The three percentage questions people ask most
Nearly every percentage problem is a version of one of three questions. This page answers all three, and shows the formula so you can check the working.
1. What is X% of Y?
Divide the percentage by 100 and multiply by the number. For example, 20% of 150 is 20 ÷ 100 × 150 = 30. This is the question behind tips, taxes and discounts.
2. X is what percent of Y?
Divide the part by the whole and multiply by 100. If you scored 42 out of 60, then 42 ÷ 60 × 100 = 70%.
3. What is the percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. If a price rises from 80 to 100, the change is (100 − 80) ÷ 80 × 100 = 25% increase. A negative result means a decrease.
Common mistakes
- Using the wrong base. A rise from 80 to 100 is +25%, but a fall from 100 to 80 is only −20%. The starting value matters.
- Adding percentages. A 10% rise followed by a 10% fall does not bring you back to the start. You end up 1% lower.
- Confusing percent and percentage points. Going from 4% to 6% is a rise of 2 percentage points, which is a 50% increase.
Quick mental tricks
- 10% of a number: move the decimal point one place left.
- 5%: half of 10%. 15%: 10% plus 5%.
- 1%: move the decimal point two places left.
Frequently asked questions
Can I use decimals and negative numbers?
Yes. Decimals work in every field. For percentage change, the starting value cannot be zero.
Why is my answer slightly different from my phone?
Results here are rounded to four decimal places. Your phone may round differently.