Percentage Calculator
The four percentage questions in one place — including the two that people reliably get wrong.
Runs entirely in your browser. Nothing you enter is uploaded.
Written and maintained by ReadoutKit / Takashi Yamazaki
How this works
Four questions that look like one
Almost every percentage problem is one of four questions, and the arithmetic for each is a single line. What makes them worth a dedicated tool is not the difficulty of the division but how easily the four get confused with one another, and how convincing a wrong answer looks once it is written down.
A percentage of a total. 15% of 200 is 30. Multiply by the rate over a hundred. This is the one people rarely get wrong.
One number as a share of another. 30 out of 200 is 15%. Divide the part by the whole. The common slip here is inverting the fraction, which turns a 15% share into a 667% one — an error large enough to notice, which is why it does less damage than the subtler mistakes below.
Change between two figures. Going from 200 to 250 is a 25% rise, because the 50 is measured against the 200 you started from. Going back from 250 to 200 is a 20% fall, because the same 50 is now measured against 250. The asymmetry surprises people every time, and it is the root of the next two sections.
Raising or cutting a value. Adding 15% to 200 gives 230. Straightforward forwards; treacherous in reverse.
Percentage points: the error that multiplies by twenty
When both of your numbers are already percentages, the gap between them is measured in percentage points, not percent. An unemployment rate moving from 5% to 6% has risen by one percentage point. It has also risen by 20%. Both are correct; they describe different things; and in most sentences only one of them is what the writer meant.
The gap between the two grows as the base shrinks. A tax rate going from 1% to 2% is a single point but a doubling. A survey result moving from 40% to 42% is two points and a 5% change. Because the percentage-change version is almost always the larger and more dramatic number, it tends to be the one that survives into headlines and slide decks, often without the underlying figures attached.
The clearest way to see the size of the mistake is to put money on it. Below, a $300,000 mortgage over 30 years: what the monthly payment becomes when the rate rises “by 1%” and when it rises “by 1 percentage point”.
| Current rate | Up 1% (relative) | Up 1 point | Extra per month | Ratio |
|---|---|---|---|---|
| 3% | 3.03% → $1,270.00 | 4% → $1,432.00 | $5.00 / $167.00 | 34× |
| 5% | 5.05% → $1,620.00 | 6% → $1,799.00 | $9.00 / $188.00 | 21× |
| 7% | 7.07% → $2,010.00 | 8% → $2,201.00 | $14.00 / $205.00 | 15× |
At a 3% starting rate, a 1% increase adds $5 a month and a one-point increase adds $167 — the same three words costing 34 times as much. The lower the starting rate, the wider that ratio gets, because one point is a larger share of a smaller number. This is the same reason a central bank always says “basis points”: one hundredth of a point, a unit with no relative reading available to be misread.
This calculator shows the point difference alongside the percentage change whenever you are comparing two figures, so the choice between them is explicit rather than accidental. The tool cannot know whether your two numbers are themselves percentages — that is context it does not have — so it presents both and leaves the judgement to you.
Why increases and decreases do not cancel
Take 100, add 50%, and you have 150. Now take 50% off. You do not get 100 back; you get 75. The rise was half of 100 and the fall was half of 150, and those are different quantities wearing the same label.
This has practical consequences well beyond arithmetic puzzles. A portfolio that drops 50% needs a 100% gain to recover, not another 50%. A price cut of 20% followed by a 20% rise leaves the customer paying 4% less than the original. A discount stacked on a discount is never the sum of the two rates. Anywhere percentages are applied in sequence, the order and the base matter.
The tool shows where the same rate applied in reverse would actually land, next to the result, so the gap is visible rather than assumed away. Starting from 100:
| Rate | After the rise | After the same fall | Shortfall | Rate that would undo it |
|---|---|---|---|---|
| 10% | 110 | 99 | 1% | -9.09% |
| 20% | 120 | 96 | 4% | -16.67% |
| 30% | 130 | 91 | 9% | -23.08% |
| 50% | 150 | 75 | 25% | -33.33% |
The shortfall is the square of the rate: 10% leaves you 1% short, 20% leaves 4%, 50% leaves 25%. The last column is the number people actually need — to undo a 20% rise you take off 16.67%, not 20%. To genuinely reverse a percentage change you divide by the factor that was applied, which is the same operation used to strip VAT out of a gross price.
