View source for Newton-metre

{{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      = 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.
| standard     = [[SI]]
| quantity     = [[torque]]
| symbol       = N&sdot;m
| symbol2      = N&nbsp;m
| units1       = [[Foot–pound–second system|FPS system]]
| inunits1     = 0.73756215 [[pound-foot (torque)|lbf.ft]]
| units2       = inch&sdot;pound-force
| inunits2     = 8.8507 in&nbsp;lbf
| units3       = inch&sdot;[[ounce-force]]
| inunits3     = 141.6 in&nbsp;oz
}}
The '''newton-metre''' or '''newton-meter''' (also non-hyphenated, '''newton metre''' or '''newton meter'''; symbol '''N&sdot;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&nbsp;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 multi-dot or space in such symbol combinations -->}} is the unit of [[torque]] (also called {{em|[[moment (physics)|moment]]}}) in the [[International System of Units]] (SI). One newton-metre is equal to the torque resulting from a [[force]] of one [[newton (unit)|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 (physics)|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 [[Dot product#Physics|in the direction]] of the force, and not the [[Cross product#Mechanics|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>Fundamentals of Physics, 9th edition by Halliday Resnick Walker, p.&nbsp;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. [https://books.google.com/books?id=nQZyAgAAQBAJ&pg=PA309 google books link]</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 [[dimensional analysis|dimensionally]] equivalent in the sense that they have the same expression in [[SI base unit]]s,

::<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 [[Pascal (unit)|Pa]] versus J/m<sup>3</sup>, [[Becquerel|Bq]] versus [[Hertz|Hz]], and [[ohm]] versus [[Sheet resistance#Units|ohm per square]].

{{clear}}

==Conversion factors==
*1 [[kilogram-force]] metre = [[standard gravity|9.80665]] N&sdot;m<ref>[https://books.google.com/books?id=hAFRfIZMzrwC&pg=PA6 ''Mechanical Engineering Formulas Pocket Guide'', p6]</ref><ref>[https://books.google.com/books?id=0g9QjxsbqmUC&pg=PA621 ''Concise encyclopedia of plastics'', by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621]</ref>
<!-- Units of force, not of torque *1 [[pound (force)|pound-force]] = [[pound (mass)|0.45359237]] [[kilogram-force]] -->
*1 newton-metre ≈ 0.73756215 [[pound-foot (torque)|pound-force]]-feet
*1 [[pound-foot (torque)|pound-foot]] ≡ 1 [[Pound (force)|pound-force]]-foot ≈ 1.35581795 N&sdot;m
*1 ounce-inch ≡ 1 [[ounce-force]]-inch ≈ 7.06155181&nbsp;mN&sdot;m (millinewton-metres)
*1 [[dyne]]-centimetre = 10<sup>−7</sup> N&sdot;m

==See also==

*[[Bending moment]]
*[[Spring scale]]
*[[Torque tester]]
*[[Newton-second]], the derived [[SI]] unit of [[impulse (physics)|impulse]]

==Notes==
{{notelist}}

==References==
{{reflist}}

{{SI units}}

[[Category:Units of torque]]
[[Category:SI derived units]]