The name Système International d'Unités (International System of Units) with the international abbreviation SI is a single international language of science and technology first introduced in 1960.

SI is a coherent system based on the seven independent physical quantities (base units) and derived quantities (derived units). Note that since 1995 supplementary units have been abandoned and moved into the class of derived SI units.Physical quantity | quantity symbol | Basic SI Unit Name | Unit Symbol |
---|---|---|---|

length | l,b,d,h,r,s,etc. | metre | m |

mass | m | kilogram | kg |

time | t | second | s |

electric current | I | ampere | A |

thermodynamic temperature | T | kelvin | K |

amount of substance | n | mole | mol |

luminous intensity | I_{v} | candela | cd |

Other physical quantities are derived from the basic units. The derived SI units are obtained by the multiplication, division, integration and differentiation of the basic units without the introduction of any numerical factors. The system of units so derived is said to be coherent.

Physical Quantity | Quantity symbol | SI Unit Name | Unit Symbol | Expression in SI base units |
---|---|---|---|---|

plane angle | α , β , γ , θ , Φ |
radian | rad | m m^{-1} |

solid angle | ω , Ω | steradian | sr | m^{2} m^{-2} |

The unit kelvin and its symbol K should be used to express both thermodynamic temperature and an interval or a difference of temperature.

In addition to the thermodynamic temperature (symbol *T*) there is also the Celsius (symbol *t*) defined by the equation *t*=*T*-*T*_{0} where *T*_{0}=273.15 K. Celsius temperature is expressed in degree Celsius (symbol °C). The unit 'degree Celsius' is equal to the unit 'kelvin', and a temperature interval or a difference of temperature may also be expressed in degrees Celsius. (The word degree and the sign ^{o} must not be used with kelvin or K).

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 particle.

In this definition, it is understood that the carbon 12 atoms are unbound, at rest and in their ground state.

The radian and steradian were classified as supplementary units.

At the time of the introduction of the International System, the question of the nature of these supplementary units was left open. Considering that plane angle is generally expressed as the ratio between two lengths and solid angle as the ratio between an area and the square or a length, it was specified that in the International System the quantities plane angle and solid angle should be considered as dimensionless derived quantities. Therefore, the supplementary units radian and steradian are to be regarded as dimensionless derived units which may be used or omitted in the expressions for derived units.

Since October , 1995, the class of supplementary units as a separate class in the SI has been removed. Thus the SI now consists of only two classes of units: base units and derived units, with the radian and steradian, which were the two supplementary units, moved into the class of SI derived units.

Physical Quantity | Quantity symbol | SI Unit | Unit Symbol |
Expression in SI base units | Alternative expressions |
---|---|---|---|---|---|

frequency | v, f | hertz | Hz | s^{-1} |
- |

force | F | newton | N | kg m s^{-2} | J m s^{-2} |

pressure | p | pascal | Pa | kg m^{-1} | N m^{-2} |

energy (all forms) | E, U, V, W,etc. | joule | J | kg m^{2} s^{-2} | N m = C V = V A s |

power | P | watt | W | kg m^{2} s^{-3} | J s^{-1 } = VA |

electric charge | Q | coulomb | C | A s | - |

electric potential difference | E, φ, ζ, Φ, η, etc. |
volt | V | kg m^{2} s^{-3} A^{-1} |
J A^{-1} s^{--1} = J C^{-1} |

electrical capacitance | C | farad | F | A^{2}s^{4} kg^{-1} m^{-2} | C V^{-1} |

electrical resistance | R | ohm | Ω | kg m^{2} s^{-3} A^{-2} | V A^{-1} |

electrical conductance | G | siemens | S | A^{2} s^{3} kg^{-1} m^{-2} |
A V^{-1} = Ω^{-1} |

magnetic flux | Φ | weber | Wb | kg m^{2} s^{-2} A^{-1} |
V s = T m^{2} |

magnetic induction | B | tesla | T | kg s^{-2} A^{-1} |
Wb m^{-2} = N A^{-1} m^{-1} |

inductance | L, M | henry | H | kg m^{2} s^{-2} A^{-2} |
V A^{-1} s = Wb A^{-1} |

