Promile

One per mille is a thousandth of a whole or also a tenth of a percent. A popular misconception is that a promile is a thousandth of a percent, but this is not true, it is really a thousandth of a whole.

We write a per mille using the symbol ‰. It looks similar to the symbol for a percentage: % but the promile has one more circle at the bottom. So, 15 ‰ is fifteen per mille, while 15% is fifteen percent. How do you calculate a per mille? Let's look at some examples:

If we want to calculate one per mille of an amount, we divide the amount by one thousand:

• 1‰ of 1000 is 1, because 1000 divided by 1000 is 1.
• 1‰ of 20 000 is 20, because 20 000 divided by 1000 is 20.

How would we calculate the promiles if we had more than one? Just use the trinomial. What is 20‰ of 5000? We can proceed as follows:

1. Calculate how much 1‰ of 5000 is. So we calculate 5000 divided by 1000, which is 5. So we know that one per mille of 5000 is 5.
2. Since we have to calculate 20 per mille of 5000, we multiply 5 by 20, so we calculate 20 · 5 = 100.

So 20‰ of 5000 is 100. Since a promile is one tenth of a percent, we can also say that twenty promiles is the same as two percent. And therefore that two percent of 5000 is 100. We can also write a per mille in the form of a fraction. If we want to calculate 20‰ of 5000, it is the same as multiplying 5000 by a fraction $\frac{20}{1000}$:

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

Per mille of alcohol in the blood

A common use of the promille is in measuring blood alcohol. This is when we say that a person has, for example, 2‰ of alcohol in their blood. This means that in one kilogram of a person's blood, two per mille of alcohol is dissolved - that's two grams of alcohol.