What is X% of Y?
X is what percent of Y?
Percent change from X to Y
About the Percentage Calculator
This free percentage calculator handles the three everyday percentage questions:
- What is X% of Y? — a tip, a discount, a tax, a commission
- X is what percent of Y? — a score, a share, a completion rate
- Percentage increase or decrease — a price change, a pay rise, growth between two months
Type the numbers and the answers update instantly, all in your browser. Nothing is uploaded.
The three calculations, and which one you need
Most percentage confusion is really a question of which of the three you are looking at. Once you can name it, the arithmetic is easy.
Finding a part of a whole — "What is 20% of 80?" Multiply: 80 × 0.20 = 16. This is tips, sales tax, discounts and commission.
Finding what portion something is — "16 is what percent of 80?" Divide then multiply by 100: 16 ÷ 80 × 100 = 20%. This is exam scores, market share and progress bars.
Finding the change between two numbers — "From 80 to 100, what changed?" Take the difference, divide by the original, multiply by 100: (100 − 80) ÷ 80 × 100 = 25%. This is prices, salaries and traffic over time.
The third one is where mistakes live, and always in the same place: the divisor. The change is always measured against where you started, never where you ended.
Why a 50% drop needs a 100% rise to recover
This surprises people every time, and it is the most useful percentage fact there is.
A price goes from 100 to 50. That is a 50% fall — the change is 50, divided by the original 100.
Now go back up: from 50 to 100. The change is still 50, but now it is divided by 50. That is a 100% rise.
The same movement is 50% one way and 100% the other, because the starting point changed. A 25% loss needs a 33% gain to undo. An 80% crash needs a 400% recovery. This is exactly why a stock that halves feels so much worse than it looks.
The rule underneath: percentages are not symmetric, and they do not add up across different bases.
Percent vs percentage point
A small distinction that changes the meaning completely, and news reports get it wrong constantly.
An interest rate moves from 2% to 3%. That is a rise of one percentage point. It is also a rise of 50 percent, because 1 is half of 2.
Both are correct. They measure different things, and the difference is not small — someone describing that same change as "up 1%" or "up 50%" is telling you two very different stories about the same number. When the thing being measured is itself a percentage, say percentage points for the absolute move and percent for the relative one.
Discounts that stack
Two discounts do not add. A shop offering "40% off, then an extra 20% off at the till" is not giving you 60%.
The second discount applies to the already-reduced price. On a 100 item: 40% off leaves 60, then 20% off that leaves 48. That is 52% off in total, not 60%. You saved four units less than the sign implied.
The same applies to price rises. Two 10% increases are not 20% — they are 21%, because the second builds on the first. Anything applied one after the other compounds instead of adding.
How to use it
- Pick the calculation you need
- Enter your numbers — the result updates as you type
Good to know
- Percent means "per hundred". 25% is just another way of writing 0.25 or 25/100.
- To find a percentage quickly, move the decimal. 10% of any number is that number with the decimal shifted one place left — 10% of 84 is 8.4. Halve it for 5%, double it for 20%.
- X% of Y is the same as Y% of X. 8% of 25 equals 25% of 8, which is 2. Sometimes the reversed version is far easier to do in your head.
- Percent change always divides by the original number. Dividing by the new one is the single most common error.
- You cannot average percentages that come from different-sized groups. A 90% pass rate in a class of 10 and 50% in a class of 90 is not a 70% average — it is 54%.
- A discount then tax is not the same as tax then discount in every tax system, so check the order your receipt uses.
Common questions
How do I calculate a percentage of a number?
Convert the percentage to a decimal and multiply. For 20% of 80, use 80 × 0.20 = 16. To go the other way and find what percent one number is of another, divide and multiply by 100: 16 ÷ 80 × 100 = 20%. The calculator above does both without the conversion step.
How do I work out percentage increase or decrease?
Subtract the old value from the new one, divide by the old value, then multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase. A negative result is a decrease. The critical detail is dividing by the original number — dividing by the new one gives a different and wrong answer.
Why isn't a 50% decrease cancelled by a 50% increase?
Because each percentage is measured against a different starting number. Falling 50% from 100 lands at 50. Rising 50% from 50 only reaches 75, since the 50% is now taken from the smaller figure. To return to 100 you would need a 100% rise. Percentage moves are not reversible by the same percentage.
What is the difference between percent and percentage points?
A percentage point is the plain arithmetic difference between two percentages; a percent is the relative change. Going from 2% to 3% is one percentage point, and also a 50% increase. Both describe the same event, so the term matters — "percentage points" removes the ambiguity when the thing you are measuring is already a percentage.
Do two discounts of 20% and 30% make 50% off?
No. They compound, because the second is taken off the already-reduced price. A 100 item drops to 80 with 20% off, then to 56 with a further 30% off — that is 44% off in total, not 50%. Stacked discounts always come to less than their sum, and stacked increases always come to more.
How do I calculate a tip?
Take the bill and multiply by the tip rate — 18% of 45 is 45 × 0.18 = 8.10. A quick mental method: find 10% by moving the decimal one place left, then halve that for 5% and add the pieces you need. For 15% of 45: 4.50 plus 2.25 is 6.75.
Does this calculator send my numbers anywhere?
No. Everything is calculated by your browser as you type, so no number ever leaves your device. The tool keeps working with your connection switched off.
Related tools
- Discount Calculator — sale prices and stacked discounts worked out for you
- Tip Calculator — tips and splitting a bill between people
- Sales Tax Calculator — add or remove tax from a price
- Compound Interest Calculator — what repeated percentage growth does over time
