Percentage Calculator
ExampleYou leave a 20% tip on a 150 restaurant bill. How much is the tip?
Answer
Fill in the blanks. The answer and its formula appear here as you type.
In short
How the Percentage Calculator works
A percentage is a part per hundred. To find X% of Y, multiply Y by X and divide by 100: 20% of 150 is 150 × 20 / 100 = 30. To find what percent A is of B, divide A by B and multiply by 100. Percent change is (new − old) / |old| × 100.
Guide
Percentage formulas
Every mode on this page is one of a few short formulas. The calculator shows the formula with your own numbers in it under each result, so you can check the math or copy it into a document.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X / 100 | 20% of 150 = 30 |
| X is what % of Y? | X / Y × 100 | 30 / 150 × 100 = 20% |
| X is Y% of what? | X × 100 / Y | 30 × 100 / 20 = 150 |
| % change from A to B | (B − A) / |A| × 100 | 50 → 65 = +30% |
| Increase A by P% | A × (1 + P / 100) | 200 + 15% = 230 |
| Decrease A by P% | A × (1 − P / 100) | 200 − 15% = 170 |
| Original price before P% off | Sale / (1 − P / 100) | 60 / 0.75 = 80 |
| Remove P% tax from a gross amount | Gross / (1 + P / 100) | 120 / 1.2 = 100 |
Guide
How do I work out a percentage increase or decrease?
Subtract the starting value from the new value, divide by the starting value, and multiply by 100. A price that goes from 50 to 65 changed by 15, and 15 / 50 × 100 = 30, so it rose 30%. If the result is negative, the value fell.
Increases and decreases are not symmetrical. Cutting 100 by 50% gives 50, but raising 50 by 50% only gets you back to 75. The percentage is always measured against the value you start from.
Guide
What is the difference between percent and percentage points?
A percentage point is the plain difference between two percentages. If an interest rate moves from 4% to 5%, it rose by 1 percentage point. Measured against the starting rate, that same move is a 25% increase. Use the Percentage points mode to see both.
Guide
How this calculator handles edge cases
Negative numbers and decimals are accepted everywhere. Commas in numbers such as 1,250 are ignored. Asking what percent a number is of 0, or for the percentage change from 0, has no answer, so the calculator says so instead of showing infinity. Results are rounded to six decimal places for display; the formula shows up to ten.
With documents
Questions
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 80 × 15 / 100 = 12.
How do I calculate percentage change?
Subtract the old value from the new value, divide by the absolute old value, and multiply by 100. Going from 50 to 65 is (65 − 50) / 50 × 100 = 30% increase.
What is the difference between a percentage increase and decrease?
An increase means the new value is larger than the starting value, so the change is positive. A decrease means the new value is smaller, so the change is negative. A 50% decrease followed by a 50% increase does not return to the start: 100 becomes 50, then 75.
How do I find the original price before a discount?
Divide the sale price by (1 − discount / 100). If an item costs 60 after a 25% discount, the original price was 60 / 0.75 = 80.
What is the difference between percent and percentage points?
Percentage points measure the plain difference between two percentages. A rate rising from 4% to 5% went up 1 percentage point, which is a 25% relative increase.
How do I convert a fraction to a percent?
Divide the numerator by the denominator and multiply by 100. 3/8 is 0.375, which is 37.5%.
Sources
Method and review
The method is described on this page and every result shows how it was reached. Last reviewed by the PurePDF team. Spotted a mistake? Tell us.
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