Percentages made easy: the three questions you'll ever need
By Johannes Nieuwboer · 5 min read
Almost every percentage question in daily life is one of three types: what is X% of Y, what percentage is X of Y, and by how much did something change. Master these and discounts, pay rises and statistics become easy to read.
1. What is X% of Y?
Multiply Y by X and divide by 100. 15% of 80 is 80 × 15 / 100 = 12. A handy trick: X% of Y equals Y% of X, so 8% of 50 is the same as 50% of 8, which is 4.
2. X is what percentage of Y?
Divide X by Y and multiply by 100. If 18 out of 24 students passed, the pass rate is 18 / 24 × 100 = 75%.
3. Percentage change
Subtract the old value from the new one, divide by the old value and multiply by 100. A price rising from $40 to $50 is (50 − 40) / 40 × 100 = 25% higher. Falling from $50 back to $40 is (40 − 50) / 50 × 100 = −20%.
Notice that the up and down percentages differ because the starting point changes. This asymmetry is why a stock that falls 50% must then rise 100% just to get back to where it started.
Percent vs. percentage points
If an interest rate rises from 2% to 3%, it went up by one percentage point — but by 50% in relative terms. News reports sometimes mix these up; always check which one is meant.
Reverse percentages
If a price after a 20% discount is $64, the original price is $64 / 0.80 = $80, not $64 × 1.20 = $76.80. The same logic applies to VAT and pay rises: divide by the multiplier to go back.