# #55: Percentages, percentage points and basis points: understand your metrics

You might find this topic weird, but understanding percentages is crucial not only in banking. What does it mean when disk space decreased by 10 percent? How to scientificly measure relative system load? And how to sound smart when applying for mortgage? You’ll learn all that in the next four minutes.

First of all, percentages are used to define a ratio of two values. For example, if your data uses 100 GiB out of 500 GiB on disk, it uses one fifth. Or 20%. 20% is basically the ratio between 100 and 500. The same applies to CPU load. Here, 80% means that for every 100 cycles, 80 are used for useful work. The remaining 20 is either waiting or simply being idle.

More often you’ll hear about percentages when some value changes over time. For example, if your disk usage grew from 100 to 130 GiB, what’s the relative increase? You divide 130 by 100 and get 1.3, or 130%. This means the new value is 130% of the initial value. This also means it grew by 30%. Surprisingly, if the disk usage now drops by 30%, it won’t go back to 100! 30% of 130 is 39 GiB. The final disk usage is 91 GiB.

But that’s not the most surprising thing with percentages. We said that the disk usage grew from 100 to 130 GiB, or by 30%. But what about the disk usage measured relatively to its size? It used to be 20% (100 out of 500 GiB used). Now it’s 130 out of 500, or 26%. Now, the question is, by how many percent did the disk usage grew? It increased from 20% to 26%, so the obvious answer is 6%, right? No, not at all!

An increase by 6% means that the final value is 106% of the initial value. For example, if we had 20 kilograms of oranges, we now have 21.2 kilograms. If we had 20 volts in a circuit, there’s 21.2 volts right now. You get the idea. So, if initially the disk occupancy was 20%, what does an increase by 6% really mean? You guessed it, now it’s 21.2% (!) This is very counterintuitive! That’s why another unit was invented, percentage points.

## Percentage points

**Percentage points** describe the change of percents.
In our example, a change from 20% to 26% means an increase by 6 percentage points.
This applies to every statistic measured in percents.
For example, when interest rate on your loan grows from 3% to 3.1%, it grows by one tenth of a percentage point.
In finance, fractions of percentage points are very common.
So another term to remember is **basis point**.
It’s nothing fancy, one basis point is simply one-hundredth of a percentage point.
So an interest rate increase from 3% to 3.1% is an increase by 10 basis points.

Pro tip: if you are negotiating your mortgage loan, ask to reduce an interest rent by a few basis points. By using fancy terminology, a banker will believe you are a more serious customer. Really.

Back to the topic. Does using percentages when describing a change from 20% to 26% make sense? We know it’s 6 percentage points. However, if you are absolutely sure people will understand you, you can technically say: an increase by 30%, from 20% to 26%. But to be honest, it’s just too confusing. Indeed, the absolute disk space grew from 100 to 130 (by 30%). But to be effective when communicating, avoid being smart and confuse people.

That’s it, thanks for listening, bye!

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