Calculators
Torque Calculator
Solve torque, force, or lever arm with τ = rF sin(θ).
Torque Calculator tool
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About This Tool
Torque, also called the moment of a force, describes the turning effect produced when a force acts at a distance from a pivot or axis. Its magnitude depends not only on force and lever-arm distance but also on the angle between them. This calculator uses τ = rF sin(θ) and can rearrange the relationship to solve for torque, force, or lever-arm distance while converting common metric and imperial units locally in your browser.
How To Use It
- Choose whether to solve for torque, force, or lever-arm distance.
- Enter the two known quantities and select their units.
- Enter the angle between the lever-arm direction and the applied force. Use 90° when the force is perpendicular to the lever arm.
- Read the result with its selected unit. When solving by division, the lever arm, force, and perpendicular force component must not create a zero divisor.
Examples
Perpendicular force
A 100 N force applied 0.5 m from a pivot at 90° produces τ = 0.5 × 100 × sin(90°) = 50 N·m.
Angled force
The same 100 N force at 30° produces 25 N·m because only the perpendicular component contributes to torque.
Find force
Producing 50 N·m with a 0.5 m lever arm at 90° requires 100 N of force.
Find lever arm
A 100 N perpendicular force needs a 0.5 m lever arm to produce 50 N·m.
Useful Notes
Torque formula
Torque magnitude is τ = rF sin(θ), where r is the distance from the rotation axis to the point where force is applied, F is force magnitude, and θ is the angle between the lever-arm vector and force.
Why the angle matters
Only the component of force perpendicular to the lever arm creates torque. Torque is maximum at 90°. At 0° or 180°, the force points along the lever arm and the torque magnitude is zero.
Torque units
The SI unit is the newton-meter (N·m). Imperial engineering commonly uses pound-force feet (lbf·ft) or pound-force inches (lbf·in). Although N·m has the same dimensions as a joule, torque and energy describe different physical quantities.
Lever arm and moment arm
This calculator uses r as the distance from the pivot to the force application point plus the explicit angle. An equivalent approach uses the perpendicular moment arm directly, in which case torque is force multiplied by that perpendicular distance.
Limitations
The calculator reports torque magnitude for a single force. It does not determine clockwise/counterclockwise sign, sum multiple torques, model distributed loads, account for three-dimensional vector direction, or replace structural or mechanical safety analysis.
FAQ
What angle should I use for a perpendicular force?
Use 90 degrees. The sine of 90° is 1, so the full force contributes to torque.
Why is torque zero at 0 degrees?
At 0° the force is parallel to the lever arm, so there is no perpendicular force component to create a turning effect about the pivot.
Is N·m the same as a joule?
They share the same base dimensions, but they represent different concepts. A newton-meter used for torque describes rotational effect, while a joule measures energy or work.
What is the difference between lever arm and moment arm?
The lever-arm vector runs from the axis to the force application point. The moment arm is the perpendicular distance from the axis to the force's line of action. The sin(θ) term converts the lever-arm distance into the effective perpendicular distance.