Definition:Metric System/Mass/Kilogram

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The kilogram is the SI base unit of mass.

It is defined as follows:

$1$ kilogram is the quantity of mass that would make 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 $1 \, \mathrm {kg} \, \mathrm m^2 \, \mathrm s^{−1}$, where the metre and the second are defined in terms of:

the speed of light $c$
the time of transition between the two hyperfine levels of the ground state of the caesium $133$ atom at rest at $0 \, \mathrm K$.

Conversion Factors

\(\ds \) \(\) \(\ds 1\) kilogram
\(\ds \) \(=\) \(\ds 1000\) grams
\(\ds \) \(\approx\) \(\ds 2 \cdotp 20462\) pounds avoirdupois


$\mathrm {kg}$

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

The $\LaTeX$ code for \(\mathrm {kg}\) is \mathrm {kg} .

Also see

Historical Note

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

  • 1799: The actual reference kilogram was manufactured as a prototype.

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

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 was sought, based on a fundamental constant.

  • 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.

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.

Linguistic Note on Kilo

The prefix kilo- derives from the Greek word χίλιοι (khilioi), which means thousand.