How to Calculate Percentages: The Five Formulas You Actually Need

Almost every everyday percentage question is one of five calculations. Here they are with examples, plus the mistakes that trip people up.

1. What is X% of Y?

X ÷ 100 × Y. 15% of 200 = 0.15 × 200 = 30.

2. X is what percent of Y?

X ÷ Y × 100. 30 out of 120 = 30 ÷ 120 × 100 = 25%.

3. Percentage change from A to B

(B − A) ÷ |A| × 100. From 80 to 100: 20 ÷ 80 × 100 = +25%. From 100 to 80: −20 ÷ 100 × 100 = −20%. The base is always the starting value, which is why the two directions differ.

4. Add X% (markup, tax, raise)

Y × (1 + X ÷ 100). $80 plus 25% = 80 × 1.25 = $100.

5. Remove X% (discount)

Y × (1 − X ÷ 100). $100 minus 20% = $80.

The percentage calculator has all five on one page and updates as you type.

The traps

• Up then down isn't zero. +10% then −10% takes 100 to 110 to 99. The second percentage applies to a different number.
• Undoing a discount. If something costs $75 after 25% off, the original isn't $75 + 25%. It's 75 ÷ 0.75 = $100.
• Removing tax. Tax included in $120 at 20% isn't $24; it's 120 − 120 ÷ 1.2 = $20. The VAT calculator does this both ways.
• Percent vs percentage points. A rate going from 5% to 7% rose 2 percentage points, but 40% in relative terms. News headlines mix these up all the time.