luminous flux | Φ | lumen | lm | cd sr | - |

illumination | E | lux | lx | cd sr m^{-2} | lm m^{-2} |

activity (of a radionuclide) | A | becquerel | Bq | s^{-1} | - |

absorbed dose | D | gray | Gy | m^{2} s^{-2} | J kg^{-1} |

dose equivalent | H | sievert | Sv | m^{2} s^{-2} | J kg^{-1} |

catalytic activity | z | katal | kat | mol s^{-1} | - |

Celsius temperature | t | degree Celsius | °C | K | - |

plane angle | α , β , γ , θ , Φ |
radian | rad | m m^{-1} | dimensionless |

solid angle | ω , Ω | steradian | sr | m^{2} m^{-2} | dimensionless |

The special names and symbols of the 22 SI derived units with special names and symbols given in table 3 above may themselves be included in the names and symbols of other SI derived units, as shown in table 5.

**Note on degree Celsius.**
The derived unit in Table 3 with the special name degree Celsius and
special symbol °C needs comment. The way temperature
scales used to be defined, it remains common practice to express a thermodynamic
temperature, symbol *T*, in terms of its difference from the reference
temperature *T*_{0 }= 273.15 K. This temperature
difference is called a Celsius temperature, symbol *t*, and is
defined by the quantity equation

The unit of Celsius temperature is the degree Celsius, symbol °C. The
numerical value of a Celsius temperature *t *expressed in degrees
Celsius is given by

It follows from the definition of *t* that the numerical
value of a given temperature difference or temperature interval will be the same for both degree Celsius and the kelvin.

Derived quantity | Quantity symbol | Name | Expression in SI base units |
---|---|---|---|

area | A | square metre | m^{2} |

volume | V | cubic metre | m^{3} |

speed, velocity | u, v, c | metre per second | m s^{-1} |

acceleration | a, g (free fall) | metre per second squared | m s^{-2} |

moment of inertia | I | kilogram square metre | kg m^{2} |

kinematic viscosity | v | square metre per second | m^{2} s^{-1} |

wave number | σ, φ | reciprocal metre | m^{-1} |

mass density | ρ | kilogram per cubic metre | kg m^{-3} |

specific volume | v | cubic metre per kilogram | m^{3} kg^{-1} |

current density | j, i | ampere per square metre | A m^{-2} |

magnetic field strength | H | ampere per metre | A m^{-1} |

concentration of substance B: | c_{B}, [B] | mole per cubic metre | mol/m^{-3} |

molar mass | M | kilogram per mole | kg mol^{-1} |

molar volume | V_{m} | cubic metre per mole | m^{3}mol^{-1} |

luminance | L | candela per square metre | cd m^{-2} |

mass fraction | w | kilogram per kilogram | dimensionless |

The table above shows some examples of derived quantities and units expressed in terms of SI base units.

Some quantities are defined as the ratios of two quantities of the same kind, and thus have a dimension expressed by the number one. Examples of such quantities are refractive index, relative permeability, and mass fraction. Other quantities having the unit 1 include "characteristic numbers" like the quantum number and numbers which represent a count, such as a number of molecules and partition function in statistical thermodynamics. All of these quantities are described as being dimensionless, or of dimension one, and have the coherent SI unit 1. Their values are simply expressed as numbers and, in general, the unit 1 is not shown. In a few cases, a special name is given to this unit, mainly to avoid confusion between some compound derived units. This is the case for the radian, steradian and neper.

Derived quantity | Quantity symbol | Name | Expression in SI base units | Alternative SI expressions |
---|---|---|---|---|

angular velocity | ω | radian per second | s^{-1} |
rad s^{-1} |

angular acceleration | α | radian per second squared | s^{-2} |
rad s^{-2} |

angular momentum | L | joule second | kg m^{2} s^{-1} | J s |

momentum | P | newton second | kg m s^{-1} | N s |

dynamic viscosity | η | pascal second | kg m^{-1}s^{-1} |
Pa s |

surface tension | γ, σ | newton per metre | kg s^{-2} |
N m^{-1} = J m^{-2} |

moment of force | υ | newton meter | kg m^{2} s^{-2} |
N m = J |

heat flux density, irradiance | Q | watt per square meter | kg s^{-3} |
W m^{-2} |

