Dimension | Unit (abbreviation) | Description | Derivation from Base Units | Clearer Derivation |
---|---|---|---|---|

Mechanics | ||||

force | newton (N) | force that accelerates a mass of 1 kilogram at a rate of 1 meter per second per second | m x kg x s^{-2} |
m x kg / s^{2} |

pressure or stress | pascal (Pa) | a pressure or stress of 1 newton per square meter | m^{-1} x kg x s^{-2} |
N / m^{2} |

General | ||||

frequency | hertz (Hz) | the frequency of any periodic event or cycle which occurs once per second | s^{-1} |
1 / s |

energy | joule (J) | work done by a force of 1 newton moving 1 meter in the direction of the force | m^{2} x kg x s^{-2} |
m^{2} x kg / s^{2} |

power | watt (W) | power that produces energy of 1 joule in one second | m^{2} x kg x s^{-3} |
J / s |

Electrical | ||||

quantity of electricity | coulomb (C) | quantity of electricity carried in one second by a current of 1 ampere | s x A | s x A |

electrical potential | volt (V) | difference of electrical potential between the ends of a conductor where 1 watt is dissipated when the current is 1 ampere | m^{2} x kg x s^{-3} x A^{-1} |
W / A or J / C |

capacitance | farad (F) | capacitance of a capacitor where a potential difference of 1 volt exists after being charged by 1 coulomb of electricity | m^{-2} x kg^{-1} x s^{4} x A^{2} |
C / V |

inductance | henry (H) | inductance of a closed circuit where 1 volt is produced by a current change of 1 ampere per second | m^{2} x kg x s^{-2} x A^{-2} |
Wb / A |

resistance | ohm (Omega) | the resistance of a conductor in which 1 volt produces a current of 1 ampere | m^{2} x kg x s^{-3} x A^{-2} |
V / A |

conductance | siemen (S) | conductance of a conductor where a current of 1 ampere is produced by 1 volt (this is the reciprocal of resistance) | m^{-2} x kg^{-1} x s^{3} x A^{2} |
A / V or (Omega)^{-1} |

mobility | m^{2} V^{-1} s^{-1} |
mobility of a | m^{-1} x kg^{-1} x s^{2} x A |
m^{2} V^{-1} s^{-1} |

Light | ||||

luminous flux | lumen (lm) | luminous flux emitted in a solid angle of 1 steradian by a point source having a uniform intensity of 1 candela - in other words, total light output from a light source in all directions combined | cd x sr | cd x sr |

illuminance | lux (lx) | illuminance produced by a luminous flux of 1 lumen uniformly distributed over an area of 1 square meter - in other words, amount of light falling on a given area | m^{-2} x cd x sr |
lm / m^{2} |

Magnetism | ||||

magnetic flux | weber (Wb) | magnetic flux in a circuit of 1 turn that produces 1 volt if the flux were reduced to zero in a time of 1 second | m^{2} x kg x s^{-2} x A^{-1} |
V x s |

flux density | tesla (T) | magnetic flux density given by a magnetic flux of 1 weber per square meter | kg x s^{-2} x A^{-1} |
Wb / A |

Note also that, when a unit is named after someone, the full unit name is written in all lower case, while the abbreviation has the first letter capitalized.

Prefix (symbol) | Multiply by | Prefix | Multiply by |
---|---|---|---|

deka (da) | 10^{1} |
deci (d) | 10^{-1} |

hecto (h) | 10^{2} |
centi (c) | 10^{-2} |

kilo (k) | 10^{3} |
milli (m) | 10^{-3} |

mega (M) | 10^{6} |
micro (u) | 10^{-6} |

giga (G) | 10^{9} |
nano (n) | 10^{-9} |

tera (T) | 10^{12} |
pico (p) | 10^{-12} |

peta (P) | 10^{15} |
femto (f) | 10^{-15} |

exa (E) | 10^{18} |
atto (a) | 10^{-18} |

zetta (Z) | 10^{21} |
zepto (z) | 10^{-21} |

yotta (Y) | 10^{24} |
yocto (y) | 10^{-24} |

The symbols for these prefixes are added onto the beginning of the symbol for the unit to get the symbol for the new unit. Because of the capitalization, there is no overlap between these prefixes and the symbols for units. An ampere-second could be abbreviated As, while an attosecond would be as.

The only unit which is treated differently is the kilogram. In this case, the prefix kilo is replaced by something else, even though kilogram is the base unit and not gram. There is no such thing as a microkilogram - this is just a milligram.

Another advantage to the SI system is that all of the units for the same dimension are related to each other by powers of ten, which makes it easy to convert. For example, it?s simple to convert from meters to millimeters (just move the decimal three places to the right), but more difficult to convert from miles to inches.

A system of units needs several *base quantities*, which define
the *base units* of the system. These are units that are defined by
real, physical examples of something, such as the kilogram being defined
by the standard reference mass, which is a real object. All other units
in a system are then defined in terms of those base units. These other
units are called *derived units* since they are derived from the base
units.

The number of base units needed depends on the scope of the system of units. The scope is just the set of all the dimensions for which the system has units. To cover all of the dimension needed for mechanics, base units for length, mass, and time are enough, and to cover thermodynamics as well, a base unit for temperature. All other units can be derived from these four.

More specifically, any derived unit can be defined as each of the four base units raised to a certain exponent, multiplied together, and then multiplied by some number. For example, the unit for acceleration can be defined as:

Acceleration = Length^{1} x Mass^{0} x Time^{-2}
x Temperature^{0} x n

Since anything raised to the power of 1 is just itself, and anything raised to the power of 0 is just 1, in this case the definition of acceleration can be simplified to:

Acceleration = Length x Time^{-2} x n

The value of n is the only part of this definition that will change from one system of units to another, and that?s the case not just for acceleration, but for any derived unit. So, the differences between systems of units are really just the values of the base units, and the values of n for all of the derived units.

Remembering that multiplying by Time^{-2} is the same as dividing
by Time2, then the definition of the units for acceleration are identical
to the mechanics formula to calculate acceleration. The only difference
is the multiplication by n.

A system of units where n is always 1 for every unit (called a *coherent*
set of units) has the advantage that the results of any calculation are
already in the correct units. It?s not necessary to remember to multiply
by anything to convert a result into the right units.

- Length
- Mass
- Time
- Temperature
- Electric Current
- Light Intensity
- Amount of Substance

This is not the same as the total output of the light source, nor is it the same as the brightness of the light when it reaches that distance of 1 meter. There are other units for these quantities, and they are derived from the candela.

Copyright © 1996 Toby Hamilton Corrections © 1999 Karol Kalna