Percentage Calculation Formula

Why do you need percentages?

Lots of information in our world comes to us as percentage. We get percentage pay rise, interest rates on our loans or investments , income taxes to pay, VAT tax to pay, discounts in shops or poll results. It’s crucial to know what they mean and how to calculate them efficiently.

Etymology of word "percent"

Percent comes from connecting two latin words:

• PER which means:
• • by, by means of
  • during (time)
  • through (space)
• Centum which mean:
• • Hundred

Even these days you can see many uses of word centum. There are the 100 cents in a dollar. Or 100 centimeters in a meter.

What percent means?

Percent which also written as % means PER 100 or OUT OF Hundred.
For example: 2 % of world population of people has green eyes it means 2 for each 100 people has green eyes. In mathematical equation it looks like this: 0.02 x 100 = 2%

Percentage calculation Formula

Calculating percentages for a round numbers like 10 or 100 or 500 is easy.
However, how to calculate 37% from 243?

Well, here is the formula:

Where "x" is a number you are looking for:
( x = 243 * 37% / 100 )

So:

And the result is:

You can also use approach called proportions.

Proportions means that ratio of percent and ratio of values are equal:


Idea here is this, you can even say that to yourself :
If 243 is 100% then x is 37%. Then on piece of paper write first statement in line 243 100 and below the x 37, like this:

Next step is to multiply them crosswise like this:

So you come up with this equation:

In next step divide both sides of the equation by 100. It looks like this:

The result is:

Notice, the previous equation is exactly like the first one for calcuation percentages. However, I think this way is easer to remember.

If you need to calculate more difficult equations you can always use our Percentage Calculator.

What percentage increase means?

When you hear your pay rise is 20 % it means you will 20 dollars more for each 100 dollars you received so far. When you hear increase by a 100% it means your salary has doubled and now you earn 200% of your previous salary or for each 100 dollars you now earn another 100 dollars ( 100% + 100% = 200%)

What percentage decrease means?

When you see 25% discount offer in a shop, it works similar as with increase. From each 100 dollars you need to pay 25 dollars less which is 75 dollars( $100 - $25 = $75 ).
So lets calculate 15% discount on 77 dollars using proportions.
Again, say this to yourself. If, 77 dollars equals 100% then how many ("x") dollars is 85%. You have this: $\frac{\mathrm{77}}{x}=\frac{\mathrm{100}}{\mathrm{85}}$
then cross multiply:
x * 100 = 77 * 85
followed by:
x = 77 * 85 / 100
x = 65.45
The price after discout is 65.45 dollars.

Common misunderstandings when describing change in percents.

There are two ways describing change of percentage.
First one is: The population growth rate over the decade has increased by 10%. If the rate was 30% and it increased by 10%. The current rate is now 33%. 30 * (10/100) = 33
The second one is: The population growth rate over the decade has increased by 10 Percentage Points . If the rate was 20% and it increased by 10 percentage points mean the rate is now 40%. 30 + 10 = 40.

What percentage point is?

The definition of percentage point is: The difference between two percentages is termed as percentage point. Percentage point is used to show the changes in an indicator with respect to its previous standings.
The difference between 30% and 40% is 10 percentage point, NOT 10 Percent. The diffrence in percentage is actually 33.3%.
It's easy to mix them up.

I hope, percentage calculation are now easier and the formula and proportions for percentages are understood better.
Here is a link to our Percentage Calculator. In case you need it.
All the best!
Dominik