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What is the 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. So, 1 N = 1 kg m s-2, or 1 kg m/s2.

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

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.  

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