Per cent mille
# Per cent mille

A per cent mille or pcm is one one-thousandth of a percent. It can be thought of as a "milli-percent". It is commonly used in epidemiology, and in nuclear reactor engineering as a unit of reactivity.

## Epidemiology

Statistics of crime rates, mortality and disease prevalence in a population are often given in "per 100 000".

## Nuclear Reactivity

In nuclear reactor engineering, a per cent mille is equal to one-thousandth of a percent of the reactivity, denoted by Greek lowercase letter rho. Reactivity is a dimensionless unit representing a departure from criticality, calculated by:

    $\rho =(k_{\text{eff}}-1)/k_{\text{eff}}$

where $k_{eff}$ denotes the effective multiplication factor for the reaction. Therefore, one pcm is equal to:

    $1~{\text{pcm}}=\rho \cdot 10^{5}$

This unit is commonly used in the operation of light-water reactor sites because reactivity values tend to be small, so measuring in pcm allows reactivity to be expressed using whole numbers.

## Related units

* Percentage point difference of 1 part in 100
* Percentage (%) 1 part in 100
* Per mille (‰) 1 part in 1,000
* Basis point (bp) difference of 1 part in 10,000
* Permyriad (‱) 1 part in 10,000
* Parts-per notation including parts-per million, parts-per billion etc
