Newton metre

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 a moment arm which 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 very different 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:

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

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 pound-force = 0.45359237 kilogram-force
• 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

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, p309. "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