# SI System

## An introduction to the SI-system

The SI system (*International System of Units*) is the modern metric system of measurement and the dominant system of international commerce and trade. SI units are gradually replacing Imperial and USCS units.

The SI is maintained by the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures) in Paris.

The SI system is founded on the

- SI base units
- SI derived units described in terms of acceptable SI units
- SI derived units with special names and symbols acceptable in SI
- SI Prefixes

### SI Base Units

The core of the SI system is a short list of base units defined in an absolute way without referring to any other units. The base units are consistent with the part of the metric system called the MKS system. The International System of Units (SI) is founded on seven base units.

Quantity | Name of Unit | Symbol |
---|---|---|

Length | metre | m |

Mass | kilogram | kg |

Time | second | s |

Electrical current | ampere | A |

Thermodynamic temperature | kelvin | K |

Luminous intensity | candela | cd |

Amount of substance | mole | mole |

### SI Derived Units with Special Names and Symbols acceptable in SI

Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.

Quantity | Name of Unit | Symbol | Expression in terms of SI base units | Expression in terms of other units |
---|---|---|---|---|

Plane angle | radian | rad | ||

Solid angle | steradian | sr | ||

Adsorbed radiation | gray | Gy | m^{2} s^{-2} | J/kg |

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

Electrical charge | coulomb | C | A s | |

Electrical conductance | siemens | S | m^{-2} kg^{-1}s^{3}A^{2} | A/V |

Electrical inductance | henry | H | m^{2} kg s^{-2} A^{-2} | |

Electrical potential | volt | V | m^{2} kg s^{-3} A^{-1} | W/A |

Electrical resistance | ohm | w | m^{2} kg s^{-3} A^{-2} | V/A |

Force | newton | N | kg ms^{-2} | |

Frequency | hertz | Hz | s^{-1} | |

Illuminance | lux | lx | m^{-2}cd sr | lm/m^{2} |

Luminous flux | lumen | lm | cd sr | |

Magnetic flux | weber | Wb | m^{2} kg s^{-2} A^{-1} | V s |

Magnetic flux density | tesla | T | kg s^{-2} A^{-1} | Wb/m^{2} |

Power or radiant flux | watt | W | kg m^{2} s^{-3} | J/s |

Pressure | pascal | Pa | kg/(m s^{2}) = (N/m^{2}) | |

Radioactivity | becquerel | Bq | s^{-1} | |

Work, energy, heat | joule | J | m^{2} kg s^{-2} | N m |

### SI Derived Units described in Terms of acceptable SI Units

Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.

Quantity | Description | Symbol | Expression in terms of SI base units |
---|---|---|---|

acceleration | meter per second squared | m/s^{2} | m s^{-2} |

area | square meter | m^{2} | m^{2} |

coefficient of heat transfer (often used symbol h or U) | watt per square meter Kelvin | W/(m^{2} K) | kg s^{-3}K^{-1} |

concentration (of amount of substance) | mole per cubic meter | mol/m^{3} | mol m^{-3} |

current density (often used symbol r) | ampere per square meter | A/m^{2} | A m^{-2} |

density (mass density) | kilogram per cubic meter | kg/m^{3} | kg m^{-3} |

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

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

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

energy density | joule per cubic meter | J/m^{3} | m^{-1} kg s^{-2} |

force | Newton | N or J/M | m kg s^{-2} |

heat capacity | joule per Kelvin | J/K | m^{2} kg s^{-2} K^{-1} |

heat flow rate (often used symbol Q or q) | watt | W or J/s | m^{2} kg s^{-3} |

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

luminance | candela per square meter | cd/m^{2} | cd m^{-2} |

magnetic field strength | ampere per meter | A/m | A m^{-1} |

modulus of elasticity (or Young's modulus) | giga Pascal | GPa | 10^{-9} m^{-1} kg s^{-2} |

molar energy | joule per mole | J/mole | m^{-2} kg s^{-2} mol^{-1} |

molar entropy (or molar heat capacity) | joule per mole Kelvin | J/(mole K) | m^{-2} kg s^{-2} K^{-1} mol^{-1} |

moment of force (or torque) | Newton meter | N m | m^{2} kg s^{-2} |

moment of inertia | kilogram meter squared | kg m^{2} | kg m^{2} |

momentum | kilogram meter per second | kg m/s | kg m s^{-1} |

permeability | Henry per meter | H/m | m kg s^{-2} A^{-2} |

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

power | kilowatt | kW | 10^{-3} m^{2} kg s^{-3} |

pressure (often used symbol P or p) | kilo Pascal | kPa | 10^{-3} m^{-1} kg s^{-2} |

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

specific heat capacity (or specific entropy, often used symbol c,_{,p}c or _{v}s) | joule per kilogram Kelvin | J/(kg K) | m^{2} s^{-2} K^{-1} |

specific volume | cubic meter per kilogram | m^{3}/kg | m^{3} kg^{-1} |

stress | mega Pascal | MPa | 10^{-6} m^{-1} kg s^{-2} |

surface tension | Newton per meter | N/m | kg s^{-2} |

thermal conductivity (often used symbol k) | watt per meter Kelvin | W/(m K) | m kg s^{-3} K^{-1} |

torque | Newton meter | N m | m^{2} kg s^{-2} |

velocity (or speed) | meters per second | m/s | m s^{-1} |

viscosity, absolute or dynamic (often used symbol m) | Pascal second | Pa s | m^{-1} kg s^{-1} |

viscosity, kinematic (often used symbol n) | square meter per second | m^{2}/s | m^{2} s^{-1} |

volume | cubic meter | m^{3} | m^{3} |

wave number | 1 per meter | 1/m | m^{-1} |

work (or energy heat, often used symbol W) | joule | J or N m | m^{2} kg s^{-2} |

### SI Prefixes

Number | Greek | Latin |

½ | hemi | semi |

1 | mono | uni |

1½ | sesqui | |

2 | di | bi |

3 | tri | ter |

4 | tetra | quandri |

5 | penta | quinque |

6 | hexa | sexi |

7 | hepta | septi |

8 | octa | octo |

9 | ennea | nona |

10 | deca | deci |

11 | hendeca | undec |

12 | dodeca | duodec |

13 | trideca | tridec |

14 | tetradeca | quatuordec |

15 | pentadeca | quindec |

16 | hexadeca | sedec |

17 | heptadeca | septendec |

20 | eicosane | vige, vice |

30 | triaconta | trige, trice |

40 | tetraconta | quadrage |

50 | pentaconta | quincuage |

60 | hexaconta | sexage |

70 | heptaconta | septuage |

80 | octaconta | octage |

90 | enneaconta | nonage |

100 | hecto | cente |

many | poly | multi |

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

10^{24} | yotta | Y |

10^{21} | zetta | Z |

10^{18} | exa | E |

10^{15} | peta | P |

10^{12} | tera | T |

10^{9} | giga | G |

10^{6} | mega | M |

10^{3} | kilo | k |

10^{2} | hecto | h |

10^{1} | deca | 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 |

10^{-21} | zepto | z |

10^{-24} | yocto | y |

The prefixes provide an order of magnitude: Ex.

*16600 m = 16.6 10*^{3}m = 16.6 km*1 centimeter = 10*^{-2}m*1 millimeter = 10*^{-3}m*1 micrometer = 10*^{-6}m*1 nanometer = 10*^{-9}m*1 mm*^{3}= (10^{-3}m)^{3}= 10^{-9}m^{3}

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