What is torque and how is it calculated?

Torque is the turning or twisting effect of a force around a pivot point. It is calculated as tau = F times r times sin(theta), where F is the force in newtons, r is the lever arm length in metres, and theta is the angle between the force vector and the lever arm. At 90 degrees (force perpendicular to arm) torque is maximised; at 0 degrees it is zero.

Why does a longer spanner make it easier to loosen a bolt?

Because torque equals force times lever arm length. A longer spanner (greater r) produces more torque for the same applied force, making it easier to overcome the thread friction. This is why breaker bars, extension tubes, and long-handled wrenches are used for stubborn fasteners.

How do you calculate power from torque?

Power P equals torque tau times angular velocity omega: P = tau x omega. Angular velocity in radians per second from RPM is RPM x 2pi / 60. So a motor producing 50 N·m at 3000 RPM (314.16 rad/s) delivers 50 x 314.16 = 15,708 watts, or about 15.7 kW.

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.

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Force (F)

Lever arm (r)

Angle (θ)

deg

Rotational speed (optional, for power)

RPM

50.00 N·m

torque

In lb-ft36.88 lb-ft

Perp force component100.00 N

Power (at RPM)enter RPM

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.

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