When a percentage is the wrong thing to report
Two situations call for absolute numbers instead. The first is a starting value of zero: percentage change divides by it, so there is no answer, and any tool that prints one is reporting a bug. Going from nought to fifty is an increase of fifty.
The second is small bases generally. A rise from 2 cases to 3 is a 50% increase, which is an accurate statement and an actively misleading one if the reader does not also see the raw counts. Percentages compress magnitude out of the picture, which is exactly what makes them useful for comparison and exactly what makes them easy to weaponise. Wherever the base is small or unstated, the absolute difference is the more honest figure — which is why it is shown here beside every result rather than left for you to work out.
Common questions
- What is the difference between 1% and 1 percentage point?
- A percentage point is the gap between two percentages; a percent is a proportion of one of them. A rate moving from 5% to 6% has risen by one percentage point and by 20%. In money: on a $300,000 mortgage over 30 years starting at 3%, a rate rise "of 1%" adds $5 a month, while a rise "of 1 percentage point" adds $167 — 34 times as much for the same three words. Central banks say "basis points" (hundredths of a point) precisely because that unit has no relative reading to be misread.
- If a price rises 20% and then falls 20%, is it back to where it started?
- No, it is 4% below. The rise is 20% of the original and the fall is 20% of the larger number, so the fall is bigger in absolute terms. The shortfall is the square of the rate: 10% leaves you 1% short, 30% leaves 9%, 50% leaves 25%. To actually return to the original after a 20% rise you need a 16.67% cut, and this calculator shows that figure next to the result.
- What is the difference between a percentage and a percentage point?
- A percentage point is the plain arithmetic gap between two percentages; a percentage change measures that gap against where you started. If an interest rate moves from 5% to 6%, that is a rise of 1 percentage point and a rise of 20%. Both statements are true and they differ by a factor of twenty. This is the single most consequential percentage error in reporting, because the two are quoted interchangeably and the larger number is the more attention-grabbing one.
- Why does a 50% rise followed by a 50% fall not return to the start?
- Because the second percentage is taken from a bigger number. Start at 100, add 50% and you have 150. Take 50% off 150 and you remove 75, landing at 75 — a quarter below where you began. The rise was measured against 100 and the fall against 150, so they are not the same quantity despite sharing a rate. The only way back to the original figure is to divide by 1.5, which corresponds to a fall of 33.3%.
- How do I reverse a percentage increase?
- Divide, do not subtract. If a price rose by 20% to reach £120, the original was 120 ÷ 1.20 = £100, not 120 − 20% = £96. The tool shows the rate that actually reverses the move, which is never simply the same rate with the sign flipped. This is the same arithmetic as removing VAT from a gross price.
- Can percentage change be calculated from a starting value of zero?
- No. Percentage change divides by the starting value, and dividing by zero has no answer. Going from 0 to 50 is not an increase of any percentage — it is an increase of 50 in absolute terms, and that is the only honest way to state it. The tool refuses rather than displaying infinity, because a percentage printed next to a zero baseline is usually the sign of a broken spreadsheet rather than a real result.
- How does this handle negative starting values?
- The change is measured against the magnitude of the starting value, so a move from −100 to −50 reads as a 50% improvement rather than a 50% decline. Applying the raw formula to negatives flips the sign and produces statements like "losses fell by −50%", which readers cannot parse. Percentage change over a sign boundary — from a loss to a profit — remains genuinely ambiguous, and is better reported as an absolute difference.
Sources
The formulas and rates used by this tool come from the documents below. Rules change; when a figure here disagrees with the source, the source is right.
Figures checked against the sources below on August 24, 2026.
- Percentages and percentage points — content style guideOffice for National Statistics