How to calculate percentage
Updated on June 18, 2026 · by Rafael Rossi
A percentage is a fraction of 100. "20%" means 20 out of every 100, or 20 ÷ 100 = 0.20. Almost every percentage calculation comes down to turning the "%" into a decimal and multiplying — and almost every percentage mistake comes from losing track of which number the calculation applies to.
The five essential operations
- A% of B = (A ÷ 100) × B
- A is what % of B = (A ÷ B) × 100
- Increase B by A% = B × (1 + A/100)
- Decrease B by A% = B × (1 − A/100)
- Change from A to B = ((B − A) ÷ A) × 100
Worked examples
15% of 240: 0.15 × 240 = 36.
45 is what percent of 300? (45 ÷ 300) × 100 = 15%.
Increase 80 by 25%: 80 × 1.25 = 100.
From 250 to 300, what changed? ((300 − 250) ÷ 250) × 100 = +20%.
A useful shortcut for mental math: A% of B always equals B% of A. Working out 4% of 75 sounds hard; 75% of 4 is obviously 3. Same number.
The mistake that costs money: percentages don't add up
This is the most expensive trap in the subject, and it shows up in sales, in salaries and in investing.
An item priced at $100 rises 10%, then falls 10%. Back to $100? No — it is $99. The 10% rise was calculated on 100 ($10); the 10% fall was calculated on 110 ($11). Different bases, different results.
The bigger the swing, the worse it gets:
| Movement | Result on $100 | To get back to $100 |
|---|---|---|
| −10% then +10% | $99 | needs +11.1% |
| −20% | $80 | needs +25% |
| −40% | $60 | needs +66.7% |
| −50% | $50 | needs +100% |
This is why an investment that halves has to double just to break even — and why losing is mathematically heavier than winning.
The same holds in the other direction: three consecutive 10% raises do not make 30%, they make 33.1%. And 5% annual inflation over ten years does not add up to 50%, it compounds to 62.9%.
"30% off plus an extra 20% at checkout" is not 50% off
The second discount applies to the already-reduced price. $100 at 30% off is $70; 20% of $70 takes off $14, leaving $56. The real discount was 44%, not 50%.
The quick way is to multiply the factors: 0.70 × 0.80 = 0.56, meaning you pay 56% of the original price. Stacked discounts always come to less than the arithmetic sum would promise.
Reverse percentage: finding the original price
You paid $80 for an item marked 20% off. What was the ticket price?
The common error is 80 × 1.20 = $96. That is wrong, because the 20% was taken off the original price, not off what you paid. The correct operation divides:
Original = Price paid ÷ (1 − discount) → 80 ÷ 0.80 = $100.
The same logic applies to backing sales tax out of a tax-inclusive total: you divide, never subtract the percentage.
Percent is not percentage point
If an interest rate goes from 5% to 7%, it rose 2 percentage points — but it rose 40 percent. Both statements are true about the same change, and mixing them up is the single most common way a headline misleads.
Rule of thumb: when the two numbers being compared are already percentages, the gap between them is measured in percentage points (pp). "Percent" is reserved for the relative change.
Beware of a small base
"Sales grew 200% this quarter" is impressive until you learn it went from 2 units to 6. A percentage is a ratio, and ratios over tiny bases produce enormous numbers with no practical meaning.
The reading rule is simple: any percentage without the absolute number beside it is half a fact. When someone shows only the relative change, the absolute figure is usually the part that weakens the argument. That holds for earnings reports, headlines and social posts alike.
The reverse applies too: a 0.3 percentage point drop in the rate on a 30-year mortgage sounds negligible and can be worth tens of thousands of dollars.
Frequently asked questions
How do I work out percentages in my head? Anchor on 10%: divide by 10. From there, 5% is half of that, 20% is double, 1% is dividing by 100. For 15% of 240: 10% = 24, 5% = 12, total 36.
How do I turn a percentage into a fraction? Put it over 100 and simplify: 25% = 25/100 = 1/4; 75% = 3/4; 12.5% = 1/8. Recognising those three saves a lot of time.
What does a change of more than 100% mean? That the quantity more than doubled. A 150% increase multiplies the value by 2.5. A decrease, by contrast, can never exceed 100%, because that would mean reaching zero.
How do I take a percentage of a percentage? Multiply the decimals. 50% of 30% is 0.5 × 0.3 = 0.15, which is 15% of the total — not 80%, and not 20%.