The torque formula
Torque is the turning effect of a force: τ = F·r, where F is the force and r is the perpendicular distance from the pivot (the lever arm). A 50 N force applied 0.3 m from the axis gives 15 N·m (newton-meters). This assumes the force is applied at a right angle to the lever arm.
The distance is measured from the pivot to the line along which the force acts, not to wherever your hand happens to be. Push straight towards the pivot and the lever arm is zero, so no matter how hard you press, nothing turns. Multiply torque by rotational speed and you have power, which is what an engine curve really shows.
How to use this calculator
Enter the force in newtons and the lever arm in meters; the result is torque in newton-meters (N·m). A longer lever arm produces more torque for the same force — which is exactly why a longer wrench loosens a stubborn bolt more easily.
Convert before entering: a mass in kilograms is not a force, so multiply by 9.81 to get newtons, and turn centimetres into metres by dividing by 100. Entering 30 cm as 30 rather than 0.3 inflates the answer a hundredfold, which is the most frequent mistake with this formula.
Torque in machines
Torque is central to engines, wrenches and gear systems. Gearing multiplies torque at the cost of speed, which you can explore with the gear ratio calculator. The force itself can be found from mass and acceleration using the force calculator.
Bolts are tightened to a specified torque because that value corresponds to a known clamping tension in the joint — too little and it works loose, too much and the thread strips.
Frequently asked questions
- How do I calculate torque?
- Multiply force by the lever-arm distance: τ = F·r. 50 N at 0.3 m is 15 N·m.
- What unit is torque measured in?
- Newton-meters (N·m) in SI units; pound-feet (lb·ft) are common in the US.
- Why does a longer wrench help?
- A longer lever arm increases the distance r, producing more torque for the same force.
- Does the angle of force matter?
- Yes. Maximum torque occurs when the force is perpendicular to the lever arm, as assumed here.
- Why is torque measured in newton-metres and not joules?
- Both work out to the same base units, but they describe different things: a joule is energy transferred along a direction of motion, while a newton-metre of torque is a turning effect around an axis. The convention keeps the two ideas from being confused.