Percentage Calculator: Every Variant, Explained
Six different percentage questions, one calculator, and the working shown every time. Most percentage mistakes are not arithmetic slips — they come from picking the wrong starting number, and that is the thing this page is really about.
Work out a share of a number — a tip, a commission, a deposit, a test score.
What is 15% of 80?
12
How it was worked out
(15 ÷ 100) × 80 = 0.15 × 80 = 12
Every calculation is carried out at full precision and only rounded when it is printed, so a rounded figure never feeds the next step. Results are shown to four decimal places (more for very small numbers) and trailing zeros are dropped. Everything runs in your browser; nothing you type is sent anywhere.
TL;DR
A percentage is always a share of something, and the something changes as you move. That is why 40 up to 50 is a 25% rise while 50 back down to 40 is only a 20% fall — the same 10 either way. The same asymmetry means a 50% loss needs a 100% gain to break even, that a discount cannot be reversed by adding it back, and that stacked discounts multiply instead of adding. Three things to carry away: percentages are not symmetric, percentage points and percent are different words, and when you know the after-figure you divide rather than add.
The same 10 is a 25% rise and a 20% fall
Go from 40 to 50 and you have added 10 to a starting number of 40, so the rise is 10 ÷ 40 = 25%. Come straight back down from 50 to 40 and you have taken the very same 10 off a starting number of 50, so the fall is 10 ÷ 50 = 20%. Nothing about the money changed. Only the base did. Every percentage question you will ever ask is secretly the question a share of what, exactly?
| The pair | Gap | Going up | Coming back down |
|---|---|---|---|
| 40 and 50 | 10 | +25% | −20% |
| 80 and 100 | 20 | +25% | −20% |
| 120 and 150 | 30 | +25% | −20% |
| 15 and 20 | 5 | +33.3333% | −25% |
| 100 and 150 | 50 | +50% | −33.3333% |
Where this costs money: a shop that raises a price 25% and later advertises “25% off” has not put it back where it was — it has left the price 6.25% below the original. And a salary cut of 10% followed by a 10% rise leaves you on 99% of what you earned before, not 100%.
Why a 50% loss needs a 100% gain
This is the asymmetry at its most expensive. Losses are measured against the bigger number you had; the recovery is measured against the smaller number you are left with. Halve 100 and you have 50, and turning 50 back into 100 means doubling it. The gap between the two figures widens fast, which is why the table below is worth keeping.
| You lose | Left from 100 | Gain needed to break even |
|---|---|---|
| −5% | 95 | +5.2632% |
| −10% | 90 | +11.1111% |
| −20% | 80 | +25% |
| −25% | 75 | +33.3333% |
| −30% | 70 | +42.8571% |
| −40% | 60 | +66.6667% |
| −50% | 50 | +100% |
| −60% | 40 | +150% |
| −70% | 30 | +233.3333% |
| −80% | 20 | +400% |
| −90% | 10 | +900% |
Read the last few rows slowly. A 90% fall is not “90% away” from recovery — it needs a 900% gain, a tenfold return, to get back to where it started. This is arithmetic, not investment advice, and it applies to any quantity that falls and has to climb back: a savings pot, a follower count, a monthly sales figure.
Percentage points and percent are not the same word
When the thing that moved is itself a percentage — an interest rate, an unemployment rate, a poll share, a tax band — there are two correct answers and they sound nothing alike. The percentage-point change is the plain gap: 4% to 6% is 2 points. The relative change compares that gap to the starting rate: 2 ÷ 4 = 50%. Both are true. Neither is a lie. But whichever one somebody chooses to put in the headline is telling you what they want you to feel, and that choice is the single most common percentage error in reporting.
