Percentage Calculator
Six calculators in one, and every answer shows the arithmetic behind it — so you can check the figure, or paste the working into an invoice, a homework sheet or an argument. Results appear as you type; nothing is sent anywhere.
The three everyday ones
Almost every percentage question in daily life is one of these three. Type into any two boxes and the answer appears underneath, with the formula it came from.
1. What is X% of a number?
2. X is what percent of Y?
3. Percentage increase or decrease
The three that catch people out
These are the percentage questions where the obvious method gives the wrong answer, and where the mistake usually costs money rather than marks. Each of the three below is a calculation the rest of this page used to explain in words and leave you to do by hand — which is a strange thing to do on a page that says these are the ones people get wrong. Now they run here, and each one tells you what the wrong answer would have been.
4. Percentage difference (when neither number came first)
Difference compares two numbers as equals — two quotes, two branches, two months that don't follow each other. If one of them came first, you want calculator 3 instead.
5. Reverse percentage — the figure before the discount or the tax
Use this whenever the number in front of you already includes the percentage: a sale price, a total with tax on it, a figure after a raise.
6. Stacked discounts
Separate them with commas. Works for two, three or more — "30, 20, 10" is fine.
How to calculate percentages
A percentage is simply a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." When you say 25%, you mean 25 out of every 100 — which is the same as the fraction 25/100 or the decimal 0.25.
Here are the formulas behind all six calculators above, in one place:
| Question | Formula | Example |
|---|---|---|
| What is 15% of 200? | (15 ÷ 100) × 200 | = 30 |
| 30 is what % of 150? | (30 ÷ 150) × 100 | = 20% |
| Change from 80 to 100? | ((100 − 80) ÷ 80) × 100 | = +25% |
| Difference between 80 and 100? | |80 − 100| ÷ ((80 + 100) ÷ 2) × 100 | = 22.22% |
| $80 after 20% off — original? | 80 ÷ (1 − 0.20) | = $100 |
| 30% then 20% off — total? | 1 − (0.70 × 0.80) | = 44% |
The pattern worth noticing is in the last two rows. When the percentage has already been applied to the number you are holding, you divide it out — you never subtract it. And when several percentages apply one after another, you multiply what is left rather than adding what is taken. Those two habits account for most percentage mistakes that reach a bank statement.
Real-life examples
Shopping discounts
A $60 jacket is 30% off. The discount is (30 ÷ 100) × 60 = $18, so you pay $42. Tip: for a quick mental estimate, find 10% first (move the decimal one place: $6) and multiply — 30% is simply 3 × $6.
Tipping at a restaurant
Your bill is $84 and you want to leave 18%. That's (18 ÷ 100) × 84 = $15.12. (We also have a dedicated tip calculator that splits the bill between friends.)
Salary raise
Your pay went from $52,000 to $56,000. The increase is ((56,000 − 52,000) ÷ 52,000) × 100 = 7.7%.
Percentage increase vs. percentage points
These two are often confused. If an interest rate rises from 4% to 6%, it increased by 2 percentage points — but by 50 percent (because 2 is half of 4). News headlines mix these up all the time, so it's a useful distinction to know.
Common mistakes to avoid
- Reversing a percentage change: a 20% drop followed by a 20% rise does not get you back to the start. $100 → $80 → $96. Calculator 3 above says so with your own numbers whenever you enter a change.
- Using the wrong base: percentage change is always measured against the original value, not the new one.
- Adding percentages of different bases: 10% of your rent plus 10% of your groceries is not 20% of anything meaningful.
- Reaching for change when you mean difference: if neither number came first, measuring against one of them arbitrarily picks a winner. Calculator 4 handles that case.
Working backwards: the reverse percentage
This is the calculation people get wrong most often, and it costs real money. If a jacket is on the rack at $80 after 20% off, the original price is not $80 + 20% = $96. The 20% was taken off the original price, not the sale price.
What $80 represents is 80% of the original. So divide, do not add:
original = sale price ÷ (1 − discount) → $80 ÷ 0.80 = $100
| You see | Discount taken | Wrong answer (adding back) | Correct original |
|---|---|---|---|
| $80 | 20% off | $96 | $100 |
| $45 | 25% off | $56.25 | $60 |
| $210 | 30% off | $273 | $300 |
| $108 | 10% added (tax) | $97.20 | $98.18 |
The same trap runs the other way with sales tax. To strip 10% tax from a $108 total you divide by 1.10 to get $98.18 — subtracting 10% would give $97.20 and quietly understate the pre-tax price. Anything of the form "the number I have already includes the percentage" is a division, never a subtraction. Calculator 5 above does both directions and shows you the wrong answer alongside the right one, because seeing the gap is what makes it stick.
Stacked discounts don't add up
"30% off, then an extra 20% at the till" sounds like 50% off. It is not, because the second discount applies to the already-reduced price:
$100 × 0.70 = $70 → $70 × 0.80 = $56 → total discount 44%, not 50%
The shortcut is to multiply what remains rather than add what is taken: 0.70 × 0.80 = 0.56, so you pay 56%. Two 50%-off coupons stack to 75% off, never 100% — which is why "the item is free" never happens. The order does not matter either: 30% then 20% and 20% then 30% both land on $56, so a shop offering to "apply the bigger one first" is offering nothing.
Percentages of percentages
When the thing being measured is itself a percentage, the language collapses. If a savings rate goes from 4% to 5%, that is either a 1 percentage point rise or a 25% increase, and both are correct. Headlines exploit this: "support surged 50%" reads dramatically but may mean a poll moved from 4% to 6%.
The rule for reading them: percentage points subtract, percentages divide. Going from 4% to 5% is 5 − 4 = 1 point, and 5 ÷ 4 = 1.25, a 25% increase. When you write the numbers yourself, say which one you mean — it is the single most common source of honest confusion in financial and statistical writing.
Frequently asked questions
How do I calculate a percentage without a calculator?
Find 10% by moving the decimal point one place left, then scale. For 35% of 80: 10% is 8, so 30% is 24, and 5% (half of 10%) is 4 — total 28.
How do I convert a fraction to a percentage?
Divide the top by the bottom and multiply by 100. For example, 3/8 = 0.375 = 37.5%.
What is a reverse percentage?
That's when you know the final value after a percentage change and want the original. If a price is $69 after a 25% discount, the original was 69 ÷ 0.75 = $92.
Can a percentage be greater than 100%?
Yes. If a value more than doubles, its increase is over 100%. Going from 40 to 100 is a 150% increase.
What is the difference between percentage change and percentage difference?
Percentage change needs a starting value and measures against it: 80 to 100 is a 25% change. Percentage difference treats the two numbers as equals and measures against their average: the difference between 80 and 100 is 22.22%. Use change when one value came first, difference when neither did.
Do two discounts of 30% and 20% add up to 50% off?
No. The second discount applies to the already-reduced price, so $100 becomes $70 and then $56 — a total of 44% off, not 50%. Multiply what remains (0.70 x 0.80 = 0.56) rather than adding what is taken.
How do I find the original price before a discount?
Divide, do not add back. A price of $80 after 20% off was $80 divided by 0.80 = $100. Adding 20% to $80 gives $96, which is wrong because the discount was taken off the original price, not off the sale price.