Newton-metre

The newton-metre (also newton metre; symbol N⋅m[1] 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 the end of a moment arm that is one metre long. The nonstandard notation Nm occurs in some fields.

For the instrument that measures forces in newtons, see Spring scale.

Newton-metre
One newton-metre is the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.
General information
Unit system	SI derived unit
Unit of	torque
Symbol	N⋅m or N m
Conversions
1 N⋅m in ...	... is equal to ...
FPS system	0.73756215 lbf ft
inch⋅pound-force	8.8507 in lbf
inch⋅ounce-force	141.6 in oz

The unit 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 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,

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

but are distinguished to avoid misunderstandings when 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.

Conversion factors

• 1 kilogram-force metre = 9.80665 N⋅m[5][6]
• 1 newton-metre ≈ 0.73756215 pound-force-feet
• 1 pound-foot ≡ 1 pound-force-foot ≈ 1.35581795 N⋅m
• 1 ounce-inch ≡ 1 ounce-force-inch ≈ 7.06155181 mN⋅m (millinewton-metres)
• 1 dyne-centimetre = 10⁻⁷ N⋅m

See also

• Bending moment
• Spring scale
• Torque tester
• Newton-second, the derived SI unit of impulse

References

1. BIPM – unit symbols
2. For example: Eshbach's handbook of engineering fundamentals - 10.4 Engineering Thermodynamics and Heat Transfer "In SI units the basic unit of energy is newton-metre".
3. Fundamentals of Physics, 9th edition by Halliday Resnick Ralker, p. 309. "The SI unit of torque is the newton-meter. In our discussion of energy we called this combination the joule. But torque is not work and torque should be expressed in newton-meters, not joules. google books link
4. BIPM - special names
5. Mechanical Engineering Formulas Pocket Guide, p6
6. Concise encyclopedia of plastics, by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621