Torque is the turning effect of a force, and it is what makes levers, cranks, bolts and winches work. This torque calculator takes a force, the distance from the pivot at which it is applied and the angle between them, then reports the torque in newton metres along with the work done over a given rotation.
What Is the Torque Calculator?
Torque measures how strongly a force tries to rotate something. A force applied far from the axis produces more torque than the same force applied close to it, which is the entire principle behind the lever and behind a spanner with a long handle.
This calculator gives you the torque in newton metres, the part of the force that actually does the turning, and the work done over a specified rotation so you can size a motor or check an energy budget.
How the Torque Formula Works
Torque = Force × Lever arm × sin(θ)
The lever arm in this formula is the perpendicular distance from the pivot to the line of action of the force, which is why the angle matters. Pull a spanner at a shallow angle and only part of your force is turning the bolt, with the rest trying to slide your hand sideways.
Work is torque multiplied by the angle of rotation expressed in radians, so a torque of 10 newton metres applied through a full turn does 10 times 2 pi, which is about 62.8 joules of work.
Why the Angle Matters So Much
At 90 degrees, the full force contributes. At 30 degrees only half of it does, because the sine of 30 degrees is 0.5. At 0 degrees the force contributes nothing to the turning moment and only pushes along the arm.
In practice this is why mechanics shift their grip on a spanner as the bolt tightens, and why the correct technique for turning a tight fastener is to pull perpendicular to the handle rather than along it.
Units and Everyday Examples
Torque is measured in newton metres, and because it is force multiplied by distance the units work out as kilogram metres squared per second squared. A car engine producing 200 newton metres at 3,000 revolutions per minute is a very different machine from one producing 200 newton metres at 10,000.
A typical hand tool produces about 10 to 30 newton metres, a torque wrench for a wheel nut is set around 100 to 200, and an engine bolt on a modern car can need 50 to 100 newton metres with a proper wrench rather than a wheel brace.
Frequently Asked Questions
What is the formula for torque?
Torque equals force multiplied by the perpendicular lever arm multiplied by the sine of the angle between them. If you already know the perpendicular distance and the angle is 90 degrees, it simplifies to force multiplied by lever arm.
What are the units of torque?
Newton metres in SI units, written N m. Torque is also often expressed in pound feet in the United States and in kilogram centimetres in older metric engineering practice.
Why does the angle of a spanner handle matter?
Only the component of the force perpendicular to the handle turns the fastener. Pulling straight along the handle produces no torque at all, while pulling at right angles to it uses the whole force, which is why the technique matters so much on a tight bolt.
How do I calculate work done using torque?
Multiply the torque in newton metres by the rotation in radians. The calculator converts the rotation from degrees for you and also shows the energy needed for one complete revolution.
Does a longer lever arm always produce more torque?
Yes, provided the force and angle stay the same, because torque is directly proportional to the lever arm. That is exactly why a long handle gives more leverage, and it is also why the effort falls as the handle gets longer.