| Rate moves | Point change | Relative change | How it usually gets reported |
|---|---|---|---|
| 2% → 3% | +1 pp | +50% | “Half as many again” — the relative figure is the one that runs. |
| 0.5% → 1% | +0.5 pp | +100% | “Risk doubles.” Half a point of real-world risk, reported as a doubling. |
| 4% → 6% | +2 pp | +50% | A mortgage rate. Lenders say “up 2 points”, borrowers feel the 50%. |
| 12% → 15% | +3 pp | +25% | Both numbers get used, usually whichever suits the argument. |
| 30% → 33% | +3 pp | +10% | Same 3 points as the row above, but only a 10% rise. The base decides. |
| 45% → 48% | +3 pp | +6.6667% | Poll shares. Here the point change is the honest one to quote. |
| 5% → 4% | −1 pp | −20% | “A fifth lower” for a press release, “down one point” for a footnote. |
| 8% → 6% | −2 pp | −25% | Unemployment. “Down a quarter” is the campaign line. |
Notice rows four, five and six: 12% → 15%, 30% → 33% and 45% → 48% are all a 3-point move, yet they read as +25%, +10% and +6.6667%. The point change is identical; only the starting rate differs. If a figure ever sounds shocking, the first question to ask is what it started from. The tool’s Percentage points tab gives you both numbers side by side so you never have to pick blind.
Working backwards: divide, never add it back
You paid 96 in a 20%-off sale. What was the ticket price? The instinct is to add 20% to 96, which gives 115.20 — and it is wrong, for exactly the reason the whole page has been circling. That 20% was a share of the original price, not of what you handed over. The original is 96 ÷ 0.8 = 120. The same logic runs in reverse for tax: if a 120 total includes 20% tax, the pre-tax figure is 120 ÷ 1.2 = 100, not 120 minus 20% (which would give 96).
| You paid | Discount was | Original (divide) | If you add it back | You’d be out by |
|---|---|---|---|---|
| 96 | 20% | 120 | 115.20 | 4.80 |
| 45 | 10% | 50 | 49.50 | 0.50 |
| 80 | 20% | 100 | 96 | 4 |
| 120 | 40% | 200 | 168 | 32 |
| 59.99 | 25% | 79.99 | 74.99 | 5 |
The last row is rounded to the nearest cent: 59.99 after 25% off comes from an original of 79.9867, which no shop would price, so read it as a 79.99 ticket. Use the Reverse percentage tab for any of these — it also tells you the cash amount you saved, or the tax portion inside a gross figure. If you are checking a sales-tax line specifically, the GST calculator does the same job with the tax rates already built in.
Two discounts multiply — they never add
“20% off, plus an extra 10% at the checkout” is not 30% off. The extra 10% is taken from the already reduced price, so the two shrink each other: 0.8 × 0.9 = 0.72, meaning you pay 72% and the real discount is 28%. The bigger the discounts, the wider the gap between what it sounds like and what it is. Two 50%-off deals do not make anything free; they make it 75% off.
| Stacked offer | Sounds like | Actually is | You pay, on 100 |
|---|---|---|---|
| 10% then 10% | 20% | 19% | 81 |
| 20% then 10% | 30% | 28% | 72 |
| 20% then 20% | 40% | 36% | 64 |
| 25% then 25% | 50% | 43.75% | 56.25 |
| 30% then 20% | 50% | 44% | 56 |
| 40% then 30% | 70% | 58% | 42 |
| 50% then 20% | 70% | 60% | 40 |
| 50% then 50% | 100% | 75% | 25 |
One useful consequence: the order does not matter. 20% then 10% and 10% then 20% both land on 72, because multiplication does not care which factor comes first. The calculator above handles one percentage at a time, so to stack them use the Add or subtract % tab twice, feeding the first answer into the second. The same multiply-don’t-add rule is why repeated inflation years compound — our inflation calculator chains them for you.
