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The SI unit of force is the newton, symbol N. The base units relevant to force are:
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
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.
SI units
Realising the metre
The measurements of life
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