Four formulas cover almost every percentage you will ever need to calculate. X% of Y is X ÷ 100 × Y. X as a percentage of Y is X ÷ Y × 100. The change from X to Y is (Y − X) ÷ X × 100. Y increased or cut by X% is Y × (1 ± X ÷ 100). None of them is harder than one multiplication and one division. What goes wrong is deciding which question you have and which number belongs on the bottom.
Which question are you actually asking?
Naming the shape of the problem takes two seconds and prevents most of the errors. The four, with numbers in them:
- What is X% of Y?
X ÷ 100 × Y. 18% of 47.50 is 0.18 × 47.50 = 8.55. Tips, commission, sales tax, a slice of a budget. - X is what percent of Y?
X ÷ Y × 100. 37 out of 50 is 37 ÷ 50 = 0.74, so 74%. Test scores, conversion rates, market share. - What is the change from X to Y?
(Y − X) ÷ X × 100. From 250 to 310 is 60 ÷ 250 = 0.24, so up 24%. The number you started at is the base. - What is Y increased or reduced by X%? Multiply by
1 + X ÷ 100or1 − X ÷ 100. A 15% rise on 200 is 200 × 1.15 = 230.
If you are switching between those all afternoon, the percentage calculator here has a button for each one and prints the sum it used underneath the answer. That line is the useful part: when a result looks wrong, it is usually because the tool read your numbers differently from how you meant them. It accepts both 1,234.56 and 1.234,56, with one case it cannot resolve — a lone comma followed by exactly three digits is always a thousands separator, so 1,500 is fifteen hundred. If you meant one and a half, type 1.5.
How to do it in your head
You only ever need to find two values directly: 10% and 1%. Everything else is addition and halving.
10% is the decimal point moved one place to the left. 1% is two places. From there, 5% is half of 10%, 20% is 10% doubled, and 15% is 10% plus 5%. To get 18% of 47.50, take 20% — that is 9.50 — and subtract 2%, which is 0.95. You land on 8.55, which is the exact answer, not an estimate.
Why X% of Y equals Y% of X
Both come out as X × Y ÷ 100, so the order never matters. 8% of 25 looks like work. Flip it: 25% of 8 is a quarter of eight, which is 2. Same answer. 4% of 75 becomes 75% of 4, which is 3. Whenever a percentage looks awkward, reverse the two numbers and check whether the flipped version is something you already know.
The percentages that are really fractions
- 50% is a half
- 25% is a quarter
- 20% is a fifth
- 12.5% is an eighth
- 33.3% is a third, near enough for anything that is not an invoice
Recognising these turns a multiplication into a division you can do standing up. 12.5% of 640 is 640 ÷ 8 = 80.
Use a multiplier instead of two steps
To add 15%, multiply by 1.15. To take 15% off, multiply by 0.85. One operation rather than two, and no chance of calculating the change and then forgetting which direction it went.
The habit earns its keep the moment you have to run the sum backwards. If a price of 120 already includes a 20% markup, the price before the markup is not 120 minus 20%. It is 120 ÷ 1.2 = 100. Subtract instead and you get 96, which is wrong by four with no obvious reason why. The same trap catches everyone who tries to strip tax out of a gross figure: pulling 20% VAT out of a total means dividing by 1.2, which is why adding VAT and removing it again need two sums that do not look like mirror images.
Why percentages refuse to add up
Percentages applied one after another multiply. They do not add, and treating them as though they do is where most confident wrong answers come from.
A salary of 40,000 that rises 5% one year and 4% the next is not up 9%. The multipliers compound: 1.05 × 1.04 = 1.092, so it is up 9.2%, and the salary is 43,680. Two tenths of a point sounds like rounding, but the gap widens with the percentages. Two successive 30% rises give 1.3 × 1.3 = 1.69, which is 69% up, not 60%.
The same rule explains three things that feel like paradoxes and are not:
- A 20% fall followed by a 20% rise leaves you down, not level: 0.8 × 1.2 = 0.96, so 4% short.
- A 50% loss needs a 100% gain to recover. Halve something and it has to double to get back.
- A rise of p% is undone by a fall of
p ÷ (100 + p)%. To reverse a 20% increase you need a 16.67% decrease, because the second percentage is taken from a bigger number.
Shop signs are where this costs money. A rack at 40% off with a further 15% off at the till leaves you paying 0.6 × 0.85 = 0.51 of the ticket, so 49% off rather than 55%. A calculator that stacks two discounts does that multiplication and runs it backwards from a sale price as well; the rest of that arithmetic — vouchers, multibuys, finding the price before the reduction — is in how to calculate a discount in your head.
