## Derived Units

With the seven fundamental units – mass, length, time, electric current, amount of substance, temperature, luminous intensity – fixed, all other measurements can be expressed in terms of these. For example the fundamental units does not contain a unit for the measurement of speed. Instead the definition of speed can be used to find a derived unit for speed:

To find the units for speed, simply substitute into the above expression the units for distance and time:

Obviously there are many possible derived units, and it is often convenient to refer to a particular derived unit by a label. For example the unit of force, kg m/s^2 , is a derived unit. This particular derived unit is often called the newton.

The system of SI units is consistent. As long as the quantities that are substituted into an equation are expressed in SI units, the answer will be expressed in SI units, but sometime SI units are inconvenient. In astronomy, the distances are so large that expressed in SI units they are always accompanied by many powers of ten. Instead, often astronomical units (1 AU is the distance between the Earth and the Sun), light years (the distance travelled by light in one year) or the parsec are used (1 parsec is the distance to the nearest star such that 1 AU would subtend an angle of 1 arcsecond orof a degree).. Some units – the hour, gram or mile for example – are in common use even though they are not SI units. All of these need to be converted into SI units before they can be used in most equations.

Some derived units are given in the table below.

 SI Derived Unit SI Base Unit Alternative Derived Unit Newton () Pascal () Same Hertz () Joule () Coulomb () Volt () Ohm () Weber () Tesla () Becquerel () Gray () Sievert () Watt ()