Torque Calculator
Torque (τ) is the measure of a force's tendency to produce rotation about an axis. The formula τ = r × F × sin(θ) shows that torque depends on three things: the distance from the pivot (lever arm r), the applied force (F), and the angle between the force vector and the lever arm. Maximum torque occurs when force is applied at 90 degrees to the lever arm. This principle underlies the design of wrenches, gears, door hinges, and mechanical engines. Enter the lever arm length in meters, the force in Newtons, and the angle in degrees to calculate the resulting torque.
Torque formula
τ = r × F × sin(θ)
Where r is the lever arm length (m), F is the applied force (N), and θ is the angle between the force vector and the lever arm (degrees). At θ = 90°, sin(θ) = 1 and torque is maximized at τ = r × F.
Understanding torque
- Torque is a vector quantity: its direction is perpendicular to both the lever arm and the force, determined by the right-hand rule.
- A longer lever arm reduces the force needed to produce a given torque, which is why torque wrenches have long handles.
- In rotational equilibrium the sum of all torques about any pivot is zero.
- Engine torque in vehicles (lb ft or N m) describes the engine's twisting force at the crankshaft.
- Torque multiplied by angular velocity gives rotational power: P = τ × ω.
Torque: frequently asked questions
What is torque?
Torque is the rotational equivalent of force. It measures how effectively a force causes an object to rotate about a pivot. Torque (tau) = r x F x sin(theta), where r is the distance from the pivot to the point of force application, F is the force magnitude, and theta is the angle between the force and the lever arm.
What is the unit of torque?
The SI unit of torque is the newton-meter (N m). In US engineering contexts foot-pounds (ft lb) are also used. One foot-pound equals approximately 1.356 N m.
When is torque at its maximum?
Torque is maximized when the force is applied perpendicular to the lever arm (theta = 90 degrees), because sin(90°) = 1. Pushing at any other angle reduces the effective torque. This is why door handles are placed at the edge farthest from the hinge.
What is the difference between torque and moment?
In physics and engineering the terms torque and moment are often used interchangeably. Torque usually refers to twisting or spinning effects on a shaft, while moment is used in structural analysis. Both are calculated as force times perpendicular distance.
How does lever arm length affect torque?
Torque is directly proportional to lever arm length r. Doubling the lever arm doubles the torque for the same force. This is the principle behind wrenches: a longer handle requires less force to produce the same torque on a bolt.
Official sources
- NIST Reference on Constants, Units, and Uncertainty: NIST Physics.
- OpenStax University Physics Volume 1: Torque.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.