Per mille

Per mille (‰) is a unit of proportion used in mathematics, statistics, and various fields to denote a value that is one-thousandth of a whole. The term originates from the Latin per mīlle, meaning "by the thousand." It is similar to percentage, which represents a quantity in parts per hundred, but per mille is used when a finer resolution is needed.

Usage

Per mille is widely used in finance, science, and engineering to express small differences in concentration, rates, and ratios. For example, in finance, it can be used to describe the interest rates on loans or the commission rates of sales. In environmental science, it might be used to quantify the concentration of pollutants in air or water. The symbol for per mille is ‰, which looks like a percent sign (%) with an extra zero in the loop.

Calculation

The value in per mille of a part of a whole is calculated by dividing the part by the whole and then multiplying by 1000.

\[ \text{Per mille} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 1000 \]

Comparison with Percentage

While both per mille and percentage are units of proportion, the key difference lies in their basis of calculation. Percentage values are parts per hundred, making them suitable for expressing larger proportions. Per mille, being parts per thousand, offers a higher precision and is used when smaller quantities need to be expressed.

Applications

1. 1. 1. Finance###

In finance, per mille is often used to describe the rates of taxation, loan interest, or investment returns, where small differences can be significant.

1. 1. 1. Science and Engineering###

In fields like chemistry and physics, per mille is used to express the concentration of solutions or the purity of materials. In civil engineering, it can describe the slope of a road or railway.

1. 1. 1. Medicine###

In medicine, per mille can be used to express blood alcohol content or the prevalence of a condition in a population.

Symbol

The symbol for per mille, ‰, is obtained by combining the percent symbol with an additional zero. It is available in most computer character sets, including Unicode and ASCII extensions.

See Also

• Percentage
• Parts-per notation
• Basis point

Per mille Resources
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