heat capacity, entropy | S | joule per kelvin | kg m^{2} s^{-2} K^{-1} |
J K^{-1} = C V K^{-1} |

specific heat capacity, specific entropy | c | joule per kilogram kelvin | m^{2} s^{-1} K^{-1} | J kg^{-1} K^{-1} |

specific energy | E | joule per kilogram | m^{2} s^{-2} |
J kg^{-1} |

thermal conductivity | λ | watt per meter kelvin | kg m^{2} s^{-3} K^{-1} | W m^{-1} K^{-1} |

electric conductivity | σ, κ | siemens per square metre | A^{2} s^{3} kg^{-1} |
S m^{-2} = A V^{-1} m^{-2} |

energy density | u | joule per cubic meter | kg m^{-1} s^{-2} |
J m^{-3} = N m^{-2} = C V m^{-3} |

electric field strength | E | volt per meter | kg m s^{-3} A^{-1} |
V m^{-1} |

electric charge density | ρ | coulomb per cubic meter | A s m^{-3} |
C m^{-3} |

electric flux density | σ | coulomb per square meter | A s m^{-2} | C m^{-2} |

permittivity | ε | farad per meter | A^{2} s^{4} kg^{-1} m^{-3} | F m^{-1} |

permeability | μ | henry per meter | kg m s^{-2} A^{-2} |
H m^{-1} |

molar energy | U_{m}, H_{m}, etc. | joule per mole | kg m^{2} s^{-2} mol^{-1} | J mol^{-1} |

molar entropy, molar heat capacity | S_{m}, C_{c,m}, C_{p,m} |
joule per mole kelvin | kg m^{2} s^{-2} mol^{-1} K^{-1} |
J mol^{-1} K^{-1} |

exposure (x and γ rays) | - | coulomb per kilogram | A s kg^{-1} |
C kg^{-1} |

absorbed dose rate | - | gray per second | m^{2} s^{-3} |
Gy s^{-1} = J kg^{-1} s^{-1} |

radiant intensity | P' | watt per steradian | kg m^{2} s^{-3} sr^{-1} | W sr^{-1} |

radiance | L | watt per square meter steradian | kg s^{-3} sr^{-1} |
W m^{-2} sr^{-1} |

catalytic (activity) concentration | - | katal per cubic meter | mol m^{-3} s^{-1} | kat m^{-3} |

The above table shows some derived quantities and units expressed in terms of SI units with special names. Some derived quantities like moment of force (newton metre) and thermodynamic energy (joule) are both quantities of energy (kg m^{2} s^{-2}) but are very often expressed differently.

Physical Quantity | Unit Name | Unit Symbol | Expression in SI Units |
---|---|---|---|

time | minute | min | 60 s |

time | hour | h | 60 min = 3600 s |

time | day | d | 24 h = 86 400 s |

angle | degree | ° | (π /180) rad |

angle | minute | ' | (1/60)° = ( π/10 800) rad |

angle | second | " | (1/60)' = (π /648 000) rad |

volume | litre | l, L | 1 dm^{3} = 10^{-3} m^{3} |

mass | tonne | t | 10^{3} kg |

field level, power level, sound pressure level, logarithmic decrement | neper | Np | 1, dimensionless |

field level, power level, sound pressure level, attenuation | bel | B | (1/2) ln 10 (Np), dimensionless |

energy | electronvolt | eV | 1 eV = 1.602 18 x 10^{-19} J, approximately |

mass | unified atomic mass unit | u | 1 u = 1.660 54 x 10^{-27} kg, approximately |

length | astronomical unit | ua | 1 ua = 1.495 98 x 10^{11} m, approximately |

The above table lists non-SI units which are accepted for use with the SI. It includes units which are in common everyday use, in particular the traditional units of time and of angle, together with a few other units which have assumed technical importance. Also included at the bottom of the table are three non-SI units, whose values expressed in SI units must be obtained by experiment and are therefore not known exactly. Their values are given with their combined standard uncertainty, which apply to the last two digits, shown in parentheses. These units are in common use in certain specialised fields.