The percentages you actually look up
Tips, sales tax, deposits, commission, VAT, a service charge — most everyday percentage questions are one of a small handful of rates against a round number. This is the grid to screenshot. Read across from the percentage to the number.
| Of → | 20 | 50 | 80 | 150 | 250 | 1,000 |
|---|---|---|---|---|---|---|
| 1% | 0.2 | 0.5 | 0.8 | 1.5 | 2.5 | 10 |
| 5% | 1 | 2.5 | 4 | 7.5 | 12.5 | 50 |
| 10% | 2 | 5 | 8 | 15 | 25 | 100 |
| 12.5% | 2.5 | 6.25 | 10 | 18.75 | 31.25 | 125 |
| 15% | 3 | 7.5 | 12 | 22.5 | 37.5 | 150 |
| 18% | 3.6 | 9 | 14.4 | 27 | 45 | 180 |
| 20% | 4 | 10 | 16 | 30 | 50 | 200 |
| 25% | 5 | 12.5 | 20 | 37.5 | 62.5 | 250 |
| 50% | 10 | 25 | 40 | 75 | 125 | 500 |
| 75% | 15 | 37.5 | 60 | 112.5 | 187.5 | 750 |
Two shortcuts worth memorising instead of the whole grid. First, 10% is the decimal point moved one place left, and everything else is built from it: 5% is half of 10%, 15% is 10% plus 5%, 20% is 10% doubled. Second, percentages are reversible — 18% of 50 is exactly the same as 50% of 18, which is 9, and the second version is the easy one. Swap them whenever it helps.
What the calculator does, and where it stops
Six tabs, two numbers each, and every answer comes with the line of arithmetic that produced it plus a plain-English note where the result is easy to misread. Sums run at full precision and are only rounded when printed, so a rounded figure never feeds the next step. Everything happens in your browser — nothing you type is sent anywhere, there is no account, and nothing is saved between visits.
- % of a number — tips, commission, deposits, a share of a bill.
- X is what % of Y — a mark out of a total, a slice of a budget, a conversion rate.
- Increase or decrease — the change between two numbers, with the direction spelled out in words.
- Add or subtract % — put tax or a rise on top, take a discount or a fee off.
- Reverse percentage — the before-figure when you only know the after-figure.
- Percentage points — both answers when the thing that moved was itself a rate.
Where it stops, plainly: it works on one percentage at a time, so stacked discounts and multi-year compounding need you to run it twice or reach for a dedicated tool. It has no history, no saved sums and no export. And a few questions genuinely have no answer rather than a wrong one — percentage change from zero, or anything as a percentage of zero — so the tool refuses those and says why instead of printing a number. For money questions that need compounding over time, the compound interest calculator and the loan comparison tool are built for it.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12. The mental shortcut is to find 10% by moving the decimal point one place left, then build from there: 10% of 80 is 8, half of that is 4, so 15% is 12.
Why is a 25% increase cancelled out by only a 20% decrease?
Because the two percentages are measured against different starting numbers. Going 40 to 50 divides the gap of 10 by 40, which is 25%. Going 50 back to 40 divides the same gap of 10 by 50, which is 20%. The gap never changed; the base did. Percentage rises and falls are never symmetric.
What is the difference between percentage points and percent?
A percentage point is the plain arithmetic gap between two percentages. Percent change compares that gap to where you started. A rate moving from 4% to 6% rose 2 percentage points and rose 50% in relative terms. Both are true, and whichever one someone quotes tells you what they want you to feel.
How do I find the original price before a discount?
Divide, do not add back. If you paid 96 after 20% off, the original was 96 divided by 0.8, which is 120. Adding 20% to 96 gives 115.20, which is wrong by 4.80, because the 20% was a share of the larger original price and not of the price you actually paid.
Is 20% off and then 10% off the same as 30% off?
No, it comes to 28% off. The second discount applies to the already reduced price, so the two multiply rather than add: 0.8 × 0.9 = 0.72, leaving you paying 72% of the original. Stacked discounts always come out smaller than the sum, and the gap widens as the discounts get bigger.
How much do I have to gain back after a 50% loss?
100%. A 50% loss leaves you with half, and turning half back into the whole means doubling it. The required recovery grows much faster than the loss: 20% down needs 25% up, 50% down needs 100% up, and 80% down needs 400% up just to return to where you started.