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 in 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 disease prevalence in a population are often given in "per 100 000".^[2][3]

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:^[4]

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

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

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

See also

• InHour (another unit of reactivity)
• Dollar (reactivity)
• Parts-per notation
• Per-unit system
• Percent point function