# newton metre

##### SI coherent derived unit whose name and symbol includes an SI coherent derived unit with a special name and symbol
Name Symbol Quantity Expressed in terms of SI base units
newton metre N m torque,
moment of force
kg m2 s−2

### Definition

The newton metre, symbol N m, is the SI derived unit of torque.

One newton metre is equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.

One newton metre of torque is equivalent to one joule per radian.

### Torque

When expressed in terms of SI base units, the newton metre and the joule are dimensionally equivalent.

The dimensional equivalence of these units arises because a torque of 1 N m applied through a full revolution requires an energy of exactly 2π joules.

$E = \tau \ \Theta$

where:

• E is the energy in joules, symbol J,
• τ is the magnitude of the torque in newton metres, symbol N m,

This equation gives rise to the alternate unit name joule per radian, symbol J rad-1:

$\tau \mspace{36mu} = \dfrac{E} {\Theta}\\ \\ \\ 1 \ \text{N m} = 1 \ \dfrac{\text{J}} {\text{rad}}$

Torque, measured in newton metres, is a rotational force, and is a vector quantity. For point particles, it is given by the cross product of the position (distance) vector and the force vector. Whereas, energy, measured in joules, is a scalar quantity.

One joule is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre. For this use, for the avoidance of confusion, the unit joule should be used, and not the newton metre.