Percentages appear in exam marks, discounts, salaries and statistics. Once you know three formulas, you can solve almost every percentage question.
Formula 1: What is X% of Y?
Result = (X ÷ 100) × Y
Example: 20% of 150 = 0.20 × 150 = 30.
Formula 2: X is what percent of Y?
Percentage = (X ÷ Y) × 100
Example: you scored 45 out of 60. 45 ÷ 60 × 100 = 75%.
Formula 3: Percentage change
Change = ((New − Old) ÷ Old) × 100
- From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase.
- From 100 to 80: (80 − 100) ÷ 100 × 100 = 20% decrease.
Skip the maths with our free percentage calculator.
Useful shortcuts
- 10% of a number: move the decimal point one place left.
- 50%: divide by 2. 25%: divide by 4.
- To add 15%: multiply by 1.15. To subtract 15%: multiply by 0.85.
A common mistake
A 50% increase followed by a 50% decrease does not bring you back to the start. If you begin with 100, a 50% rise gives 150, and a 50% fall from 150 gives 75. Percentage change always uses the old value as its base.
Percentages and grades
Need to convert a grade point average? Read how to convert CGPA to percentage.
Calculate percentage: frequently asked questions
How do I turn a fraction into a percentage?
Divide the top number by the bottom number and multiply by 100. For example, 3/4 = 0.75 = 75%.
How do I find the original price after a discount?
Divide the sale price by (1 minus the discount). For a 20% discount, divide by 0.8.
Can a percentage be more than 100?
Yes. For example, a value that doubles has increased by 100%, and a value that triples by 200%.
