Newton-metre

newton-metre
A force of one newton applied perpendicularly to the end of a moment arm that is one metre long results in one newton-metre of torque.
General information
Unit system	SI
Unit of	torque
Symbol	N⋅m, 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 newton-metre (also non-hyphenated, newton metre; symbol N⋅m^[1] or N m^[1])^[a] is the unit of torque (also called moment) in the International System of Units (SI). 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 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 (i.e. the lever arm length) 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] "Even though torque has the same dimension as energy (SI unit joule), the joule is never used for expressing torque".^[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 in terms of applicable kind of quantity, 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 SI unit of impulse

Notes

1. The nonstandard notation "Nm" occurs in some fields.

References

1. "BIPM – unit symbols". Archived from the original on 2017-10-01. Retrieved 2016-10-18.
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. Halliday Resnick Walker, Fundamentals of Physics (9th ed.), 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
4. "BIPM – special names". Archived from the original on 2019-03-21. Retrieved 2015-09-27.
5. "Mechanical Engineering Formulas Pocket Guide". p. 6.
6. Donald V. Rosato; Marlene G. Rosato; Dominick V. Rosato. "Concise encyclopedia of plastics". p. 621.