How to Calculate Percentage
Updated · 4 min read
“Per cent” means “per hundred”. 25% is 25 out of every 100, or 0.25. Almost every percentage question is one of four types. Here’s the formula for each, with a worked example.
To skip the arithmetic, the percentage calculator solves all four and shows the formula it used.
1. What is X% of Y?
Formula: X ÷ 100 × Y
Example: 15% of 80 = 15 ÷ 100 × 80 = 12. Use this for tips, tax and “how much is the discount?”
Mental shortcut: 10% is the number with the decimal point moved one place left (10% of 80 = 8). 5% is half of that (4), so 15% is 8 + 4 = 12.
2. X is what percent of Y?
Formula: X ÷ Y × 100
Example: you scored 42 out of 60. 42 ÷ 60 × 100 = 70%.
3. Percentage increase or decrease
Formula: (new − old) ÷ old × 100
Example: a price rises from 80 to 100. (100 − 80) ÷ 80 × 100 = +25%. If it falls from 100 to 80: (80 − 100) ÷ 100 × 100 = −20%.
Notice these aren’t the same size. The change is always measured against the starting value, which is different in each direction.
4. Add or subtract a percentage
Formula: Y × (1 + X ÷ 100) to add, Y × (1 − X ÷ 100) to subtract
Example: a 60 item with 20% off costs 60 × 0.8 = 48. Adding 19% VAT to 100 gives 100 × 1.19 = 119.
Common mistakes
- Removing a percentage that was added. A price of 119 including 19% tax is not 119 − 19%. The original price is 119 ÷ 1.19 = 100, while 119 − 19% gives 96.39.
- Adding percentages in a row. A 10% rise followed by another 10% rise is 21%, not 20%, because the second rise applies to the already-increased value.
- Percentage vs. percentage points. An interest rate going from 2% to 3% is a rise of 1 percentage point, but a 50% increase in the rate.