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,
θ is the angle moved in radians, symbol rad.

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.