The three percentage questions
Percent means "per hundred", and every percentage problem you meet in real life reduces to one of three shapes. Learn to spot the shape and the arithmetic takes seconds.
1. What is X% of Y?
Divide the percent by 100, multiply by the number. A 15% tip on a 240 bill: 15 ÷ 100 × 240 = 36. A quicker mental route: 10% of 240 is 24, half of that again is 12, and 24 + 12 = 36. Ten-percent-first is the fastest party trick in arithmetic.
2. X is what percent of Y?
Divide the part by the whole, multiply by 100. Scoring 45 out of 180 on a test: 45 ÷ 180 × 100 = 25%. The order matters; the number after "of" always goes on the bottom.
3. What is the change from X to Y?
Take the difference, divide by where you started, multiply by 100. Rent going from 120 to 150: (150 − 120) ÷ 120 × 100 = a 25% increase. Starting point on the bottom, always, which is why a rise from 100 to 150 is +50% but the fall back from 150 to 100 is only −33%.
Percentage points are not percent
An interest rate moving from 4% to 6% has risen by two percentage points, and by 50 percent. Both statements are true and they sound wildly different, which is exactly why headlines pick whichever suits the story. When you read a percentage claim about something that is already a percentage, check which of the two is meant before reacting.
The reverse-percentage trap
A jacket costs 80 after a 20% discount. The original price was not 96. The 20% came off the original, unknown price, not off the 80, so you divide instead of multiply: 80 ÷ 0.8 = 100. Any time you know the "after" number and the percentage that produced it, divide by (1 ± the rate). Working backwards from a VAT-inclusive price works the same way: a 120 total at 20% VAT was 120 ÷ 1.2 = 100 before tax.
Up 50%, down 50%, not back where you started
Gains and losses are measured from different baselines, so they do not cancel. A 100 portfolio that rises 50% hits 150; a 50% fall from there lands at 75, not 100. The bigger the swing, the crueller the asymmetry: down 50% needs up 100% to recover. Keep this in your pocket whenever anyone quotes you a sequence of percentage moves.
Questions people ask
Can a percentage be more than 100?
Whenever the part is bigger than the thing you are comparing it to. Selling 240 tickets for a 180-seat venue is 133% capacity. Growth can also exceed 100%: from 40 to 100 is a 150% increase. The scale has no ceiling.
What does a negative percentage change mean?
A decrease. From 150 to 120 is −20%. The calculator handles negative start or end values too, though be careful reading those: going from −50 to 50 is a 200% change on paper and usually better described in plain numbers.
What is the difference between percent off and percent of?
"20% of 80" is 16. "20% off 80" is 80 minus that 16, so 64. Off means subtract the percentage from the original; of means the percentage itself. Shops rely on the two being easy to blur.
How do I add a percentage to a number?
Multiply by one-plus-the-rate. Adding 20% VAT to 250: 250 × 1.2 = 300. It is the same answer as working out 20% and adding it on, one step shorter, and it reverses cleanly when you need the pre-tax figure back.
Percentages are exact; the decisions built on them are yours. For money questions involving tax or interest, the dedicated calculators on our build list will show jurisdiction-specific working.