# Per cent mille

A per cent mille or pcm is one one-thousandth of a percent.[1] It can be thought of as a "milli-percent". It is commonly used in epidemiology, and nuclear reactor engineering as a unit of reactivity.

Visualisation of 1%, 1‰, 1‱, 1 pcm and 1 ppm as fractions of the large block (larger version)

## Epidemiology

Statistics of crime rates, mortality and prevalence of disease in a population are often given in "per 100 000".[2][3]

## 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:[4]

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

where keff denotes the effective multiplication factor for the reaction. Therefore, one pcm is equal to:[5]

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

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.[6]