 # The SI / metric system

SI (Système International d'Unités) is the modernized version of the metric system. It is used on an international basis and in science and mathematical areas.

There are critics opposing this standard, but it has been widely accepted around the world. I personally have nothing against this system, but I would like to point out that the system itself is basically ok (more or less, I guess), but it seems administration of the system are leaving much for improvement and maybe should be more strict and precise in order to support its scientific and practical value.

## SI base units

 Unit Type Unit Name Symbol Definition Length meter m 1/299,792,458 of the distance travelled by light in a vacuum in one second Unit of mass kilogram kg A kilogram is equal to the mass of the international Platinum-Iridium prototype kept in Paris. Time second s Defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the Caesium-133 atom. Electric Current ampere A The amount of current that if maintained in two parallel rectilinear conductors (of infinite length and negligible circular cross-section) placed 1 metre apart in a vacuum, would produce a force between these conductors equal to 2 * 10-7 newton per metre. Temperature kelvin K The fraction 1/273.16 of the thermodynamic temperature at the triple point of water. Amount of Substance mole mol The amount of substance which contains as many elementary units as there are atoms in 0.012 kg of pure Carbon-12. Luminous Intensity candela cd One 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.

Supplementary units:

 Unit Type Unit Name Symbol Definition plane angle radian rad m*m-1 = 1 solid angle steradian sr m2*m-2 = 1

## Prefixes

All metric units can be used as fractions or multiples by using prefixes. Note the case of the letters, and its significance. M ismega while m is milli, and k is kilo while K is kelvin etc. Here are some examples of the most common prefixes:

 Prefix Name Symbol Factor Prefix Name Symbol Factor yotta Y 1024 deci d 10-1 zetta Z 1021 centi c 10-2 exa E 1018 milli m 10-3 peta P 1015 micro µ 10-6 tera T 1012 nano n 10-9 giga G 109 pico p 10-12 mega M 106 femto f 10-15 kilo k 103 atto a 10-18 hecto h 102 zepto z 10-21 deka da 101 yocto y 10-24

## Some SI Derived Units with special names

 Physical Quantity Name of Unit Symbol Definition frequency hertz Hz 1/s energy joule J kg*m2/s2 force newton N kg*m/s2 pressure pascal Pa kg/m*s2 power watt W kg*m2/s3 electric charge coulomb C A*s electric potential volt V kg*m2/A*s3 electric resistance ohm Ω kg*m2/A2*s3 capacitance farad F A2*s4/kg*m2 inductance henry H kg*m2/A2*s2 magnetic flux weber Wb kg*m2/A*s2 magnetic flux density tesla T kg/A*s2

## Some fundamental physical constants:

 Constant Symbol Value speed of light in a vacuum c 299,792,458 m/s gravitational constant G 6.67*10-11m3/kg*s2 Avogadro constant NA 6.022*1023 mol-1 universal gas constant R 8.31 J/mol * K Boltzmann's constant k 1.38*10-23 J/K elementary charge e 1.60*10-19 C permittivity of free space ε0 8.85*10-12C2/N*m2 permeability of free space μo 4π*10-7 T*m/A electron mass me 9.11*10-31 kg proton mass mp 1.67*10-27 kg neutron mass mn 1.67*10-27 kg Planck's constant 6.63*10-34 J*s electron charge-to-mass ratio -e/me -1.76*1011 C/kg proton-electron mass ratio mp/me 1840 molar volume of ideal gas at STP 22400 cm3/mol Bohr magneton µB 9.27*10-24 J/T magnetic flux quantum Φ0 = h/2e 2.07*10-15 Wb Rydberg constant R∞ 1.10*107 m-1

## Some astronomical constants

 Constant Symbol Value standard gravity at earth's surface g 9.80665 m/s2 equatorial radius of earth Re 6.374*106 m mass of earth Me 5.976*1024 kg mass of moon 7.350*1022 kg = 0.0123 Me mean radius of moon's orbit around earth 3.844*108 m mass of sun 1.989*1030 kg mean radius of earth's orbit around the sun AU 1.496*1011 m period of earth's orbit around sun yr 3.156*107 s diameter of our galaxy 7.5*1020 m mass of our galaxy 2.7*1041 kg = ( 1.4*1011 ) * Mass of sun

## Some conversions of NON-SI Units to SI Units

Energy:

1 electron-volt (eV) = 1.6022 * 10-19 J
1 erg = 10-7 J
1 British thermal unit (BTU) = 1055 J
1 calorie (cal) = 4.186 J
1 kilowatt-hour (kWh) = 3.6 * 106 J

Mass:

1 gram (g) = 10-3 kg
1 atomic mass unit (u) = 931.5 MeV/c2 = 1.661 * 10-27 kg
1 MeV/c2 = 1.783 * 10-30 kg

Force:

1 dyne = 10-5 N
1 pound (lb or #) = 4.448 N

Length:

1 centimeter (cm) = 10-2 m
1 kilometer (km) = 103 m
1 fermi = 10-15 m
1 Angstrom (Å) = 10-10 m
1 inch (in or ") = 0.0254 m
1 foot (ft) = 0.3048 m
1 mile (mi) = 1609.3 m
1 astronomical unit (AU) = 1.496 * 1011 m
1 light-year (ly) = 9.46 * 1015 m
1 parsec (ps) = 3.09 * 1016 m

Angle:

1 degree (°) = 1.745 * 10-2 rad
1 min (') = 2.909 * 10-4 rad
1 second (") = 4.848 * 10-6 rad

Volume:

1 liter (L) = 10-3 m3

Power:

1 kilowatt (kW) = 103 W
1 horsepower (hp) = 745.7 W

Pressure:

1 bar = 105 Pa
1 atmosphere (atm) = 1.013 * 105 Pa
1 pound per square inch (lb/in2) = 6.895 * 103 Pa

Time:

1 year = 3.156 * 107 s
1 day (d) = 8.640 * 104 s
1 hour (h) = 3600 s
1 minute (min) = 60 s

Speed:

1 mile per hour (mi/h) = 0.447 m/s

Magnetic field:

1 gauss = 10-4 T