Per Mille
When working with per mille, it is almost the same as with percent. The difference is simply that you calculate out of one thousand instead of one hundred.
The word per mille comes from Latin and means "per thousand".
Per mille is written with the symbol ‰ and is the same as thousandths.
$$ \large 1\ \text{‰} = \frac{1}{1000} = 0.001 $$
Other examples:
$$ \large 25\ \text{‰} = \frac{25}{1000} = 0.025 $$
$$ \large 100\ \text{‰} = \frac{100}{1000} = 0.10 $$
$$ \large 175\ \text{‰} = \frac{175}{1000} = 0.175 $$
Find per mille part
If per mille is the same as thousandths, it means that 1000 ‰ is the whole.
1000 ‰ of 500 is therefore 500 – the whole.
100 ‰ is one tenth: 50.
But what if it is 37 ‰ of 500?
To find a per mille part of a number, first find 1 ‰ by dividing by 1000. Then multiply by 37:
$$ \large \frac{37 \cdot 500}{1000} = 18.5 $$
You can also think: First find 1 per mille and then multiply by the number of per mille.
Add per mille
Sometimes you need to find how much a number increases if it grows by a certain per mille. Let us say an amount of 400 increases by 25 ‰.
First find 25 ‰ of 400:
$$ \large \frac{25 \cdot 400}{1000} = 10 $$
The amount therefore grows by 10, so the new amount is:
$$ \large 400 + 10 = 410 $$
You can also calculate it directly by multiplying with 1.025:
$$ \large 400 \cdot 1.025 = 410 $$
Subtract per mille
If an amount decreases by a certain per mille, subtract the per mille part. Let us say 400 decreases by 25 ‰.
First find 25 ‰ of 400:
$$ \large \frac{25 \cdot 400}{1000} = 10 $$
So the new amount is:
$$ \large 400 - 10 = 390 $$
Or directly calculated with a factor of 0.975:
$$ \large 400 \cdot 0.975 = 390 $$
Per mille in practice
Per mille is often used when dealing with very small parts. For example:
- Blood alcohol level (e.g. 0.5 ‰).
- Error rate in production (e.g. 2 ‰ of all items).
Summary
- Per mille means "per thousand".
- 1 ‰ = 0.001.
- 1000 ‰ is the whole, 100 ‰ is one tenth.
- Per mille is calculated like percent, but divide by 1000 instead of 100.