How to calculate percentages

“Percent” means “per hundred”: 15% is 15 out of every 100, or 0.15. Almost every percentage question is one of four calculations. Once you know which one you are facing, the math is a single step.

1. What is X% of a number?

Convert the percentage to a decimal (divide by 100) and multiply.

15% of 80 = 80 × 0.15 = 12.

A handy shortcut: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4.

2. What percent is one number of another?

Divide the part by the whole and multiply by 100.

12 out of 48 = 12 ÷ 48 × 100 = 25%.

3. Percentage change

Subtract the old value from the new one, divide by the old value, and multiply by 100.

A price rising from $50 to $65 is (65 − 50) ÷ 50 × 100 = 30% increase. Falling back from $65 to $50 is (50 − 65) ÷ 65 × 100 = −23.1%. The same $15 gap is a different percentage because the starting point is different.

Percentage change from zero can’t be calculated — there is no starting amount to compare against.

4. Working backwards from a percentage

If you know a part and the percentage it represents, divide by the percentage as a decimal.

$30 is 20% of what? 30 ÷ 0.20 = $150.

This is also how you find an original price: a jacket costs $126 after 30% off, so $126 is 70% of the original price, and 126 ÷ 0.70 = $180.

Common traps

Increases and decreases don’t cancel

Raise $120 by 25% and then cut it by 20%: 120 × 1.25 × 0.80 = $120. It comes back exactly here, but a 25% rise followed by a 25% cut does not: 120 × 1.25 × 0.75 = $112.50. After a drop of X%, you need a rise of more than X% to get back to where you were.

Stacked discounts don’t add up

20% off and then an extra 10% off is not 30% off. $100 × 0.80 × 0.90 = $72, a total discount of 28%. The discount calculator shows the effective rate.

Percent versus percentage points

If a mortgage rate rises from 6% to 7%, it went up by 1 percentage point, but by 16.7 percent (1 ÷ 6). News reports mix these up; the difference is large when rates are low.

Adding tax

To add 8% sales tax to $40, multiply by 1.08: $43.20. To remove tax from a total that already includes it, divide by 1.08 — subtracting 8% of the total gives the wrong answer.