Percentage Calculator
This tool covers the three cases that come up all the time: calculating the percentage of an amount (discounts, tips, commissions), finding out what percentage one value represents of another, and measuring the change between two figures.
The three formulas
Y × X ÷ 100A ÷ B × 100(Final − Initial) ÷ Initial × 100For change, a negative result means a decrease.
Example
A €150 jacket with a 20% discount: the discount is 150 × 20 ÷ 100 = €30, and you pay €120. If the price later rises from €120 to €150, the change is (150 − 120) ÷ 120 × 100 = +25%.
Frequently asked questions
Why doesn't decreasing by 20% and then increasing by 20% return the original price?
Because each percentage is applied to a different base. From €100, a −20% leaves €80, and a +20% on €80 is €96, not €100. To undo a 20% discount you need to increase by 25%.
How do I remove a percentage already included in a price?
Divide by 1 plus the percentage as a decimal. To remove a 21% already included: price ÷ 1.21.
What's the difference between percentage points and percent?
If something goes from 10% to 12%, it's risen by 2 percentage points, but by 20% in relative terms. Mixing these up is a very common mistake when reading the news.