Percentage Calculator
Free percentage calculator. Find X% of Y, what percent X is of Y, or the percent change between two values. Instant.
What a percentage calculator does
Percentages cause more everyday arithmetic mistakes than any other operation, mostly because the same word covers three different questions. This calculator separates them into three modes so you use the right formula: what is X% of Y, X is what percent of Y, and the percentage change from X to Y. Pick the tab that matches your question and the answer updates as you type.
How the three modes work
- X% of Y: value = X ÷ 100 × Y. Use it for discounts, tips, tax, and any “find the portion” question.
- X is what percent of Y: percent = X ÷ Y × 100. Use it to express one number as a share of another, like a test score.
- Percentage change from X to Y: change = (Y − X) ÷ |X| × 100. A positive result is an increase, a negative one a decrease; the tool also shows the absolute difference.
Worked examples
Using the calculator’s default values for each mode:
| Mode | Input | Calculation | Result |
|---|---|---|---|
| X% of Y | 20% of 150 | 20 ÷ 100 × 150 | 30 |
| X is what % of Y | 30 of 150 | 30 ÷ 150 × 100 | 20% |
| % change | 50 → 65 | (65 − 50) ÷ 50 × 100 | 30% increase (absolute change 15) |
Percentage change vs percentage points
These are not interchangeable. If a rate moves from 5% to 6%, that is an increase of one percentage point, but a 20% change relative to where it started. Headlines often mix the two deliberately. When a number is itself a percentage, say both: “up one point, or 20% of the previous rate.”
Common mistakes
- Adding then subtracting the same percent. A 20% rise followed by a 20% fall does not return you to the start — you end 4% lower, because the second percentage applies to the larger number.
- Computing change from the wrong base. Percent change divides by the starting value. Reversing the direction gives a different magnitude: 50→65 is +30%, but 65→50 is −23%.
- Confusing percent with percentage point. A move from 2% to 3% is one point, not one percent.
- Dividing by the new value. Discounts and markups are easy to misread: a price marked down 25% then taxed 10% is not back to the original.
Frequently asked questions
How do I calculate a discount?
Use the X% of Y mode with the discount as X and the price as Y to get the amount off, then subtract it — or calculate the pay price directly by using (100 − discount)% of the original. A 30% discount on $80 removes $24, leaving $56.
How do I work out a reverse percentage?
If a price of $110 already includes 10% tax, the pre-tax amount is 110 ÷ 1.10 = $100, not 110 − 10%. Use the “is what percent” mode to check the pieces, or divide by one plus the rate for a clean reverse.
What is the difference between percent change and percent difference?
Percent change compares an old value to a new one and divides by the old value. Percent difference compares two values with no natural “before,” so it divides by their average instead. For most “how much did it change” questions, you want percent change.
Why does a 50% drop need a 100% rise to recover?
Because the recovery percentage is measured against the smaller base. Falling from $100 to $50 is a 50% loss, but getting from $50 back to $100 is a 100% gain. That asymmetry is why losses are harder to undo than they look.
Percentages sit behind most of the other tools here — a tip is a percentage of the bill, and markup and margin are two percentages of different bases. Once the three modes are clear, those tools stop being guessing games.