Torque
Compute moment, rotational force, and torque vectors. Free online calculator with formulas and step-by-step solutions.
Key formula
tau = rFsin(theta)
How do you calculate torque?
Torque is τ = r F sinθ. Multiply force by the perpendicular lever arm: r⊥ = r sinθ. When force is perpendicular to the radius (θ = 90°), sinθ = 1 and τ = rF. Rearrange to F = τ/(r sinθ) or r = τ/(F sinθ).
About this tool
Torque is the turning effect of a force about a pivot. This page keeps τ = rF sinθ visible so you can solve for torque, force, or lever arm without forgetting the angle factor.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: perpendicular force
r = 0.50 m, F = 40 N, θ = 90°. τ = (0.50)(40)(1) = 20 N·m.
Example 2: force at 30°
r = 0.80 m, F = 25 N, θ = 30°. τ = (0.80)(25) sin30° = 20 × 0.5 = 10 N·m.
Example 3: find force
τ = 12 N·m, r = 0.40 m, θ = 90°. F = τ/r = 12/0.40 = 30 N perpendicular to the arm.
Frequently asked questions
What is the torque formula?
τ = r F sinθ, where r is the distance from the pivot, F is force, and θ is the angle between the position vector and the force. Units are N·m.
What is a lever arm?
The perpendicular distance from the pivot to the line of action of the force. Using r⊥ = r sinθ lets you write τ = F r⊥.
When is torque maximum?
For fixed r and F, torque is maximum at θ = 90° when sinθ = 1. Pushing perpendicular to the wrench handle is most effective.
Is N·m the same as a joule?
They have the same base units, but torque is a rotational effect, not energy. Keep torque in N·m and energy/work in joules as separate concepts.
How does torque relate to force?
Force causes linear acceleration (F = ma). Torque causes angular acceleration about a pivot. Use the force calculator for F = ma and this tool for turning problems.