Torque Calculator
Torque is the rotational equivalent of force: it measures the turning or twisting effect of a force acting around a pivot point. Every time you tighten a bolt, push open a door, or turn a steering wheel, you are applying torque. The formula is τ = F r sin(θ), where F is the applied force in newtons, r is the distance from the pivot to where the force is applied (the lever arm) in metres, and θ is the angle between the force vector and the lever arm. The sine term is essential because only the component of the force perpendicular to the lever arm causes rotation. At θ = 90 degrees, sin(θ) = 1 and all of the force contributes to turning. At 0 degrees, the force acts along the arm and produces no torque at all, which is why pushing a door straight toward its hinges does nothing. The default example uses F = 100 N, r = 0.5 m, and θ = 90 degrees, giving τ = 100 times 0.5 times 1 = 50 N m. This calculator also converts the torque to pound-feet (useful for engine and automotive specifications) and shows the perpendicular force component. It includes a power mode: enter the torque and the rotational speed in RPM or rad/s and it calculates the rotational power in watts and kilowatts using P = τ times ω. Results update as you type. Use this tool for physics homework, for tightening fasteners to a specification, for understanding engine ratings, or for any problem involving levers and rotation.
Torque = F x r x sin(theta). Maximum at 90 degrees. Power = torque x angular velocity. Rounded for display.
How it works
Torque: τ = F r sin(θ) in newton metres. Only the component of force perpendicular to the lever arm produces rotation; the sine term extracts it. Converting to pound-feet: multiply N m by 0.7376. Rotational power: P = τω where angular velocity ω = RPM times 2π / 60. So entering RPM converts to rad/s, which is multiplied by the torque to give power in watts.
Worked example
A force of 100 N applied at 90 degrees to a lever arm of 0.5 m. Torque = 100 times 0.5 times sin(90) = 100 times 0.5 times 1 = 50.00 N m. In pound-feet: 50 times 0.7376 = 36.88 lb-ft. The perpendicular force component is 100 times sin(90) = 100 N. These match the default values pre-filled above.
Related calculators
- Angular Velocity Calculator: convert RPM to rad/s.
- Centripetal Force Calculator: inward force for circular motion.
- Work Calculator: work done by a force over a distance.
- Moment of Inertia Calculator: resistance to changes in spin.