Torque Calculator
Compute rotational torque (the turning effect of a force) from the lever arm, applied force and the angle between them.
m
N
deg
N·m
τ = r · F · sin θ
- 1
sin θ
sin(90°) = 1 - 2
Torque τ = r × F × sin θ
0.5 × 100 × 1 = 50
How does this calculator work?
Torque equals the lever arm times the force times the sine of the angle between them: τ = r·F·sin θ, measured in newton-metres. A force applied perpendicular (90°) gives maximum torque, while a force aligned with the arm gives none. Enter any two of τ, r, and F to solve for the third.
Formula
How this is calculated
Torque (τ) measures how strongly a force tends to rotate an object about a pivot. It is the product of the lever arm r (the distance in metres from the axis of rotation to the point where the force is applied), the force F in newtons, and the sine of the angle θ between the lever arm and the force direction. The result is expressed in newton-metres (N·m).
When the force is applied perpendicular to the lever arm (θ = 90°), sin θ = 1 and torque is maximised at τ = r·F. As the angle approaches 0° or 180°, the force points along the arm, sin θ approaches 0, and the torque vanishes because no rotation is produced. This calculator lets you leave any one of τ, r, or F blank and solves for it: F = τ / (r·sin θ) and r = τ / (F·sin θ).
Assumptions: the force is treated as a single point load and the lever arm is rigid. Division-by-zero cases (for example solving for force when r·sin θ = 0) are guarded and return no result. Angles are entered in degrees and converted internally to radians.
Frequently asked questions
Force is a linear push or pull measured in newtons, while torque is the rotational equivalent measured in newton-metres. Torque depends on both the force and the perpendicular distance from the pivot, so a small force at a long lever arm can produce a large torque.
Only the component of force perpendicular to the lever arm produces rotation. The sin θ term extracts that component, so torque is greatest at 90° and zero when the force is parallel to the arm.
The SI unit is the newton-metre (N·m). It is dimensionally the same as the joule but is kept distinct because torque is a rotational quantity, not an energy.
Also known as
TG we-Calculate Editorial Team. (2026). Torque Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/torque-calculator
TG we-Calculate Editorial Team. "Torque Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/torque-calculator.
TG we-Calculate Editorial Team, "Torque Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/torque-calculator
@misc{wecalculate_torque_calculator, title = {Torque Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/torque-calculator}}, year = {2026}, note = {TG we-Calculate} }
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