# 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 $0 \ \mathrm K$.

### Symbol

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

## Also see

## 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.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**kilogram** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**kilogram** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**kilogram**