Physical Quantities

Prefixes  General introduction to systems of units  Introduction to the SI system of units

Table of the SI System of Units

Dimension Unit (abbreviation) Description Derivation from Base Units Clearer Derivation
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 / s2
pressure or stress pascal (Pa) a pressure or stress of 1 newton per square meter m-1 x kg x s-2 N / m2
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 m2 x kg x s-2 m2 x kg / s2
power watt (W) power that produces energy of 1 joule in one second m2 x kg x s-3 J / s
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 m2 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 s4 x A2 C / V
inductance henry (H) inductance of a closed circuit where 1 volt is produced by a current change of 1 ampere per second m2 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 m2 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 s3 x A2 A / V or (Omega)-1
mobility m2 V-1 s-1 mobility of a m-1 x kg-1 x s2 x A m2 V-1 s-1
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 / m2
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 m2 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.


Both the base units and the derived units in SI can have any of a number of prefixes added. These prefixes are used to multiply or divide the size of the base unit to produce another, more convenient unit. The same prefixes are used for all units. These prefixes and their values are:
Prefix (symbol) Multiply by Prefix Multiply by
deka (da) 101 deci (d) 10-1
hecto (h) 102 centi (c) 10-2
kilo (k) 103 milli (m) 10-3
mega (M) 106 micro (u) 10-6
giga (G) 109 nano (n) 10-9
tera (T) 1012 pico (p) 10-12
peta (P) 1015 femto (f) 10-15
exa (E) 1018 atto (a) 10-18
zetta (Z) 1021 zepto (z) 10-21
yotta (Y) 1024 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.

Systems of Units

A system of units is just a set of one or more separate units. Systems of units typically define several units for each dimension. For example, the imperial system of units defines inches, feet, yards, and miles all as units of length. Systems of units also generally cover more than one dimension - the imperial system also includes units for mass, force, temperature, and so on.

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 = Length1 x Mass0 x Time-2 x Temperature0 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.

The SI System of Units

The International System of Units is the modern version of the metric system. This system is also known by the abbreviation SI, a short form of the system?s name in French (Système International d?Unités.) It is a coherent system, and has seven independent base units. SI has base units for: By using defining base units for these seven dimension, SI units can be used easily for not just mechanics and thermodynamics, but also chemistry, electrical calculations, and many other areas. The definitions of the base units are:


The SI unit for length is the meter (m). It?s defined as the length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second. This isn?t a derived unit because its definition includes a specific physical thing (light) as well as another SI unit (the second).


The SI unit for mass is the kilogram (kg), which is equal to the mass of the international prototype kilogram.


The SI unit for time is the second (s). It?s defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. More simply, it?s the time it takes for a certain number of light waves of a certain colour of light to go by.


The kelvin (K) is the SI unit for thermodynamic temperature. It?s 1/273.16 of the thermodynamic temperature of the triple point of water, or in other words, the temperature of the triple point of water is 273.16 kelvin. If you take an enclosed volume and fill it only with water (no air), and then cool it until ice, water, and water vapor are all present and in equilibrium (neither increasing nor decreasing in quantity), then this will always take place at exactly the same temperature. This is much more accurate than just measuring freezing or boiling temperature, which change with air pressure and even the motion of the water.

Electric Current

The SI unit for current is the ampere (A). An ampere as a constant current flowing through parallel conductors 1 meter apart, which would cause a force of 2x10-7 newtons per meter of conductor length.

Light Intensity

The candela (cd) is the SI unit for light intensity. It is defined as a light source that emits monochromatic radiation of frequency 540x1012 hertz and has an intensity of 1/683 watts per steradian. Put more simply, it?s the intensity of a light source of a particular colour that causes 1/683 watts to fall on an area of 1 square meter when it?s one meter from that light source.

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.

Amount of Substance

SI also has a definition for a specific number of elementary entities, which could be atoms, molecules, electrons, or just about anything else. The unit is call the mole (mol), and it?s defined as the number of atoms present in 0.012 kilograms of carbon-12. In other words, 1 mole of carbon-12 has a mass of 12 grams.

Derived SI Units

The following table shows the derived SI units along with the dimension that they represent, and how they are derived from the seven base SI units. The additional unit "steradian" is used for some of the units that deal with light. A radian is an angle defined by the center of a circle and two points on the circle which are the same distance apart as the circle?s radius. In other words if you take a circle with a radius of 1 meter, and measure points 1 meter apart around it, the angle they measure will be 1 radian. A steradian (sr) is just a radian extended in two dimensions, which could be imagined as pyramid shape instead of a wedge. Note that the unit of length does not have to be meters. Radians and steradians don?t change no matter what units are used to explain them.

Copyright © 1996 Toby Hamilton     Corrections © 1999 Karol Kalna