Percentage Calculator
Free percentage calculator. Work out X% of a number, what percent X is of Y, and percentage increase or decrease — instantly.
What is X% of Y?
30.00
15.00% of 200.00
X is what % of Y?
20.00%
30.00 out of 150.00
% increase / decrease
25.00%
Increase
Most percentage confusion comes from not being clear which of three different questions is being asked: what is X% of Y, what percentage is X of Y, or how much has something changed. This calculator handles all three separately so you cannot accidentally answer the wrong one.
Enter your numbers in the mode you need and the result appears instantly, along with the arithmetic used to get there.
How to use the Percentage Calculator
Choose the calculation type
Percentage of a number, one number as a percentage of another, or percentage increase and decrease.
Enter your two values
The labels change with the mode so it is always clear which number goes where.
Read the answer
The result updates as you type, with the working shown underneath.
Switch modes to cross-check
Answering the same question from the other direction is a quick way to confirm you framed it correctly.
The three core formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 15% of 240 = 36 |
| X is what % of Y? | (X ÷ Y) × 100 | 36 of 240 = 15% |
| % change from A to B | ((B − A) ÷ A) × 100 | 240 → 288 = +20% |
| Reverse percentage | total ÷ (1 + rate) | $120 after 20% off came from $150 |
Percentage increase and decrease do not cancel out
This is the single most common percentage error. A price that rises 20% and then falls 20% does not return to where it started.
Start at $100. Up 20% gives $120. Down 20% of $120 is a $24 fall, landing at $96 — a 4% net loss. The reason is that each percentage applies to a different base.
The same trap appears in investing: a portfolio that falls 50% needs a 100% gain to recover, not another 50%.
Percentage points versus percent
If an interest rate moves from 4% to 6%, it has risen by two percentage points — but by 50 percent. Both statements are true and they describe the same change.
News and marketing frequently blur this. When a figure is itself a percentage, always check whether a reported change is in points or in relative terms; the difference can be enormous.
Working backwards from a discounted price
To find an original price from a post-discount amount, divide rather than add back. An item costing $80 after 20% off came from 80 ÷ 0.80 = $100. Adding 20% to $80 gives $96, which is wrong.
The same applies to tax-inclusive totals: a $110 total including 10% tax came from 110 ÷ 1.10 = $100. Use the discount calculator for sale prices and the sales tax calculator for tax.
Mental shortcuts worth knowing
- 10% — move the decimal one place left. 10% of 847 is 84.7.
- 5% — half of 10%. 5% of 847 is 42.35.
- 1% — move the decimal two places. 1% of 847 is 8.47.
- Percentages are commutative. 18% of 50 equals 50% of 18 — which is just 9. Flip whichever way is easier.
- 15% — 10% plus half of it. 20% — 10% doubled.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply. 15% of 240 is 0.15 × 240 = 36.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. 36 out of 240 is (36 ÷ 240) × 100 = 15%.
How do I calculate percentage change?
Subtract the old value from the new, divide by the old value, then multiply by 100. From 240 to 288 is ((288 − 240) ÷ 240) × 100 = 20% increase.
What is the difference between percent and percentage points?
A move from 4% to 6% is two percentage points, but a 50% relative increase. Points describe absolute movement between percentages; percent describes relative change.
Why does 20% off then 20% on not return to the start?
Because the second percentage applies to a different base. $100 up 20% is $120; 20% off $120 is $96, not $100.
How do I find the original price before a discount?
Divide the sale price by one minus the discount. $80 after 20% off came from 80 ÷ 0.80 = $100.
How much gain do I need to recover a loss?
More than the loss. Down 20% needs +25%; down 50% needs +100%; down 80% needs +400%.
Can percentages exceed 100?
Yes, whenever the part is larger than the whole — growth from 50 to 150 is a 200% increase. It only becomes meaningless for proportions of a fixed total.
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