SI base units

 

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent.

 

Unit of length : meter  The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.         

Unit of mass: kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.         

Unit of time: second The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.         

Unit of electric current: ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length. 

Unit of thermodynamic temperature: kelvin The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. 

Unit of amount of substance: mole

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

 

 Unit of luminous intensity: candela The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

SI base units

 

         SI base unit

 

              Base quantity

 

          Name                   Symbol

length

meter

m

mass

kilogram

kg

time

second

s

electric current

ampere

A

Thermodynamic temperature

kelvin

K

amount of substance

mole

mol

luminous intensity

candela

cd

 

 

 

Examples of SI derived units

 

SI derived unit

Derived quantity

Name

Symbol

area

square meter

 m2

volume

cubic meter

 m3

speed, velocity

meter per second

 ms-1

acceleration

meter per second squared  

 ms-2

wave number

reciprocal meter

 m-1

mass density

kilogram per cubic meter

 kg m-3

specific volume

cubic meter per kilogram

 m3kg-1

current density

ampere per square meter

 A m-2

magnetic field strength  

ampere per meter

 A m-1

amount-of-substance concentration

mole per cubic meter

 mol m-3

luminance

candela per square meter

 cd m-2

mass fraction

kilogram per kilogram, which may be represented by the number 1

kg kg-1 = 1

 

 

SI derived units with special names and symbols

 

SI derived unit

Derived quantity

Name

Symbol

Expression in terms of other SI units

Expression in terms of SI base units

 

plane angle

radian

rad

-

m·m-1 = 1

 

solid angle

steradian

sr

-

m2·m-2 = 1

 

frequency

hertz

Hz

-

s-1

 

force

newton

N

-

m·kg·s-2

 

pressure, stress

pascal

Pa

N/m2

m-1·kg·s-2

 

energy, work, quantity of heat  

joule

J

N·m

m2·kg·s-2

 

power, radiant flux

watt

W

J/s

m2·kg·s-3

 

electric charge, quantity of electricity

coulomb

C

-

s·A

 

electric potential difference,
electromotive force

volt

V

W/A

m2·kg·s-3·A-1

 

capacitance

farad

F

C/V

m-2·kg-1·s4·A2

 

electric resistance

ohm

W

V/A

m2·kg·s-3·A-2

 

electric conductance

siemens

S

A/V

m-2·kg-1·s3·A2

 

magnetic flux

weber

Wb

V·s

m2·kg·s-2·A-1

 

magnetic flux density

tesla

T

Wb/m2

kg·s-2·A-1

 

inductance

henry

H

Wb/A

m2·kg·s-2·A-2

 

Celsius temperature

degree Celsius

°C

-

K

 

luminous flux

lumen

lm

cd·sr (c)

m2·m-2·cd = cd

 

illuminance

lux

lx

lm/m2

m2·m-4·cd =

m-2·cd

 

activity (of a radionuclide)

becquerel

Bq

-

s-1

 

absorbed dose, specific energy (imparted), kerma

gray

Gy

J/kg

m2·s-2

 

 

 

Examples of SI derived units whose names and symbols include SI derived units with special names and symbols

 

SI derived unit

Derived quantity

Name

Symbol

dynamic viscosity

pascal second

Pa·s

moment of force

newton meter

N·m

surface tension

newton per meter

N m-1

angular velocity

radian per second

rad s-1

angular acceleration

radian per second squared

rad s-2

heat flux density, irradiance

watt per square meter

W m-2

heat capacity, entropy

joule per kelvin

J K-1

specific heat capacity, specific entropy

joule per kilogram kelvin

J (kg·K)-1

specific energy

joule per kilogram

J kg-1

thermal conductivity

watt per meter kelvin

W(m·K) -1

energy density

joule per cubic meter

J m-3

electric field strength

volt per meter

V m-1

electric charge density

coulomb per cubic meter

C m-3

electric flux density

coulomb per square meter

C m-2

permittivity

farad per meter

F m-1

permeability

henry per meter

H m-1

molar energy

joule per mole

J mol-1

molar entropy, molar heat capacity

joule per mole kelvin

J (mol·K) -1

exposure (x and g-rays)

coulomb per kilogram

C kg-1

absorbed dose rate

gray per second

Gy s-1

radiant intensity

watt per steradian

W sr-1

radiance

watt per square meter steradian

W (m2·sr) -1

catalytic (activity) concentration

katal per cubic meter

kat m-3

 

 

Decimal multiples and sub-multiples of SI units

 

Factor

Name 

Symbol

 

Factor

Name 

Symbol

 

1024

yotta

Y

10-1

deci

d

 

1021

zetta

Z

10-2

centi

c

 

1018

exa

E

10-3

milli

m

 

1015

peta

P

10-6

micro

µ

 

1012

tera

T

10-9

nano

n

 

109

giga

G

10-12

pico

p

 

106

mega

M

10-15

femto

f

 

103

kilo

k

10-18

atto

a

 

102

hecto

h

10-21

zepto

z

 

101

deca

da

10-24

yocto

y

 

 

 

It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names of Table 5 are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.

 

Example 1: 10-6 kg = 1 mg (one milligram), but not 10-6 kg = 1 µkg (one microkilogram)

 

Example 2: Consider the earlier example of the height of the Washington Monument. We may write hW = 169 000 mm = 16 900 cm = 169 m = 0.169 km using the millimeter (SI prefix milli, symbol m), centimeter (SI prefix centi, symbol c), or kilometer (SI prefix kilo, symbol k).

 

Units outside the SI that are accepted for use with the SI

Name

Symbol

Value in SI units

minute (time)

min

1 min = 60 s

hour

h

1 h = 60 min = 3600 s

day

d

1 d = 24 h = 86 400 s

degree (angle)

°

1° =( p/180) rad

minute (angle)

'

1'= (1/60)° = p/10 800) rad

second (angle)

''

1'' = (1/60)'= p/648 000) rad

liter

L

1 L = 1 dm3 = 10-3 m3

metric ton

t

1 t = 103 kg

electronvolt (d)

eV

1 eV = 1.602 18 x 10-19 J, approximately

unified atomic mass unit (e)

u

1 u = 1.660 54 x 10-27 kg, approximately

astronomical unit (f)

ua

1 ua = 1.495 98 x 1011 m, approximately

 

Other units outside the SI that are currently accepted for use with the SI, subject to further review

 

Name

Symbol   

Value in SI units

nautical mile

 

1 nautical mile = 1852 m

velocity

 knot

1 nautical mile per hour = (1852/3600) m/s

are

a

1 a = 1 dam2 = 102 m2

hectare 

ha

1 ha = 1 hm2 = 104 m2

bar

bar

1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa

ångström

Å

1 Å = 0.1 nm = 10-10 m

barn

b

1 b = 100 fm2 = 10-28 m2

curie

Ci

1 Ci = 3.7 x 1010 Bq

roentgen

R

1 R = 2.58 x 10-4 C/kg

rad

rad

1 rad = 1 cGy = 10-2 Gy

rem

rem

1 rem = 1 cSv = 10-2 Sv

 

 

References:

Siedler, G., 1998: SI units in oceanography, Berichte aus dem IfM, Kiel, No.101, 1-18