The formula
τ = F · d · sin θ
| Symbol | Quantity | Unit |
|---|---|---|
| T | Torque | N·m |
| F | Force | N |
| d | Distance to the axis | m |
| θ | Angle with the arm | ° |
What it means
Torque measures how effectively a force turns something. Distance from the axis matters as much as the force itself, which is why a longer spanner loosens a tighter bolt with the same effort.
How to work it out by hand
- Take the force in newtons
- Multiply by the distance from the axis in metres
- Multiply by the sine of the angle between them
What is worth knowing
The sine term is why pushing along the arm does nothing: at 0° the sine is zero and so is the torque. At 90° the sine is one and the force is fully effective, which is the intuition behind pushing a door at its edge rather than near the hinge. The units are newton-metres, the same dimensions as the joule, but torque is deliberately never written in joules — it is a rotational quantity rather than an energy, and keeping the names apart keeps the physics straight.