Per mille

One per mille is a thousandth of the whole, or equivalently a tenth of a per cent. A popular mistake is to think that a per mille is a thousandth of a per cent, but that is not true – it really is a thousandth of the whole.

We write per mille with the symbol ‰. It looks similar to the per cent sign, %, but the per mille sign has one more circle at the bottom. So 15 ‰ is fifteen per mille, whereas 15% is fifteen per cent. How do we calculate with per mille? Let’s look at some examples:

If we want to find one per mille of some amount, we divide the amount by a thousand:

• 1 ‰ of 1,000 is 1, because 1,000 divided by 1,000 is 1.
• 1 ‰ of 20,000 is 20, because 20,000 divided by 1,000 is 20.

How would we calculate with more per mille? We can simply use the unitary method. What is 20 ‰ of 5,000? We can go about it like this:

1. We work out what 1 ‰ of 5,000 is. That is 5,000 divided by 1,000, which is 5. So we know that one per mille of 5,000 is 5.
2. Since we have to find 20 per mille of 5,000, we multiply the 5 by twenty, that is, we work out 20 · 5 = 100.

So 20 ‰ of 5,000 is 100. Because a per mille is a tenth of a per cent, we can also say that twenty per mille is the same as two per cent. And so two per cent of 5,000 is 100. We can also write per mille as a fraction. If we want to find 20 ‰ of 5,000, that is the same as multiplying 5,000 by the fraction $\frac{20}{1000}$:

$$5000\cdot \frac{20}{1000}=100$$

Alcohol in the blood

Per mille is often used for measuring alcohol in the blood. Then we say that a person has, for example, 2 ‰ of alcohol in their blood. This means that in one kilogram of human blood there are two per mille of dissolved alcohol – which is two grams of alcohol.