The five percentage questions
A percentage is a fraction out of 100: 12% means 12 out of every 100, or 0.12. Nearly every percentage problem is one of five questions, and each has one formula.
- What is X% of Y? Multiply: Y × X ÷ 100. For 12% of 250 that is 250 × 0.12 = 30.
- X is what percent of Y? Divide, then multiply by 100: X ÷ Y × 100. 30 out of 250 is 30 ÷ 250 × 100 = 12%.
- Percentage change from X to Y: (Y − X) ÷ X × 100. From 100 to 120 is +20%. From 120 back to 100 is about −16.67%.
- Increase or decrease Y by X%: Y × (1 ± X ÷ 100). 250 increased by 12% is 250 × 1.12 = 280.
- Find the original: divide by the same factor instead of multiplying. If 120 is the price after a 20% rise, the original was 120 ÷ 1.2 = 100.
The last two are the same sum run in opposite directions, and that is where people go wrong. A 20% rise takes 100 to 120, but taking 20% off 120 gives 96, not 100, because the 20% is now a share of a bigger number. The percentage increase calculator, the percentage decrease calculator and the percentage change calculator each go deeper on one of these.
Percent or percentage points?
If an interest rate moves from 4% to 5%, it rose by 1 percentage point, but by 25% in relative terms (1 ÷ 4 = 0.25). Headlines mix these up all the time. To get the relative figure, put 4 and 5 into Percentage change. The percentage points are just the difference, 5 − 4 = 1, which you can do in your head.
Mental shortcuts worth knowing
- 10%: move the decimal point one place left. 10% of 250 is 25.
- 1%: move it two places. 1% of 250 is 2.5.
- 5%: half of 10%. 15%: 10% plus 5%. 20%: double 10%.
- 25% is a quarter, 50% is half and 75% is three quarters.
- Swap them: X% of Y always equals Y% of X. 8% of 50 is awkward, but 50% of 8 is 4, so 8% of 50 is 4.
Use the calculator to check your mental answer, or when the numbers are not round.
How rounding is handled
The calculator keeps your numbers as exact decimals and rounds once, at the end, to the decimal places you choose (2 by default). Halves round away from zero, so 1.005 becomes 1.01, which plain computer arithmetic gets wrong. When an answer is rounded, the working shows ≈ instead of =. A value that is not zero is never shown as zero: 0.004% stays 0.004% even at two decimal places.