Percentage Calculator
Instantly calculate percentages, percentage increase/decrease, percentage change, and reverse percentages, with full step-by-step working shown for every result.
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How This Calculator Works
Most percentage calculators only handle one type of question, usually just "X% of Y." But if you've ever tried to work out a rent increase, check a discount, or figure out what percentage of a test you got right, you know percentage problems don't all fit that one shape. This tool has five modes so you can pick the one that actually matches what you're trying to work out, rather than forcing your question into the wrong formula.
Related Calculators
1. Basic Percentage: X% of Y
This is the one everyone knows: working out a tip, a discount, or how much tax gets added to a total.
Say you're leaving a 15% tip on a $67 bill:
(15 ÷ 100) × 67 = $10.05
2. X is what percent of Y?
This one flips the question around. You already have both numbers and want to know the relationship between them. A test score is the classic example, but it's the same maths as working out what share of your income goes toward rent.
You got 30 out of 200 on a quiz:
(30 ÷ 200) × 100 = 15%
3. Percentage Increase or Decrease
Whenever there's a "before" and an "after" (a pay raise, a price hike, weight lost, a growth rate), this is the formula that applies. It's also the one people get wrong most often, because the direction of the change matters (more on that below).
Rent went from $80 to $100 a month:
((100 − 80) ÷ 80) × 100 = 25% increase
4. Reverse Percentage
Sometimes you know the end result and the percentage, but not the original number. This comes up a lot with sale prices, where a tag might say "this is 70% of the original price" without telling you what that original price actually was.
$45 is 15% of what number?
45 ÷ (15 ÷ 100) = $300
5. Percentage Difference
This last one is a bit different from the rest. There's no "original" value here, just two numbers you want to compare on equal footing. It's the right tool for comparing prices between two stores, or two measurements that came from different sources.
Store A sells an item for $120, Store B for $150:
(|120−150| ÷ ((120+150)÷2)) × 100 = 22.2% difference
Where This Actually Comes Up
Bills & Expenses
A payslip breaks down tax and pension contributions as percentages of gross pay, and it's worth actually checking those numbers rather than assuming they're right. Rent increases are a good example of where this matters: if your lease caps increases at 5% and your rent goes from $1,400 to $1,470, is that within the limit? ((1470−1400)÷1400)×100 works out to exactly 5%, right at the cap and not over it. Small differences like this are easy to miss if you're just eyeballing the numbers.
Shopping & Discounts
A "30% off" sticker only tells you the discount rate, not the actual price. And "buy one, get one 50% off" deals are often less generous than they sound once you work out the true average discount across both items. If a jacket is marked down to $42 and the tag claims 30% off, you can check that yourself: 42 ÷ (70÷100) = $60, so the maths holds up. Comparing pack sizes at the supermarket is a similar case, except that's really a percentage-difference question rather than a basic one, which is part of why it helps to have more than one mode available. If you'd rather work in fractions than percentages for a comparison like this, the Fraction Calculator handles the same maths in that format.
Students
Percentage questions turn up outside of maths class more than people expect: percentage yield in chemistry, population growth in geography, profit margin in a business studies assignment, all using the same handful of formulas above, just dressed up differently depending on the subject. Checking your own working against a calculator that shows its steps (rather than just spitting out a final number) tends to catch a different kind of mistake than checking the answer alone. Usually it's the formula choice that's wrong, not the arithmetic.
Work
Quarterly revenue growth, a supplier's price increase, margin on a product line, how much of a budget's been spent. These are all percentage-change questions, and they're worth double-checking in a spreadsheet since it's easy to divide by the wrong base number without noticing (see below).
Percentage Formulas at a Glance
| Question type | Formula | Example |
|---|---|---|
| X% of Y | (X ÷ 100) × Y | 15% of 200 = 30 |
| X is what % of Y | (X ÷ Y) × 100 | 30 is 15% of 200 |
| % increase/decrease | ((New−Orig)÷Orig)×100 | 80→100 = +25% |
| Reverse percentage | Result ÷ (Pct÷100) | 45 is 15% of 300 |
| % difference | (|A−B|÷((A+B)÷2))×100 | 120 vs 150 = 22.2% |
Common Mistakes
Frequently Asked Questions
How do I calculate a percentage increase between two numbers?
Subtract the original value from the new value, divide by the original value, then multiply by 100. Use the "% Increase / Decrease" tab above and it will show each step.
What's the difference between "percentage of" and "percentage change"?
"Percentage of" finds a portion of a fixed number (e.g. 20% of 50 = 10). "Percentage change" compares two different numbers to see how much one grew or shrank relative to the other. They use different formulas and answer different questions.
How do I reverse a percentage to find the original number?
Divide the known result by the percentage (expressed as a decimal). For example, if $45 is 15% of an unknown number, divide 45 by 0.15 to get 300. Use the "Reverse Percentage" tab above.
Why is my percentage increase and decrease not symmetrical?
Because the "original" value changes depending on direction. Going from 100 to 80 is a 20% decrease, but going back from 80 to 100 is a 25% increase, since 25% is calculated against the smaller base of 80, not 100.
Can I use this calculator for discounts and sale prices?
Yes. Use the basic "X% of Y" mode to find the discount amount, or the "Reverse Percentage" mode if you know the sale price and want to find the original price.
If I apply a 10% decrease then a 10% increase, do I end up back where I started?
No. Each percentage change applies to the current value, not the original one, so a 10% decrease followed by a 10% increase leaves you slightly below where you started ($100 drops to $90, then rises to $99, not back to $100). This is one of the most common percentage misunderstandings, covered in the "Common Mistakes" section above.
What's the difference between percentage change and percentage difference?
Percentage change compares a "before" and "after" value and depends on direction (which number is original). Percentage difference compares two values symmetrically with no assumed order, which makes it better suited to comparisons like pricing between two stores. Use the "% Difference" tab above for this case.