National Physical Laboratory

How does 'force' fit into the SI system? (FAQ - Force)

The Système International d'unités - the SI system - is the coherent system of units adopted and recommended by the General Conference on Weights and Measures (CGPM). It is based on seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

As discussed in more detail in an earlier FAQ, the SI unit of force is the newton - abbreviation N - and it is defined as the force which would give to a mass of one kilogram an acceleration of one metre per second, per second. Force is not therefore a base quantity but a derived quantity, with dimensions of length (L), mass (M), and time (T). This can be illustrated from the fundamental equation:

force = mass × acceleration

The dimensions of force are the combined dimensions of mass and acceleration (distance per second per second) which is expressed dimensionally as M L T-2. Substituting units for quantities we get kg·m/s2 or kilogram metres per second per second.

Last Updated: 25 Mar 2010
Created: 8 Oct 2007


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