Physical quantity | Unit name | Unit symbol | Expression in SI units |
---|---|---|---|

length | nautical mile | - | 1852 m |

velocity | knot | - | nautical mile per hour = (1852/3600) m s^{-1} |

area | are | a | da m^{2} = 10^{2} m^{2} |

area | hectare | ha | hm^{2} = 10^{4} m^{2} |

pressure | bar | bar | 0.1 MPa = 100 kPa =
1000 hPa = 10^{5} Pa |

length | ångström | Å | 0.1 nm = 10^{-10} m |

area | barn | b | 100 fm^{2} = 10^{-28} m^{2} |

The above table lists some other non-SI units which are currently accepted for use with the SI to satisfy the needs of commercial, legal and specialised scientific interests. These units should be defined in relation to the SI in every document in which they are used. Their use is not encouraged.

Physical quantity | Unit name | Unit symbol | Expression in SI units |
---|---|---|---|

energy | erg | erg | 10^{-7} J |

force | dyne | dyn | 10^{-5} N |

dynamic viscosity | poise | P | dyn s cm^{-2} = 0.1 Pa s |

kinematic viscosity | stokes | St | cm^{2} s^{-1} = 10^{-4} m^{2} s^{-1} |

magnetic induction | gauss | G | 10^{-4} T |

magnetic field strength | oersted | Oe | (1000/4π) A m^{-1} |

magnetic flux | maxwell | Mx | 10^{-8} Wb |

luminance | stilb | sb | cd cm^{-2} = 10^{4} cd m^{-2} |

illumination | phot | ph | 10^{4} lx |

acceleration (due to gravity) | gal | Gal | 1 cm s^{-2} = 10^{-2} m s^{-2} |

Some non-SI units are still occasionally used. Some are important for the interpretation of older scientific texts, but their use is not encouraged. The above table shows the relationship between CGS units and the SI, and lists those CGS units that were assigned special names. In the field of mechanics, the CGS system of units was built upon three quantities and the corresponding base units: the centimetre, the gram and the second. In the field of electricity and magnetism, units were expressed in terms of these three base units. Because this can be done in different ways, it led to the establishment of several different systems, for example, the CGS Electrostatic System, the CGS Electromagnetic System and the CGS Gaussian System. In these three last-mentioned systems, the system of quantities and the corresponding system of equations differ from those used with SI units.

Physical quantity | Unit name | Unit symbol | Expression in SI units |
---|---|---|---|

activity (of a radionuclide) | curie | Ci | 3.7 x 10^{10} Bq |

exposure (x and γ rays) | röntgen | R | 2.58 x 10^{-4} C kg s^{-1} |

absorbed dose | rad | rad | cGy = 10^{-2} Gy |

dose equivalent | rem | rem | cSv = 10^{-2} Sv |

length (x-ray wavelength) | X unit | - | 1.002 x 10^{-4} nm approximately |

magnetic induction | gamma | γ | nT = 10^{-9} T |

flux, radio astronomy | jansky | Jy | 10^{-26} W m^{-2} Hz^{-1} |

length | fermi | - | fm = 10^{-15} m |

mass | metric carat | - | 200 mg = 2 x 10^{-4} kg |

pressure | torr | Torr | (101 325/760) Pa |

pressure | standard atmosphere | atm | 760 mmHg = 101 325 Pa |

pressure | millimeter of mercury | mmHg | 133.322 39 Pa |

energy | thermochemical calorie | cal_{th} | 4.184 J |

length | micron | µ | 1 µm = 10^{-6} m |

time | year | a | 365.242 199 days = 31 556 925.974 7 s |

force | kilogram-force | kgf | 9.806 65 N |

The table above lists units which are common in older texts and also some are units derived directly from a measurement system like barometric pressure measurement in mmHg. For current texts, it should be noted that if these units are used the advantages of the SI are lost. The relation of these units to the SI should be specified in every document in which they are used.

