Per mil

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Unit system
Unit of
Symbol	‰
Named after

The per mil (also spelled per mille, permil, or permille) is a unit of measurement used to denote a fraction of a whole, specifically one part per thousand. It is symbolized by the sign ‰, which is similar to the percent sign (%) but with an additional zero.

Definition

The per mil is defined as one part in a thousand, or 1/1000. It is used in various fields to express small differences or concentrations, such as in chemistry, finance, and meteorology.

Mathematically, one per mil is expressed as:

1‰ = 0.001 = 1/1000 = 0.1%

Usage

The per mil is commonly used in situations where the percentage is too large to express the precision needed. For example, in chemistry, it is often used to express the concentration of a substance in a solution. In finance, it can be used to describe interest rates or fees that are very small.

Examples

• In meteorology, the per mil is used to express the salinity of seawater. For instance, a salinity of 35‰ means that there are 35 grams of salt per 1000 grams of seawater.
• In finance, a bond might have a yield of 5‰, meaning it yields 5 parts per thousand of its face value.

Comparison with Percent and Parts Per Million

The per mil is part of a series of units used to express fractions of a whole:

• Percent (1 part per hundred, symbol: %)
• Per mil (1 part per thousand, symbol: ‰)
• Parts per million (1 part per million, symbol: ppm)

These units are used based on the level of precision required. Percent is used for larger fractions, per mil for intermediate fractions, and parts per million for very small fractions.

History

The concept of per mil has been used for centuries, particularly in fields that require precise measurements. The symbol ‰ was first used in the 18th century and has since become standardized in scientific and financial contexts.

Also see

• Percent
• Parts per million
• Concentration
• Salinity
• Interest rate