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Per Mille — Definition, Formula & Examples

Per mille (‰) is a way of expressing a number as a fraction of one thousand. Just as percent (%) means "per hundred," per mille means "per thousand," so 1‰ equals 0.001.

The per mille symbol ‰ denotes a ratio in which the denominator is 1,000. A value of nn‰ is equivalent to n1000\frac{n}{1000}, or equivalently 0.1n%0.1n\%.

Key Formula

n‰=n1000=0.1n%n\text{‰} = \frac{n}{1000} = 0.1n\%
Where:
  • nn = The number of parts per thousand

How It Works

To use per mille, divide the part by the whole and multiply by 1,000. For example, if 7 out of every 1,000 items are defective, the defect rate is 7‰. To convert per mille to percent, divide by 10: 7‰=0.7%7\text{‰} = 0.7\%. To convert percent to per mille, multiply by 10: 3%=30‰3\% = 30\text{‰}. Per mille is handy when percentages would produce awkward decimals.

Worked Example

Problem: A city's population grew by 15,000 people out of a total population of 5,000,000. Express this growth rate in per mille.
Divide part by whole: Divide the growth by the total population.
15,0005,000,000=0.003\frac{15{,}000}{5{,}000{,}000} = 0.003
Multiply by 1,000: Convert the decimal to per mille.
0.003×1,000=3‰0.003 \times 1{,}000 = 3\text{‰}
Answer: The population growth rate is 3‰ (three per mille), which equals 0.3%.

Why It Matters

Per mille appears in finance (interest rates on bonds), demographics (birth and death rates), and engineering (material tolerances). Many European countries use ‰ on tax documents and in statistics where percent values would be inconveniently small decimals.

Common Mistakes

Mistake: Confusing ‰ (per mille) with % (percent) and treating them as the same thing.
Correction: Per mille divides by 1,000, while percent divides by 100. A value of 5‰ is ten times smaller than 5%, since 5‰=0.5%5\text{‰} = 0.5\%.

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