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International System of Units

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The International System of Units is a decimal system of weights and measures which is based on and extends the metric system. It is abbreviated as SI in all languages.

SI includes seven basic units (see table 1). The metre, defined to be 1,650,763.73 wavelengths in vacuum of the red-orange line of the krypton-86 spectrum, is the SI unit for length. The kilogram, which is approximately 2.2 pounds avoirdupois and equals 1,000 grams (as defined by the platinum-iridium prototype kilogram held by the International Bureau of Weights and Measures in Sèvres, France), is the SI unit for mass. It is the sole base unit that remains defined by an artefact. It is also the only SI unit with a prefix as part of its name and symbol. The second, or the duration of 9,192,631,770 cycles of the radiation corresponding to a specified transition of the caesium-133 atom, is the SI unit for time. The ampere is the SI unit for electric current. It is the constant current produced by one volt which, when maintained in two parallel conductors separated by one metre in vacuum, generates an electromagnetic force of 2 x 10-7 N m-1. The kelvin, which is equal to 1/273.16 of the thermodynamic temperature at the triple point of water, is the SI unit for thermodynamic temperature. The kelvin’s magnitude equals that of the degree Celsius; however, a temperature expressed in degrees Celsius is the numerical equivalent of the temperature in kelvins less 273.15. The mole is the SI unit for amount of substance; it contains as many elementary units of substance as there are atoms in 0.012 kg of carbon-12. Elementary units must be specified, as they may be atoms, electrons, ions, molecules, radicals, etc. The candela is the SI unit for luminous intensity. It equals the luminous intensity of the black-body radiation, in the perpendicular direction, from an area of 1/600,000 square metres at platinum’s freezing temperature (2,042 kelvins) under 101,325 pascals of pressure, which approximates the intensity of a single paraffin candle.

Table 1. SI base units

Quantity

SI unit name

Symbol

Length

Metre

m

Mass1

Kilogram

kg

Time

Second

s

Electric current

Ampere

A

Thermodynamic temperature

Kelvin2

K

Amount of substance

Mole

mol

Luminous intensity

Candela

cd

1 "Weight” is often used to mean “mass”.
2 The name “degree kelvin” and the symbol “degK” were declared obsolete
at a 1967 international conference.

SI also includes two supplementary units (see table 2). Radian and steradian are the dimensionless units for the dimensionless quantities plane angle and solid angle, respectively. Units for other quantities are derived from the seven basic and two supplementary units.

Table 2. SI supplementary units

Quantity

SI unit name

Symbol

Expression in terms of SI base units

Plane angle

Radian

rad

m·m 1 =1

Solid angle

Steradian

sr

m2 ·m 2 =1

Table 3 lists selected SI derived units expressed in terms of base units. Derived units with special names and symbols are listed in table 4. These may be used to express other derived units (see table 5). The two supplementary units may also be used to express derived units (see table 6).

The 16 prefixes used to create multiples and submultiples of SI units are listed in table 7. Since multiple prefixes cannot be used, these prefixes are used with gram (g), but not with kilogram (kg).

A number of units that are not part of SI are widely used, especially in the United States. Those which are considered acceptable for use with SI in the US are listed in table 8. A conversion table for SI units is provided in table 9.

Table 3. Selected SI derived units expressed in terms of base units

Quantity

SI unit name

Symbol

Area

Square metre

m2

Volume

Cubic metre

m3

Speed, velocity

Metre per second

m/s

Acceleration

Metre per second squared

m/s2

Wave number

Reciprocal metre

m 1

Density, mass density

Kilogram per cubic metre

kg/m3

Specific volume

Cubic metre per kilogram

m3/kg

Current density

Ampere per square metre

A/m2

Magnetic field strength

Ampere per metre

A/m

Concentration (of amount of substance)

mole per cubic metre

mol/m3

Luminance

Candela per square metre

cd/m2

 

Table 4. SI derived units with special names

Quantity

SI unit name

Symbol

Expression in terms
of other units

Frequency

Hertz

Hz

s 1

Force

Newton

N

m·kg/s2

Pressure, stress

Pascal

Pa

N/m2

Energy, work, quantity of heat

Joule

J

N·m

Power, radiant flux

Watt

W

J/s

Electric charge, quantity of electricity

Coulumb

C

s·A

Electric potential, potential difference, electromotive force

Volt

V

W/A

Capacitance

Farad

F

C/V

Electric resistance

Ohm

Omega

V/A

Electric conductance

Siemens

S

A/V

Magnetic flux

Weber

Wb

V·s

Magnetic flux density

Tesla

T

Wb/m2

Inductance

Henry

H

Wb/A

Celsius temperature1

Degree Celsius

C

K

Luminous flux

Lumen

lm

cd·sr

Activity (of a radionuclide)

Becquerel

Bq

s 1

Absorbed dose, specific energy imparted, kerma, absorbed dose index

Gray

Gy

J/kg

Dose equivalent, dose equivalent index

Sievert

Sv

J/kg

1 In addition to the thermodynamic temperature (T) expressed in kelvins (see table 105.1), Celsius
temperature (t) is also used and is defined by the equation t = T – T0 where T0 = 273.15 K by
definition. The unit “degree Celsius”, which is equal to the unit “kelvin”, is used to express Celsius
temperature.  Here, the term “degree Celsius” is a special name substituted for “kelvin”.
However, a difference or interval of Celsius temperature can be expressed in either kelvins
or degrees Celsius.

