Percentage calculator — five percentage questions, each with the working shown

Turn the percentage into a decimal by dividing it by 100, then multiply. For 15% of 240: 15 ÷ 100 = 0.15, and 240 × 0.15 = 36. "Per cent" means "per hundred", so 15% is literally 15 hundredths, and multiplying by a number of hundredths is the whole operation. Two shortcuts follow from it and are worth knowing by heart. Ten per cent is the number with the decimal point moved one place left, so 10% of 240 is 24 — and every other round percentage is built from that: 5% is half of it, 20% is double it, 15% is 10% plus 5%. And percentages commute, which surprises people: 15% of 240 and 240% of 15 are both 36, because both are 15 × 240 ÷ 100. When one of the two is easy, do that one instead. Working out 4% of 75 is awkward; 75% of 4 is three, in your head.

Divide the part by the whole, then multiply by 100. For "36 is what percent of 240": 36 ÷ 240 = 0.15, and 0.15 × 100 = 15%. The part goes on top; the whole goes underneath. Getting them the wrong way round gives 240 ÷ 36 = 666.67%, which is a real answer to a different question — what percentage 240 is of 36. If your answer comes out far above 100% when you expected something small, that swap is almost always the reason. There is one case with no answer at all: the whole cannot be zero. A percentage is a share of something, and there are no shares of nothing, so the calculator stops and says so rather than printing infinity.

This is the most common mistake in the whole subject, and it is expensive because both readings sound reasonable. If an interest rate goes from 5% to 6%, that is a rise of one percentage point — the plain difference between the two percentages. It is also a rise of 20%, because 1 ÷ 5 = 0.2, and the increase is measured against where the rate started. Both statements are true and they describe the same change; they are just measured against different things. Percentage points measure against the scale, percent measures against the starting value. So a headline saying "rates up 20%" and one saying "rates up one point" can both be honest about a move from 5% to 6% — and a headline that says "up 20 points" about the same move is wrong by a factor of twenty. Whenever a number is itself already a percentage — an interest rate, a tax rate, an unemployment rate, a margin, a poll share — say "percentage points" for the difference and keep "percent" for the change relative to the old figure. The change mode in the calculator above always gives you the second one.

Because the second percentage is taken from a different, larger number. Start at 100 and add 50%: you add 50 and land on 150. Now take 50% off 150: you take away 75, not 50, and land on 75. You are 25 below where you began, after a rise and a fall of the same percentage. The rise was 50 of 100; the fall was 75 of 150. To get from 150 back to exactly 100 you need to lose 50 out of 150, which is a fall of 33.33%. This asymmetry is why an investment that drops 50% needs to double — a 100% gain — just to break even, and why a 20% cut followed by a 20% rise leaves you at 96 rather than 100. Percentage rises and falls of the same size never cancel; only the multipliers do, and 1.5 × 0.5 is 0.75, not 1.

For the same reason as above: the 20% off was taken from the original price, and the 20% you would add back would be taken from the smaller, discounted price. If something cost 100 and is now 80, adding 20% to 80 gives 96 — four short. To reverse a percentage you divide by the multiplier instead of multiplying by it. A 20% discount multiplied the price by 0.8, so the original is 80 ÷ 0.8 = 100. That division is what the reverse mode above does, and it prints a check line that multiplies the answer back by 0.8 so you can see it lands on 80 again. The one case with no answer is a 100% discount: it multiplies every price by zero, so every original price gives the same zero and none of them can be recovered. The calculator blocks that case and explains it rather than dividing by zero.

Use the reverse mode, one layer at a time, in the opposite order to the way they were added — and read the actual rates off your own receipt, because they change and they differ by what is being sold. Take a restaurant bill built the usual Malaysian way: a menu price, then a service charge on top of it, then service tax charged on the total including that service charge. On a menu price of 100 with a 10% service charge, the subtotal is 110; a 6% service tax on 110 is 6.60, and the bill is 116.60. Notice that this is not the same as adding 16% to 100, which would give 116 — the tax is charged on the service charge as well, and that stacking is worth 60 sen here and rather more on a large bill. To go backwards from 116.60: reverse the 6% increase first, 116.60 ÷ 1.06 = 110, then reverse the 10%, 110 ÷ 1.1 = 100. Doing it in the wrong order gives a different and wrong answer, because each layer was applied to the running total rather than to the menu price.

No — it is 28% off, and the gap is always in the shop's favour. Start at 100: 20% off leaves 80, and 10% off 80 takes away 8, leaving 72. That is 28 off the original, not 30, because the second discount is applied to the already-reduced price. The general rule is that discounts multiply rather than add: 0.8 × 0.9 = 0.72. Two 50% discounts do not make anything free, they make it 75% off. Three 10% discounts come to 27.1% off, not 30%. The order does not matter — 10% then 20% also lands on 72 — but the total is always less than the sum of the parts. Use the "increase or decrease" mode twice, feeding the first answer into the second, and the reverse mode when you want to know what single discount matches a stack of them.

No. Nothing is uploaded and nothing is saved. The whole calculator is JavaScript running in this tab, so the numbers never leave your device, there is no server involved at any point, and it keeps working with the connection switched off. This page also writes nothing to your browser's storage — reload it and the fields are back at their starting values, because a percentage question is answered in one sitting and keeping the last one bought nothing worth the promise. Like the rest of this site, the page itself carries advertising, which is explained on the privacy page.