton-metre (N·m). It shares dimensions with the joule but is a distinct quantity — a twisting effect rather than energy — so torque is never written in joules.
Why does a longer wrench make loosening easier?+
Torque is proportional to the lever-arm length, so a longer wrench produces more torque for the same force. Doubling the length doubles the turning effect on the bolt.
What angle gives the most torque?+
A force applied at 90° to the lever arm, where sin(θ) = 1. Pushing along the arm (0° or 180°) gives zero torque; at 30° you get only half the maximum.
How do I find the force needed for a target torque?+
Divide the torque by the lever arm and the sine of the angle: F = τ ÷ (r × sin θ). To get 10 N·m on a perpendicular 0.5 m arm needs 20 N.