Percent or percentage point?
These measure different things and the difference is not pedantry. A mortgage rate moving from 4% to 5% has risen one percentage point, and has also risen 25%. Both statements are true, and which one gets printed usually depends on how dramatic the writer wants to sound.
The rule: percentage points for the gap between two percentages, percent for the size of a change measured against where it started. A candidate going from 30% to 33% in a poll gained three percentage points, or ten percent.
Why the base matters more than the percentage
"Sales are up 300%" is not information until someone says up from what, and over what period. Three sales becoming twelve is up 300%. So is three million becoming twelve million. The percentage is identical and the two facts are nothing alike.
Two specific confusions to watch for:
- "200% of" is not "200% more than." 200% of 50 is 100. An increase of 200% on 50 gives 150. The gap between those two readings is an entire extra copy of the original number.
- You cannot average percentages unless the bases match. If 50% of a ten-person team hit their target and 90% of a ninety-person team did, the overall figure is 86%, not 70%. Add the parts, add the wholes, and divide once at the end.
How to check an answer you do not trust
Three checks, in the order that catches the most mistakes:
- Is it on the right side of 100? If the part is smaller than the whole, the answer has to be under 100%, so a result of 800% means the division went the wrong way round. Percentage change is the exception — that one can legitimately be any size.
- Round and estimate. 17% is close to a sixth, and a sixth of 300 is 50, so 17% of 312 should land near 50. The exact answer is 53.04. Anything near 5 or 530 is a decimal point in the wrong place.
- Multiply back. If you worked out a 24% increase starting from 250, check that 250 × 1.24 really is 310.
Where these shortcuts fall short
Mental arithmetic is for estimating and for checking, not for anything that has to balance. Rounding each line of a document separately and then adding them up can give a different total from applying the percentage once to the total — usually by a cent or two, which is exactly the size of error someone notices.
Two more limits worth knowing. Percentages of money run into ordinary binary floating point: ask a browser for 0.1 + 0.2 and it returns 0.30000000000000004, because neither value has an exact binary form. Every calculator built on the same arithmetic has the same gap; most round it away before you see it, and the one here rounds for display too. At two decimal places it never shows. And percentage change from a starting value of zero has no answer at all, because the formula divides by that starting value. Quote the absolute difference instead — "went from 0 to 40" says something, and "up 4000%" does not.
Each of the four questions gets its own button in the percentage calculator, which shows the arithmetic it used under every result so you can see how it read your numbers. It runs in this tab, with nothing sent anywhere.
A restaurant table is where this arithmetic usually has to happen fast, and the figure to aim for is not the same everywhere — how much to tip, by country covers what is actually expected where.
Frequently asked questions
How do you calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. 18% of 47.50 is 0.18 × 47.50 = 8.55. In your head it is easier to build the answer from 10% and 1%: 20% of 47.50 is 9.50, minus 2% (0.95), which gives the same 8.55.
How do I work out a percentage increase?
Subtract the old value from the new one, divide by the old value, then multiply by 100. Going from 250 to 310 is 60 ÷ 250 × 100 = 24%. The starting value always goes on the bottom. Dividing by the new value instead is the usual slip, and it quietly gives a smaller number.
What is the fastest way to calculate percentages in your head?
Find 10% by moving the decimal point one place left, and 1% by moving it two places, then add and halve those to build what you need. It also helps to remember that X% of Y equals Y% of X, so 8% of 25 can be read as 25% of 8, which is 2.
How do I remove a percentage that has already been added to a price?
Divide by the multiplier instead of subtracting the percentage. A price of 120 that includes a 20% addition came from 120 ÷ 1.2 = 100, not from 120 minus 20%, which would give 96. In general, an increase of p% is reversed by a decrease of p ÷ (100 + p) percent.
What is the difference between a percent and a percentage point?
A percentage point is the gap between two percentages; a percent is the size of a change measured against where it started. A rate going from 4% to 5% has risen one percentage point, and has also risen 25%. Both are accurate, and the bigger-sounding one tends to be the one that gets printed.
Can you average two percentages?
Only if they are measured against groups of the same size. If 50% of a ten-person team hit their target and 90% of a ninety-person team did, the combined figure is 86%, not the 70% you get by averaging the two percentages. Add the parts, add the wholes, and divide once at the end.
Last updated September 19, 2026