Three ways to ask a percentage question
A percent is a hundredth: 15 % means 15/100 = 0.15. Almost every percentage question is one of three shapes, and each has its own formula.
- What is 15 % of 80? Multiply: 0.15 × 80 = 12. Use it for tips, discounts and tax.
- 12 is what percent of 80? Divide and scale: 12 ÷ 80 × 100 = 15 %. Use it for test scores and shares of a total.
- What is the change from 80 to 100? Take the difference over the starting value: (100 − 80) ÷ 80 × 100 = +25 %.
A common trap
Percent changes are not symmetric. Going from 100 to 80 is −20 %, but going back from 80 to 100 is +25 %, because the base changed. A 50 % fall followed by a 50 % rise leaves you at 75 % of where you started.
Percentage points are different again: an interest rate moving from 3 % to 4 % rose by one percentage point, which is a 33 % relative increase.
How this works
of: result = a ÷ 100 × b
isWhat: result = a ÷ b × 100
change: result = (b − a) ÷ |a| × 100
The change mode divides by the absolute value of the starting number, so a move from −50 to −25 reads as a 50 % increase. Division by zero is reported rather than shown as infinity.
Frequently asked
How do I calculate a percentage of a number?
Divide the percent by 100 and multiply: 20 % of 250 is 0.20 × 250 = 50.
How do I work out a percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100: from 40 to 50 is 10 ÷ 40 × 100 = 25 %.
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages (3 % → 4 % is +1 point); percent change is relative (+33 %).
Can I undo a discount by adding the same percent back?
No. After a 20 % discount you need a 25 % increase to return to the original price.
Sources
Reviewed Oct 17, 2026 · test vectors fixtures/calculators/math/percentage/