Prefix-------- | Symbol |
Factor------------------- |
--------------- | ---------- |

yotta | Y |
1 000 000 000 000 000 000 000 000 | = 10 ^{24 } | (e+24) |

zetta |
Z | 1 000 000 000 000 000 000 000 | = 10 ^{21} | (e+21) |

exa | E |
1 000 000 000 000 000 000 | = 10 ^{18} | (e+18) |

peta | P | 1 000 000 000 000 000 | = 10 ^{15} | (e+15) |

tera | T | 1 000 000 000 000 | = 10 ^{12} | (e+12) |

giga | G | 1 000 000 000 | = 10 ^{9} | (e+9) |

mega | M | 1 000 000 | = 10 ^{6} | (e+6) |

kilo | k | 1 000 | = 10 ^{3} | (e+3) |

hecto | h | 100 | = 10 ^{2} | (e+2) |

deca | da | 10 | = 10 ^{1} | (e+1) |

------------------ | ------------ | 1 -------------------------------------------------------------- | --------------- | ---------- |

deci | d | 0.1 | = 10 ^{-1} | (e-1) |

centi | c | 0.01 | = 10 ^{-2} | (e-2) |

milli |
m | 0.001 | = 10 ^{-3} | (e-3) |

micro |
µ | 0.000 001 | = 10 ^{-6} | (e-6) |

nano |
n | 0.000 000 001 | = 10 ^{-9} | (e-9) |

pico | p | 0.000 000 000 001 | = 10 ^{-12} | (e-12) |

femto |
f | 0.000 000 000 000 001 | = 10 ^{-15} | (e-15) |

atto |
a | 0.000 000 000 000 000 001 | = 10 ^{-18} | (e-18) |

zepto |
z | 0.000 000 000 000 000 000 001 | = 10 ^{-21} | (e-21) |

yocto | y |
0.000 000 000 000 000 000 000 001 | = 10 ^{-24} | (e-24) |

Table 11. Prefixes for SI Units and Derived SI Units.

Example: 10

Physical Quantity | Symbol | Value in SI Units |
---|---|---|

speed of light in vacuum | c, c_{o} | 299 792 458 m s^{-1} |

elementary charge | e | 1.602 176 53(14) x 10^{-19} C |

Planck constant | h | 6.626 0693(11) x 10^{-34} J s |

Avogadro constant | L, N_{A} | 6.022 1415(10) x 10^{23} mol^{-1} |

electron mass | m_{e} | 9.109 3826(16) x 10^{-31} kg |

proton mass | m_{p} | 1.672 621 71(29) x 10^{-27} kg |

electronvolt | eV | 1.602 176 53(14) x 10^{-19} J |

Faraday constant | F | 9.648 533 83(83) x 10^{4} C mol^{-1} |

Hartree energy | E_{h} | 4.359 744 17(75) x 10^{-18} J |

Bohr radius | a_{o} | 5.291 772 108(18) x 10^{-11} m |

Bohr magneton | µ_{B} | 9.274 009 49(80) x 10^{-24} J T^{-1} |

nuclear magneton | µ_{N} | 5.050 783 43(43) x 10^{-27} J T^{-1} |

Rydberg constant | R_{¥} | 10 973 731.568 525(73) m^{-1} |

molar gas constant | R | 8.314 472(15) J mol^{-1} K^{-1} |

Boltzmann constant | k, k_{B} | 1.380 650 5(24) x 10^{-23} J K^{-1} |

gravitational constant | G | 6.6742(10) x 10^{-11} m^{3} kg^{-1} s^{-2} |

standard acceleration of gravity | g_{n} | 9.806 65 m s^{-2} |

triple point of water | T_{tp}(H_{2}0) | 273.16 K |

zero of Celsius scale | T(0^{o}C) | 273.15 K |

molar volume of ideal gas (273.15 K, 100 kPa) | V_{m} |
22.710 981(40) x 10^{-3} m^{3} mol^{-1} |

magnetic constant (permeability of vacuum) | µ_{o} |
4p x 10^{-7} =12.566 370 614 x 10 ^{-7} N A^{-2} |

electric constant (permittivity of vacuum) | e_{o} |
8.854 187 817 x 10^{-12} F m^{-1} |