# Definition:Kilogram

## Definition

The kilogram is the SI base unit of mass.

It is defined as being equal to:

The fixed numerical value of the Planck constant $h$ to be $6 \cdotp 62607015 \times 10^{-34}$ when expressed in the unit Joule seconds.

The Joule second is equal to $\mathrm {kg} \mathrm m^2 \mathrm s^{−1}$, where the metre and the second are defined in terms of the speed of light $c$ and the time of transition between the two hyperfine levels of the ground state of the caesium $133$ atom at rest at $0 \ \mathrm K$.

 $\displaystyle$  $\displaystyle 1$ kilogram $\displaystyle$ $=$ $\displaystyle 1000$ grams

### Symbol

The symbol for the kilogram is $\mathrm {kg}$.

## Historical Note

The kilogram was defined in $1795$ as $1000$ times one gram.

This itself was defined as the mass of one cubic centimetre of water at the melting point of ice.

Subsequently, the actual reference kilogram was manufactured as a prototype in $1799$.

It had a mass equal to the mass of $1 \, \mathrm {dm}^3$ of water at its maximum density, approximately $4^\circ C$.

The International Prototype Kilogram (IPK) was derived from this in $1875$.

This has a mass which is almost exactly equal to the mass of one litre of water.

The weight of the IPK has been known to vary, and so a more stable alternative is being sought, based on a fundamental constant.

In $2011$, a decision was reached in principle that it should be redefined in terms of Planck's constant.

The actual decision was deferred to $2014$, and was once then deferred to the next meeting.

As from $20$ May $2019$, the kilogram is no longer defined by a physical artefact, being the last of the fundamental units of physics which was so defined.

## Linguistic Note

The original British English spelling of kilogram was kilogramme.

However, this is rarely used nowadays, as the American kilogram is now the international standard.