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