Table 5. Examples of SI derived units expressed with special names

Quantity

SI unit name

Symbol

Dynamic viscosity

Pascal second

Pa·s

Moment of force

Newton metre

N·m

Surface tension

Newton per metre

N/m

Heat flux density, irradiance

Watt per square metre

W/m2

Heat capacity, entropy

Joule per kelvin

J/K

Specific heat capacity, specific entropy

Joule per kilogram kelvin

J/(kg·K)

Specific energy

Joule per kilogram

J/kg

Thermal conductivity

Watt per metre kelvin

W/(m·K)

Energy density

Joule per cubic metre

J/m3

Electric field strength

Volt per metre

V/m

Electric charge density

Coulomb per cubic metre

C/m3

Electric flux density

Coulomb per square metre

C/m2

Permittivity

Farad per metre

F/m

Permeability

Henry per metre

H/m

Molar energy

Joule per metre

J/mol

Molar entropy, molar heat capacity

Joule per mole kelvin

J/(mol·K)

Exposure (x and gamma rays)

Coulomb per kilogram

C/kg

Absorbed dose rate

Gray per second

Gy/s

 

Table 6. Examples of SI derived units formed with supplementary units

Quantity

SI unit name

Symbol

Angular velocity

Radian per second

rad/s

Angular acceleration

Radian per second squared

rad/s2

Radiant intensity

Watt per steradian

W/sr

Radiance

Watt per square metre steradian

W/(m2·sr)

 

Table 7. SI prefixes

Factor

Prefix

Symbol

1018

exa

E

1015

peta

P

1012

tera

T

109

giga

G

106

mega

M

103

kilo

k

102

hecto

h

101

deka

da

10- 1

deci

d

10- 2

centi

c

10- 3

milli

m

10- 6

micro

μ

10- 9

nano

n

10- 12

pico

p

10- 15

femto

f

10- 18

atto

a

 

Table 8. Units in use with SI

Name

Symbol

Value in SI unit

Minute (time)

min

1 min = 60 s

Hour

h

1 h = 60 min = 3,600 s

Day

d

1 d = 24 h = 86,400 s

Degree (angle)

1 = (pi/180) rad

Minute (angle)

1  = (1/60) = (pi/10,800) rad

Second (angle)

1  = (1/60) = (pi/648,000) rad

Litre

l1

1 l = 1 dm3 = 10 3 m3

Tonne2

t

1 t = 103 kg

Hectare (land area)

ha

1 ha = 1 hm2 = 104 m2

Electronvolt3

eV

1 eV = 1.602 18 x 10 19 J

Unified atomic mass unit3

u

1 u = 1.660 54 x 10 27 kg

1 Both “l” and “L” are accepted as symbols for litre.
2 In some countries, such as the United States, “metric ton” is used instead of “tonne”.
3 The values of these units in SI units are not known exactly; the values must be obtained
through experiment. The electronvolt is the kinetic energy acquired by an electron passing
through a potential difference of 1 volt in a vacuum.  The unified atomic mass unit equals 1/12 of
the mass of the atom of the nuclide 12C.

 Table 9. Conversion of non-SI units to SI units

From/to

To/from

Multiply by/divide by

Inch (in)

m

2.54 x 10 2

Feet (ft)

m

0.3048

Square inch (in2 )

m2

6.4516 x 10 4

Square foot (ft2 )

m2

9.2903 x 10 2

Cubic inch (in3 )

m3

1.638 71 x 10 5

Cubic foot (ft3 )

m3

2.831 68 x 10 2

Litre (l)

m3

10 3

Gallon (gal)

m3

4.546 09 x 10 3

Mile/hour (mi hr 1 )

m s 1

0.477 04

Kilometre/hour (km hr 1 )

m s 1

0.277 78

Pound (lb)

kg

0.453 592

Gram/cm3 (g cm 3 )

kg m 3

103

Pound/in3

kg m 3

2.767 99 x 104

mmHG

Pa

133.322

Atmosphere (atm)

Pa

1.013 25 x 105

Horsepower (hp)

W

745.7

erg

J

10 7

Electronvolt (eV)

J

1.602 10 x 10 19

Kilowatt-hour (kW hr)

J

3.6 x 106

Calorie (cal)

J

4.1868

Dyne

N

10 5

kgf

N

9.806 65

Poundal

N

0.138 255

lbf

N

4.448 22

 

Acknowledgement: The information in the tables is based primarily on data from the US National Institute of Standards and Technology (NIST).

 

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