Newton metre

For the instrument that measures forces in newtons, see Force meter.

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 ft lbf
inch⋅pound-force	8.8507 in lbf
inch⋅ounce-force	141.6 in oz

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 the end of a moment arm that 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 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:

1N⋅m=1kg⋅m2s2,1J=1kg⋅m2s2{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}}}}

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.

Conversion factors

• 1 kilogram-force metre = 9.80665 N⋅m^[5][6]
  


• 1 newton metre ≈ 0.73756215 pound-force-feet (often "foot-pounds")


• 1 pound-foot (often "foot-pound") ≡ 1 pound-force-foot ≈ 1.35581795 N⋅m


• 1 ounce-inch (often "inch-ounce") ≡ 1 ounce-force-inch ≈ 7.06155181 mN⋅m(milliNewtons-metre)


• 1 dyne-centimetre = 10⁻⁷ N⋅m


• 1 joule = 1 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. 
   ^ ^ab 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
   

v t e SI units
Base units	ampere candela kelvin kilogram metre mole second
Derived units with special names	becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber
Other accepted units	astronomical unit bar dalton day decibel degree of arc electronvolt hectare hour litre minute minute and second of arc neper tonne atomic units natural units
See also	Conversion of units Metric prefixes 2019 redefinition Systems of measurement
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