{{short description|SI unit of torque}} {{for|the instrument that measures forces in newtons|Spring scale}} {{infobox unit | name = newton-metre | image = Newton-metre.png | caption = 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. | standard = SI | quantity = torque | symbol = N⋅m | symbol2 = N m | units1 = FPS system | inunits1 = 0.73756215 lbf⋅ft | units2 = inch⋅pound-force | inunits2 = 8.8507 in lbf | units3 = inch⋅ounce-force | inunits3 = 141.6 in oz }} The '''newton-metre''' (also non-hyphenated, '''newton metre'''; also known as '''newton-meter'''; symbol '''N⋅m'''<ref name="BIPM-SI-5.1">{{cite web |url=http://www.bipm.org/en/publications/si-brochure/section5-1.html |title=BIPM – unit symbols |access-date=2016-10-18 |archive-date=2017-10-01 |archive-url=https://web.archive.org/web/20171001230808/http://www.bipm.org/en/publications/si-brochure/section5-1.html |url-status=dead }}</ref> or '''N m'''<ref name="BIPM-SI-5.1"/>){{efn|The nonstandard notation "Nm" occurs in some fields.<!-- The medical literature contains a lot of "Nm" with reference to biophysical torque in orthopedic and prosthodontic contexts, but SI requires either a centred dot or space in such symbol combinations -->}} is the unit of torque (also called {{em|moment of force}}) 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.<ref name=Eshbach>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".</ref> 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,<ref>{{citation |title=Fundamentals of Physics |edition=9th |author=Halliday Resnick Walker |page=309 |quote=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 |url=https://books.google.com/books?id=nQZyAgAAQBAJ&pg=PA309 }}</ref> since it can lead to confusion as to whether a given quantity expressed in newton-metres is a torque or a quantity of energy.<ref name=bipm222/> "Even though torque has the same dimension as energy (SI unit joule), the joule is never used for expressing torque".<ref name=bipm222>{{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2-2.html |title=BIPM – special names |access-date=2015-09-27 |archive-date=2019-03-21 |archive-url=https://web.archive.org/web/20190321011225/https://www.bipm.org/en/publications/si-brochure/section2-2-2.html |url-status=dead }}</ref>
Newton-metres and joules are dimensionally equivalent in the sense that they have the same expression in SI base units, : <math>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}</math> 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/m<sup>3</sup>, Bq versus Hz, Watt versus Volt-ampere, and ohm versus ohm per square.
== Conversion factors == * 1 kilogram-force-metre = 9.80665 N⋅m<ref>{{cite web |url=https://books.google.com/books?id=hAFRfIZMzrwC&pg=PA6 |title=Mechanical Engineering Formulas Pocket Guide |page=6 }}</ref><ref>{{cite web |url=https://books.google.com/books?id=0g9QjxsbqmUC&pg=PA621 |title=Concise encyclopedia of plastics |author1=Donald V. Rosato |author2=Marlene G. Rosato |author3=Dominick V. Rosato |page=621 }}</ref> <!-- Units of force, not of torque *1 pound-force = 0.45359237 kilogram-force --> * 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<sup>−7</sup> N⋅m
== See also ==
* Bending moment * Spring scale * Torque tester * Newton-second, the SI unit of impulse
== Notes == {{notelist}}
== References == {{reflist}}
{{SI units}}
Category:Units of torque Category:SI derived units