How to calculate percentages
A percentage is a number expressed as a fraction of 100: 25% means 25 out of 100, or 0.25. This calculator solves the four most common percentage problems. Pick one, enter two numbers and the answer appears instantly with the formula used.
Percentage formulas
- X% of Y = X ÷ 100 × Y
- X is what % of Y = X ÷ Y × 100
- Percentage change = (new − old) ÷ |old| × 100
- Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Examples
- What is 20% of 150? 20 ÷ 100 × 150 = 30.
- 30 is what percent of 150? 30 ÷ 150 × 100 = 20%.
- Percentage change from 150 to 180: (180 − 150) ÷ 150 × 100 = 20% increase.
- Percentage difference between 150 and 180: 30 ÷ 165 × 100 ≈ 18.18%.
Percentage change vs percentage difference
Use percentage change when one value is the starting point and the other comes after it, such as a price going from $150 to $180. Use percentage difference when the two values are on equal footing, such as comparing prices in two stores — it uses their average as the base, so the order does not matter.
Percent vs percentage points
If an interest rate rises from 4% to 5%, it went up by 1 percentage point, but by 25 percent (1 ÷ 4 × 100). Mixing the two is a common mistake in news and finance.
Everyday uses
- discounts and sale prices — 30% off $80 saves $24;
- tips and sales tax;
- grades and test scores;
- growth of prices, salaries and investments.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 80 is 15 × 80 ÷ 100 = 12.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 50 to 60 is a 20% increase.
Why is a 50% drop not undone by a 50% rise?
Because each percentage is taken from a different base. 100 minus 50% is 50, and 50 plus 50% is only 75.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages; percent measures the relative change. From 4% to 5% is 1 percentage point, or a 25% increase.