Percentage Calculator
Seven different percentage questions, each with the working shown. Pick the one that matches what you are actually trying to find — that choice is where most percentage mistakes happen.
20 ÷ 100 × 80 = 16Calculated on your device — nothing is sent anywhere.
How to use the percentage calculator
- Choose the question you are actually trying to answer using the buttons at the top. This is the important step — the seven modes give genuinely different answers.
- Fill in the two numbers. The question reads as a sentence, so you can check it says what you mean before reading the result.
- Read the answer and the formula. The working is shown underneath so you can verify it or reproduce it elsewhere.
- Copy the result if you need it somewhere else.
Everything is calculated on your device. Nothing is uploaded.
When you would need this
Working out a discount. Both directions come up: what a 30% saving is worth, and what an item cost before it was reduced.
Checking a bill or invoice. Confirming that tax has been added at the right rate, or that a stated discount matches the amount actually taken off.
Understanding a change. Sales up from 240 to 300 is a 25% increase. Reporting that as "up 60" is accurate but far less useful for comparison.
Calculating a tip, a commission or a margin. All the same operation with different names.
Interpreting statistics. News reports quote percentages constantly, and knowing how to reverse one tells you what the underlying numbers were.
The percentage mistakes that cost real money
Reversing a discount by adding the same percentage. This is the single most expensive percentage error. A jacket reduced by 40% to £60 did not cost £84 before — it cost £100. The discount was 40% of the original, and the original is what you are trying to find. Divide by 0.6, do not multiply by 1.4. The gap grows with the discount: at 50% off, adding it back understates the original by 25%.
Chaining percentages as if they add up. Two successive 10% discounts are not 20% off. The second applies to the already-reduced price, so £100 becomes £90 then £81 — a 19% total saving. Retailers know this, which is why "extra 10% off sale prices" is worth less than it sounds. Tax works the same way in reverse.
Confusing percentage and percentage points. A poll moving from 40% to 44% has risen 4 percentage points, or 10 percent. Both statements are true and they sound wildly different. When someone quotes a percentage change of a figure that is itself a percentage, check which they mean.
Averaging percentages. The average of 50% and 100% is not 75% unless both were calculated from the same base. Scoring 1 out of 2 and then 10 out of 10 gives 11 out of 12, which is 92% — not 75%. Percentages can only be averaged meaningfully when their denominators match.
Rounding at every step. Rounding to two decimal places after each operation compounds a small error into a visible one across a long calculation. Carry full precision through and round once at the end.
Tips for getting it right
Say the question out loud before choosing a mode. "What is 15% of 200" and "15 is what percent of 200" sound similar and are not. Reading the sentence the calculator builds is a reliable check that you picked the right one.
Sanity-check the direction. A percentage of a number is smaller than the number when the percentage is under 100. If a result is larger than expected, you have probably used the reverse mode by mistake.
Use the check line. Reverse percentage and discount modes show a verification underneath — "20% of 125 is 25". If that does not match your starting figure, the inputs are the wrong way round.
For repeated changes, multiply factors. A 10% rise followed by a 5% fall is 1.10 × 0.95 = 1.045, a 4.5% net rise. This is faster and less error-prone than stepping through each change, and it makes the order-independence obvious.
Limits and requirements
Some operations are genuinely undefined. Percentage change from zero and reverse percentage with 0% have no answer, and the calculator says so rather than returning a misleading number.
Floating-point precision. Results are rounded to six decimal places, which is well beyond what any practical use needs and removes binary floating-point artefacts. For financial work, round to your currency's smallest unit as the final step.
This is arithmetic, not financial advice. Compound interest, loan repayments and tax liabilities involve more than a single percentage. Use the dedicated calculators for those, and confirm anything consequential with an accountant.
Percentage points are not handled as a separate unit. The tool works in percentages. If you need percentage-point differences, subtract the two percentages directly.
Privacy: how this tool handles your numbers
Every calculation happens in your browser, on your device. Nothing is transmitted to a server, logged, or stored, and closing the tab discards everything.
That matters more than it first appears. The numbers people put into a percentage calculator are rarely abstract — they are salaries being compared, debts being worked through, invoice totals being checked, margins on a business that has not launched, or the deposit on a house. None of it is anyone else's business.
You can verify this rather than trusting it. Open your browser's developer tools, switch to the Network tab, and use the calculator — no request carries your figures. Or disconnect from the internet after the page loads; it keeps working, because the arithmetic is already running on your machine.
Frequently asked questions
Why are there seven different calculators instead of one?
Because 'percentage' covers several different questions with different answers. 'What is 20% of 80' gives 16. '20 is what percent of 80' gives 25%. 'What is 80 minus 20%' gives 64. '80 is 20% of what' gives 400. Reaching for the wrong one is by far the most common percentage error, and a single box cannot tell which you meant. Picking the question first makes it hard to get wrong.
Why does adding 20% then taking 20% off not return me to where I started?
Because the second percentage is applied to a bigger number. Adding 20% to 100 gives 120. Taking 20% off 120 removes 24, not 20, leaving 96. The percentage is always of whatever it is applied to, and after the first step that base has changed. This catches people out constantly with sale prices and tax.
How do I find the original price before a discount?
Divide, do not add back. A £80 item after 20% off came from £100, because £80 is 80% of the original — so £80 ÷ 0.8 = £100. Adding 20% to £80 gives £96, which is wrong. The 'price before discount' mode does this correctly, and shows the division so you can check it.
Can I use negative numbers?
Yes, and the percentage change mode handles them properly. Change is measured against the absolute value of the starting number, so going from -50 to -25 is reported as a 50% move rather than -50%. That matches how people describe a debt halving. A few operations remain genuinely undefined — percentage change from zero, for instance — and those return an explanation rather than a misleading number.
Why can't I calculate percentage change from zero?
Because it is mathematically undefined. Percentage change divides by the starting value, and dividing by zero has no answer. Intuitively: going from 0 sales to 10 sales is an infinite increase, not a percentage. When a starting value is zero, report the absolute change instead.
Are my numbers sent anywhere?
No. Every calculation runs in your browser on your own device. Nothing is transmitted or stored. This matters more than it might seem, since the figures people put into percentage calculators are often salaries, debts, invoice amounts and profit margins.
How precise are the results?
Calculations use standard double-precision floating point and are rounded to six decimal places for display, which removes the artefacts that would otherwise show 0.1 + 0.2 as 0.30000000000000004. For money, round to your currency's smallest unit at the end rather than at each step — rounding early is a common source of totals that are out by a penny.
Does this handle percentage points versus percentages?
The tool calculates percentages. Percentage points are a different thing and worth knowing: if a rate rises from 4% to 6%, that is a rise of 2 percentage points but a 50% increase. Both are correct and they describe the same move. Newspapers conflate them regularly, usually choosing whichever sounds more dramatic.