Torque
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Torque is the rotational cousin of force: how hard something is twisted about a pivot. Push a 0.3 m wrench with 100 N perpendicular to the handle and you apply 0.3 × 100 × sin 90° = 30 N·m. Only the force component perpendicular to the lever arm turns the bolt — pushing along the handle (θ = 0°) accomplishes nothing, which is exactly what sin θ encodes. Archimedes understood the leverage half of this over two millennia ago: "give me a place to stand and I will move the Earth".
The practical lesson is in the trade-off — a longer wrench delivers the same torque with less force, which is why breaker bars exist and why door handles sit far from the hinges. When solving for θ, the arcsin returns only the principal branch, angles up to 90°; the supplementary angle 180° − θ produces the identical torque, so check which geometry matches your setup.
- = Torque
- = Lever arm length
- = Applied force
- = Angle between arm and force
- Torque — Torque with a Lever Arm (τ = rF sin θ), Rotational Power (P = τω)
- Lever arm length — Torque with a Lever Arm (τ = rF sin θ), Mechanical Advantage of a Lever
- Applied force — Newton's Second Law, Work (W = Fd cos θ)
- Angle between arm and force — Work (W = Fd cos θ), Torque with a Lever Arm (τ = rF sin θ)