National Physical Laboratory

SI Unit of Force

The International System of Units (SI) is widely used for trade, science, and engineering. The SI unit of force is the newton, symbol N. The base units relevant to force are:

  • the metre, unit of length, symbol m,
  • the kilogram, unit of mass, symbol kg,
  • the second, unit of time, symbol s.

Force is defined as the rate of change of momentum. For an unchanging mass, this is equivalent to mass x acceleration. Thus 1 N = 1 kg·m·s-2.

Historically there have been a variety of units of force, and conversion factors to some of these are given in the table below. Exact conversions are shown in bold, others are quoted to seven significant figures.

Some force conversion factors from non-SI units:

Unit Symbol Equivalent SI Value
dyne dyn 10.0 µN
grain-force grf 635.460 2 µN
gram-force gf 9.806 65 mN
poundal pdl 138.255 0 mN
ounce-force (avdp) ozf 278.013 9 mN
pound-force lbf 4.448 222 N
kilogram-force kgf 9.806 65 N
kilopond kp 9.806 65 N
sthène sthène 1.0 kN
kip (= 1 000 lbf) kip 4.448 222 kN
US ton-force (= 2 000 lbf) (short) tonf (US) 8.896 443 kN
tonne-force (= 1 000 kgf) (metric) tf 9.806 65 kN
UK ton-force (= 2 240 lbf) (long) tonf (UK) 9.964 016 kN


The use of abbreviated forms for large and small numbers is encouraged by the SI system. SI prefixes represent multiples of 103 or 10‑3. A list of further SI units and SI prefixes can be found in the SI Units area.

Last Updated: 1 Dec 2010
Created: 1 Dec 2010