What this calculates
This tool handles the five percentage questions that come up most often: a percentage of a number, a number increased or decreased by a percentage, what percentage one number is of another, and the percentage difference between two values. Pick the question from the dropdown and the answer updates as you type — there is no Calculate button.
Every answer comes with the arithmetic that produced it, so you can check the working or copy it into homework, an invoice or a message.
The formula
Each mode uses a different formula. All five reduce to the same idea: a percentage is a fraction with 100 on the bottom.
Percentage of a number
number × (percent ÷ 100)Increase by a percentage
number + (number × percent ÷ 100)Decrease by a percentage
number − (number × percent ÷ 100)X is what percent of Y
(X ÷ Y) × 100Percentage difference between A and B
|A − B| ÷ ((A + B) ÷ 2) × 100The last one is the odd one out. Percentage change measures movement from a starting value and divides by that value. Percentage difference compares two values that have no natural order, so it divides by their average instead — which is why swapping A and B changes nothing.
Worked example
Now run it backwards to check. If you know the jacket dropped from 2,400 to 1,560, what percentage came off? Switch to X is what percent of Y with the saving as the part and the original as the whole: 840 ÷ 2,400 = 0.35, or 35%. The two modes agree, which is the fastest way to catch a mistake.
When to use it, and the mistakes to avoid
Reach for this calculator for discounts and sale prices, tips and service charges, marks and grades, commission and interest, test coverage and pass rates, and any time you need to describe a change in plain language.
A few traps catch people out repeatedly:
- Percentages don't reverse. Up 10% then down 10% leaves you below where you started, because the second percentage is taken from a bigger number. Use the X is what percent of Y mode to recover the true change.
- Percentage points are not percentages. A rate moving from 5% to 7% has risen by two percentage points, but by 40% in percentage terms. Both are correct; say which one you mean.
- Don't add percentages of different totals. 20% of one number plus 20% of another is not 20% of anything unless the totals match. Add the amounts, then take the percentage of the combined total.
- Choose the right denominator. "What percent is X of Y" puts the part on top and the whole underneath. Flipping them answers a genuinely different question.
- Round once, at the end. Rounding a percentage mid-calculation carries the error into every step after it.
FAQ
How do I calculate a percentage of a number by hand?
Divide the percentage by 100, then multiply by the number. For 15% of 200: 15 ÷ 100 = 0.15, and 0.15 × 200 = 30. For the round numbers you meet most often there are shortcuts — 10% is the number with the decimal point moved one place left, 5% is half of that, and 20% is double it.
Why doesn't a 10% rise followed by a 10% fall bring me back to where I started?
Because the second percentage is taken from a different, larger number. 100 increased by 10% is 110, but 10% of 110 is 11, not 10 — so taking it off leaves 99. The bigger the percentage, the bigger the gap: a 50% rise then a 50% fall leaves you 25% below where you began.
What is the difference between percentage change and percentage difference?
Percentage change has a direction: it measures how far a value moved from a known starting point, and it divides by that starting value. Percentage difference has no direction — it compares two values of equal standing by dividing by their average, so swapping the two values gives the same answer.
Can a percentage be more than 100?
Yes. 100% simply means the whole of something, so 250% of 40 is 100 — two and a half times the original. Percentages above 100 are normal for growth, markups and returns. They only look wrong when the quantity genuinely cannot exceed the whole, such as a share of votes cast.
How do I work out what percentage one number is of another?
Divide the part by the whole, then multiply by 100. If 30 students out of 200 passed, that is 30 ÷ 200 = 0.15, and 0.15 × 100 = 15%. Keep the part on top: dividing the other way round answers a different question.
Do percentage results need rounding?
Round only at the very end, and only for display. Rounding partway through — for example turning 22.222% into 22% before multiplying — pushes the error into every step that follows. This calculator carries the full precision through the working and rounds only what you see.