# SI System

## An introduction to the SI metric 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 |

**Metre**- is the length of a path traveled by light in vacuum during a time interval of 1/299792458 of a second**Kilogram**- is equal to the mass of the international prototype of the kilogram**Second**- is the duration of 9192631770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of caesium-133 atom**Ampere**- is the constant current in two parallel conductors of infinite length with negligible circular cross section and placed 1 metre apart in vacuum - that produces a force equal to 2 10^{-7}newton per metre of length between the conductors**Kelvin**- is the 1/273.16 fraction of the thermodynamic temperature of the triple point of water**Mole**- is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12**Candela**- is the luminous intensity in a given direction of a source that emits monochromatic radiations of 540 10^{12}hertz frequency with a radiant intensity of 1/683 watt per steradian in the direction

### 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 | Ω | 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} | |

Temperature relative to 273.15 K | degree Celsius | °C | K | |

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 |

A strength of the SI system is the use of prefixes to indicate multiples or submultiples of units as indicated below.

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}

### Non-Si Units Accepted for Use with the International System

Name | Symbol | Value in SI Units |
---|---|---|

minute | min | 1 min = 60 s |

hour | h | 1 h = 60 min = 3600 s |

day | d | 1 d = 24 h = 86400 s |

degree | ° | 1° = (π/180) rad |

minute | ' | 1' = (1/60)° = (π/10800) rad |

second | '' | 1'' = (1/60)' = (π/648000) rad |

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

metric ton | t | 1 t = 10^{3} kg |

neper | Np | 1 Np = 1 |

bel | B | 1 B = (1/2) ln 10 Np |

nautical mile | 1 nautical mile = 1852 m | |

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

are | a | 1 a = 1 dam^{2 = }10^{2} m^{2} |

hectare | ha | 1 ha = 1 hm^{2} = 10^{4} m^{2} |

bar | bar | 1 bar = 0.1 MPa = 100 kPa = 10^{5} Pa |

ångström | Å | 1 Å = 0.1 nm = 10^{-10} m |

barn | b | 1 b = 100 fm^{2} = 10^{-28} m^{2} |

- neper and bel is used to express values of logarithmic quantities like power level, field level and so on