# Newton metre

(Redirected from Newton-meter)

The newton metre (also newton-metre, symbol N m or N·m)[1] is a unit of torque (also called "moment") in the SI system. One newton metre is equal to the torque resulting from a force of one newton applied perpendicularly to a moment arm which is one metre long.

It is also used less commonly as a unit of work, or energy, in which case it is equivalent to the more common and standard SI unit of energy, the joule.[2] In this very different usage the metre term represents the distance travelled or displacement in the direction of the force, and not the perpendicular distance from a fulcrum as it does when used to express torque. This usage is generally discouraged,[3] since it can lead to confusion as to whether a given quantity expressed in newton metres is a torque or a quantity of energy.[4] However, since torque represents energy transferred or expended per angle of revolution, one newton metre of torque is equivalent to one joule per radian.[4]

Newton metres and joules are dimensionally equivalent in the sense that they have the same expression in SI base units:

${\displaystyle 1\,\mathrm {N} \!\cdot \!\mathrm {m} =1{\frac {\mathrm {kg} \,\mathrm {m} ^{2}}{\mathrm {s} ^{2}}}\quad ,\quad 1\,\mathrm {J} =1{\frac {\mathrm {kg} \,\mathrm {m} ^{2}}{\mathrm {s} ^{2}}}}$

Again, N⋅m and J are distinguished in order to avoid misunderstandings where a torque is mistaken for an energy or vice versa. Similar examples of dimensionally equivalent units include Pa versus J/m³, Bq versus Hz, and ohm versus ohm per square.