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International System of Units

Last updated 2026-04-09 by Dr John Elfick

International System of Units, SI units, (French: Système international d'unités)

6.3.1.0 SI, The 7 base units

1. Length, 2. Mass, 3. Time, 4. Electric current, 5. Temperature, 6. Amount of substance, 7. Luminous intensity

The of measurement that form the basis of any system of measurement are the defined mechanical units of mass, length and time.

Some fundamental systems also include a unit of electricity.

Coordinate systems are used to define the position of a point on a plane using two co-ordinates or in space using three co-ordinates, e.g. Cartesian coordinate system.

Table 6.3.1 The 7 base units

Quantity Dimension Name of SI unit Symbol
1. length
 L metre m
2. mass M kilogram kg
3. time T second s
4. electric current I ampere A
5. thermodynamic temperature
 . kelvin K
6. amount of substance . mole mol
7. luminous intensity J candela cd

6.3.2.0 SI derived units

Acceleration, Angle (plane angle),

Density,

Electric capacitance, Electric charge, Electric potential difference, Electric resistance, Energy (work),

Force, Frequency,

Momentum,

Power, Pressure (stress),

Radioactivity,

Velocity (speed), Viscosity

These units are physical quantities formed from the base units.

Some of these units are as follows:

Table 6.3.2.0 SI derived units

Quantity Dimension Unit name Symbol Equivalent
1. Velocity (speed) L T-1 . v
 m s-1
2. Acceleration L T-2 . a
 m s-2
3. Momentum M L T-1 . Mv
 kg m s-1
4. Force
 M L T-2. newton
 N kg m s-2 = J m-1
5. Pressure (stress) M L-1T-2 pascal Pa N m-2
6. Energy (work) M L2T-2 joule J N m
7. Power M L2 T-3 watt W J s-1
8. Electric charge . coulomb C A s
9. Electric potential difference .
 volt
 V
 W A-1.
10. Electric capacitance . farad F C V-1
11. Electric resistance . ohm ω V A-1
12. Frequency T-1 hertz Hz s-1
13. Radioactivity T-1 becquerel Bq s-1
14. Viscosity
 M L-1T-1
 poise
 P
 1 P = 0.1 NM-2s
15. Density M L-3 . kg m-3 .
16. Plane angle . radian rad = 180o / pi

6.3.3.0 Table 6.3.3.0 Other derived units based on SI

Physical quantity Name of unit Symbol
Surface tension newton per metre N m-1
Electric field strength volt per metre V m-1
Magnetic field strength ampere per metre A m-1
Specific heat capacity joule per kilogram kelvin J kg-1 K-1
Concentration mole per cubic metre mol m-3
Conductivity
 mho or siemans
 mho, -1 (s)

6.3.4.0 Table 6.3.4.0 Units used with SI units (Area, Mass, Pressure, Volume)

Physical quantity Name of unit Symbol Definition of unit
Area hectare ha 104 m2
Mass tonne t 103 kg = Mg
Pressure bar bar 105 N m-2
Volume litre l 10-3 m3 = dm3

6.3.5.0 SI, CGS and FPS conversion, metric conversion

CGS = centimetre-gram-second (system)

FPS = foot-pound-second (system) (British Weights and Measures Act, 1824)

The FPS unit of mass is the slug, i.e. the mass that will accelerate at 1 ft sec-2 when a one pound force acts on it.

MK or MESA = metre, kilogram, second, (ampere)

Table 6.3.6 SI, CGS and FPS conversion, metric conversion

Physical
quantity		 CGS unit
.
 FPS unit
.
Length
(m = metre)		 centimetre, 1 cm
= 10-2 m
 foot, 1 ft
= 0.3048 m
" . inch, 1 in
= 2.54 × 10-2 m
" . mile, 1 mile
= 1.61 km
Mass
(kg = kilogram)		 gram, 1 g
= 10-3 kg
 pound, 1 lb
= 0.4536 kg
" . ounce, 1 oz
= 28.35 g
" . ton, 1 ton
= 1.016 × 103 kg
Volume 1 cm3
= 10-6 m3		 1 ft3
= 2.832 × 10-2 m2
"
"
 1 litre,
L =10-3 m3
 1 in3 = 1.639 × 10-5 m2
1 cubic inch = 16.39 cc
" 1 millilitre,
1 mL = 1 cm3
Density
.
 1 g cm-3
= 10-3 kg m-3		 .
Velocity
or speed		 1 cm s-1
= 10-2 m s-1		 .
" 100 km/hour 62.5 miles/hour
Force
.
 dyne, 1 dyne
= 10-5 N		 .
Pressure,
stress		 1 dyne cm2
= 10-1 Pa		 .
" bar, 1 bar
= 105 Pa		 1 bar
= 750.07 mm Hg
" millibar
= 100 Pa		 .
Energy, work
(J = joule)		 erg, 1 erg
= 10-7 J		 .
Power
(W = watt)		 1 erg S-1
= 10-7 W		 horsepower,
1 hp = 745.7 W
Viscosity
.
 poise, 1 P
= 10-1NM-2s		 .
Thermal
energy		 International calorie
= 4.186 J		 British thermal unit
1 BTU = 1.055 × 103 J

6.3.6.0 SI prefixes, Decimal fractions and multiples

Table 6.3.5 SI prefixes, Decimal fractions and multiples

Symbol
 Prefix
 Decimal
 Short scale
 10n
Y
 yotta
 1 000, 000, 000, 000, 000, 000, 000, 000
 septillion
 1024
Z
 zetta
 1 000, 000, 000, 000, 000, 000, 000
 sextillion
 1021
E
 exa
 1 000, 000, 000, 000, 000, 000
 quintillion
 1018
P
 peta
 1 000, 000, 000, 000, 000
 quadrillion
 1015
T tera
 1 000, 000, 000, 000 trillion
 1012
G giga
 1 000, 000, 000 billion
 109
M mega
 1 000, 000 million
 106
k kilo
 1 000 thousand
 103
h hecto
 100 hundred
 102
da deca
 10 ten
 10
.
1
 one
 100
d deci
 0.1 tenth
 10-1
c centi
 0.01 hundredth
 10-2
m milli
 0.001 thousandth
 10-3
mu, micro
 0.000 001 millionth
 10-6
n nano
 0.000 000 001 billionth
 10-9
p pico
 0.000 000 000 001 trillionth
 10-12
f
 femto
 0.000 000 000 000 001 quadrillionth
 10-15
a
 atto
 0.000 000 000 000 000 001 quintillionth
 10-18
z
 zepto
 0.000 000 000 000 000 000 001 sextillionth
 10-21
y
 yocto
 0.000 000 000 000 000 000 000 001 septillionth
 10-24

Some people also want "hella" for 1027.

Myria (10, 000) is no longer used.

Water is measured in kilolitres, megalitres and gigalitres, e.g. gigalitres per year, GL / Y.

A Short Scale "trillion" = a Long Scale, (now discarded), "billion",

A Short Scale "trillionth" = a Long Scale, (now discarded), "billionth".

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