Newton metre

Newton metre is a unit of torque (also called "moment") in the SI system.^[1] Less commonly, it is used as a unit of energy, in which case it is synonymous with the more common and standard SI unit of energy, the joule.^[2] The symbolic form is N m or N·m,^[3] and sometimes hyphenated newton-metre. 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.

A newton metre is dimensionally equal to a joule, the SI unit of energy and work. However, it is not appropriate to express a torque in joules — the units are helpful to distinguish a torque quantity from an energy quantity.^[4] The two quantities, torque and energy, are physically quite different despite being dimensionally equivalent. For example, energy is a scalar while torque is a vector (in fact, a pseudovector). Also, a given force applied to an object can contribute torque but not work, or work but not torque, or both, or neither.

Conversely, Newton metre is sometimes used as a unit of energy, instead of joule.^[2] As above, this practice is discouraged by the SI authority, since it can lead to confusion as to whether a given quantity expressed in newton metres is a torque or an energy.^[5]

On the other hand, there are relations between torque and energy that shed light on their dimensional relationship. In particular, a torque can contribute to rotational energy; the work done in this process (measured in J) is equal to the torque (measured in N m) times the angle through which the body rotates in the direction of the torque.^[6] This accounts for the use of an alternative unit for torque, Joule per radian (J/rad)

Conversion factors

• 1 joule = 1 N·m
• 1 newton metre = 0.7375621 foot-pound force (often "foot-pound")
• 1 metre kilogram-force = 9.80665 N·m
• 1 centimetre kilogram-force = 98.0665 mN·m
• 1 foot-pound force (often "foot-pounds") = 1 pound-force foot (often "pound-feet") ≈ 1.3558 N·m
• 1 inch ounce-force = 7.0615518 mN·m
• 1 dyne centimetre = 10⁻⁷ N·m

See also

• Foot-pound force
• Spring scale
• Torque
• Torque tester

References