How to use the Percentage Calculator
- Find the card that matches your question, for example “Percent change from X to Y” for a price or salary change.
- Type your numbers into the boxes. The answer updates as you type in the gray box below.
- In “Increase or decrease X by P%”, switch between Increase and Decrease for markups, raises or markdowns.
- Each result shows the full calculation, so you can check it or copy it into a report or spreadsheet.
The four percentage formulas
Percent of a number: X × P ÷ 100. For example, 15% of 80 is 80 × 15 ÷ 100 = 12. What percent one number is of another: part ÷ whole × 100. A test score of 42 out of 48 is 42 ÷ 48 × 100 = 87.5%.
Percent change: (new − old) ÷ old × 100. A salary that goes from $62,000 to $65,100 rose (65,100 − 62,000) ÷ 62,000 × 100 = 5%. Increase or decrease by a percent: X × (1 + P%) or X × (1 − P%). A $250 item marked up 20% costs $300; marked down 20% it costs $200.
Everyday examples: sales tax, tips and discounts
Sales tax is added to the shelf price in the US, so use “Increase X by P%”. A $59.99 purchase with 8.25% sales tax comes to 59.99 × 1.0825 ≈ $64.94, of which about $4.95 is tax. A tip works the same way: an 18% tip on a $64.50 check is 64.50 × 0.18 ≈ $11.61.
To work backwards from a sale price, divide instead of multiply. If a jacket costs $48 after 20% off, the original price was 48 ÷ (1 − 0.20) = $60. Subtracting 20% from $48 would give the wrong answer, because the discount was taken from the original price, not the sale price.
Percent vs. percentage points
When a rate moves from 6% to 7%, it went up one percentage point, but it rose (7 − 6) ÷ 6 ≈ 16.7% in relative terms. News reports about interest rates, unemployment and polls usually mean percentage points. Mixing up the two can make a change look six times bigger or smaller than it is.
Why up 25% then down 20% gets you back to the start
Successive percentage changes multiply rather than add, because each change uses a new base. A $100 stock that gains 25% is worth $125; a 20% drop from $125 takes it back to $100, since 1.25 × 0.8 = 1. In the other direction, a 50% loss needs a 100% gain to break even. When you combine several changes, multiply the factors (1 + change) together instead of adding the percentages.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 20% of 150 is 150 × 20 ÷ 100 = 30. You can also convert the percent to a decimal first: 150 × 0.20 = 30.
How do I calculate percent increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. Going from 50 to 65 is (65 − 50) ÷ 50 × 100 = 30%. A negative result means a decrease.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 45 out of 60 is 45 ÷ 60 × 100 = 75%.
Can a percentage be more than 100%?
Yes. If revenue grows from $100,000 to $250,000, that is a 150% increase, and 150 is 150% of 100. A decrease, however, can’t be more than 100% for a quantity that can’t go below zero.
Why can’t I calculate percent change from 0?
Percent change divides by the starting value, and dividing by zero is undefined. Describe a change from 0 in absolute terms instead, for example “up 25 units”.
What is the difference between percent change and percent difference?
Percent change compares a new value with an original one. Percent difference compares two values with no clear starting point and divides by their average: for 40 and 60 it is 20 ÷ 50 × 100 = 40%.
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