Torque Calculator
Turning moment from a force, a lever arm and the angle between them.
What is Torque?
Torque is the turning effect of a force: how hard you can rotate something. What matters is not just the force but how far from the pivot it is applied and at what angle, which is why a long spanner loosens a bolt that a short one cannot.
How it works
τ = rF sin θ, where r is the distance from the pivot to where the force is applied and θ is the angle between the lever arm and the force. A force at 90° to the arm gives the largest torque for that force; a force along the arm gives none at all. The tool also solves for the angle when the other three values are known.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
Why does a longer spanner work better?
Because torque multiplies the force by the lever arm. Doubling the length of the handle doubles the turning effect for the same push, which is exactly what the r term says.
Is torque the same as work?
No, though both can be written in N·m. Torque is force times a perpendicular distance; work is force times a distance moved along the force. The units look identical but the quantities are different, which is why torque is usually written N·m and never joules.
At what angle is torque greatest?
90°. The sine of 90° is 1, so the full force contributes. Pushing along the handle (0° or 180°) produces no turning effect at all.