The SI / metric system
SI base units
Prefixes
Some SI Derived Units with special names
Some fundamental physical constants
Some astronomical constants
Some conversions of NON-SI Units to SI
Units
SI related links
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 10^{12} 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 | m^{2}*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 | 10^{24} | deci | d | 10^{-1} | |
zetta | Z | 10^{21} | centi | c | 10^{-2} | |
exa | E | 10^{18} | milli | m | 10^{-3} | |
peta | P | 10^{15} | micro | µ | 10^{-6} | |
tera | T | 10^{12} | nano | n | 10^{-9} | |
giga | G | 10^{9} | pico | p | 10^{-12} | |
mega | M | 10^{6} | femto | f | 10^{-15} | |
kilo | k | 10^{3} | atto | a | 10^{-18} | |
hecto | h | 10^{2} | zepto | z | 10^{-21} | |
deka | da | 10^{1} | 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*m^{2}/s^{2} |
force | newton | N | kg*m/s^{2} |
pressure | pascal | Pa | kg/m*s^{2} |
power | watt | W | kg*m^{2}/s^{3} |
electric charge | coulomb | C | A*s |
electric potential | volt | V | kg*m^{2}/A*s^{3} |
electric resistance | ohm | Ω | kg*m^{2}/A^{2}*s^{3} |
capacitance | farad | F | A^{2}*s^{4}/kg*m^{2} |
inductance | henry | H | kg*m^{2}/A^{2}*s^{2} |
magnetic flux | weber | Wb | kg*m^{2}/A*s^{2} |
magnetic flux density | tesla | T | kg/A*s^{2} |
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^{-11}m^{3}/kg*s^{2} |
Avogadro constant | N_{A} | 6.022*10^{23} 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 | ε_{0} | 8.85*10^{-12}C^{2}/N*m^{2} |
permeability of free space | μ_{o} | 4π*10^{-7} T*m/A |
electron mass | m_{e} | 9.11*10^{-31} kg |
proton mass | m_{p} | 1.67*10^{-27} kg |
neutron mass | m_{n} | 1.67*10^{-27} kg |
Planck's constant | 6.63*10^{-34} J*s | |
electron charge-to-mass ratio | -e/m_{e} | -1.76*10^{11} C/kg |
proton-electron mass ratio | m_{p}/m_{e} | 1840 |
molar volume of ideal gas at STP | 22400 cm^{3}/mol | |
Bohr magneton | µ_{B} | 9.27*10^{-24} J/T |
magnetic flux quantum | Φ_{0} = h/2e | 2.07*10^{-15} Wb |
Rydberg constant | R_{∞} | 1.10*10^{7} m^{-1} |
Some astronomical constants
Constant | Symbol | Value |
standard gravity at earth's surface | g | 9.80665 m/s^{2} |
equatorial radius of earth | R_{e} | 6.374*10^{6} m |
mass of earth | M_{e} | 5.976*10^{24} kg |
mass of moon | 7.350*10^{22} kg = 0.0123 M_{e} | |
mean radius of moon's orbit around earth | 3.844*10^{8} m | |
mass of sun | 1.989*10^{30} kg | |
mean radius of earth's orbit around the sun | AU | 1.496*10^{11} m |
period of earth's orbit around sun | yr | 3.156*10^{7} s |
diameter of our galaxy | 7.5*10^{20} m | |
mass of our galaxy | 2.7*10^{41} kg = ( 1.4*10^{11} ) * 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 * 10^{6} J
Mass:
1 gram (g) = 10^{-3} kg
1 atomic mass unit (u) = 931.5 MeV/c^{2} = 1.661 *
10^{-27} kg
1 MeV/c^{2} = 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) = 10^{3} 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 * 10^{11} m
1 light-year (ly) = 9.46 * 10^{15} m
1 parsec (ps) = 3.09 * 10^{16} 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} m^{3}
Power:
1 kilowatt (kW) = 10^{3} W
1 horsepower (hp) = 745.7 W
Pressure:
1 bar = 10^{5} Pa
1 atmosphere (atm) = 1.013 * 10^{5} Pa
1 pound per square inch (lb/in^{2}) = 6.895 *
10^{3} Pa
Time:
1 year = 3.156 * 10^{7} s
1 day (d) = 8.640 * 10^{4} 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
SI related links
Bureau International des Poids et Mesures - The SI system
NIST SI related - Current definitions and similar