Percentage Calculator With the Working Shown

Pick the question you are actually being asked

The four modes are four different questions, and most lost marks come from answering the wrong one. Read the question for what is known and what is missing. If the original amount is missing and you have been given the amount after a change, it is a reverse percentage, whatever words the question uses.

Type the two numbers and everything appears together: the answer, the multiplier line, the route you would use without a calculator, and the multiplier table for that percentage. In reverse mode you also tell it whether the change was a rise or a fall, because the two divide by different numbers.

Nothing is stored. The arithmetic runs in your browser, no account is needed, and the numbers are gone when you close the tab.

• Find a percentage of an amount — 15% of PKR 6,000, the VAT on a bill, a discount.
• One number as a percentage of another — 42 out of 60 as a percentage.
• Percentage change — a price, a population or a mark that has moved from one value to another.
• Reverse percentage — a jacket costs USD 68 after 15% off; what was the ticket price?

The multiplier line, and the 10% route beside it

Every percentage question is a multiplication. 15% of 240 is 240 × 0.15. A 12% rise is × 1.12, a 12% fall is × 0.88, and two 5% rises one after the other are × 1.05², which is × 1.1025 rather than × 1.10. The tool prints that line for whichever mode you are in, because it is the line that earns method marks and the only one that scales to compound growth without learning anything new.

Undoing a change means dividing by the multiplier rather than multiplying by a different one. That is the whole of reverse percentages, and it is why the tool shows the division and then a check that multiplies the answer back to the amount you started with.

The non-calculator route is built the way a tutor builds it on paper. 10% comes from moving every digit one place, 5% is half of that, 1% is two places, and the pieces are added up. 15% is 10% + 5%. 37% is 10% three times, then 5%, then 1% twice. Paper 1 has no calculator on it, so this is the half of the answer that gets practised least and tested most.

• A rise of 12% → × 1.12
• A fall of 12% → × 0.88
• Two rises of 5% → × 1.05² = × 1.1025
• Undoing a rise of 12% → ÷ 1.12

What this deliberately does not do

It does not know your tax rate, your VAT rate, your bank's interest rate or your country's inflation figure, and it will not guess at any of them. Type in the percentage the question gives you; nothing here supplies one on your behalf.

It does not turn a percentage into a grade. Grade boundaries are set after each series has been marked and no awarding body publishes them in advance, so our GCSE mark calculator refuses to predict one and this tool takes the same posture rather than inventing a threshold to fill the gap.

It does not round the method, only the display. Figures are shown to four significant figures, so a recurring answer such as 33.33% is a rounded view of a calculation that was never rounded. In a multi-step question, carry the full value forward and round at the end.

The four mistakes worth naming

The reverse-percentage trap is the biggest. Given a price of PKR 6,720 after a 12% rise, students take 12% off 6,720 and write 5,913.60. The right answer is 6,720 ÷ 1.12 = 6,000, because the 12% was a percentage of the original price, not of the new one.

Percentage change is divided by the original value, not the new one. Going from 50 to 65 is a rise of 15 ÷ 50 = 30%, and dividing by 65 instead gives 23.08%, which answers a question nobody asked.

Two changes do not add up. A 20% rise followed by a 20% fall is × 1.2 × 0.8 = × 0.96, so you finish 4% below where you started rather than back at it. Two 10% rises are × 1.21, not × 1.20.

Per cent and percentage points are different things. A rate moving from 4% to 6% has risen by two percentage points and by 50 per cent, and an exam question will mean exactly one of those.

• Subtracting 12% from the new amount instead of dividing by 1.12.
• Dividing a percentage change by the new value instead of the original.
• Treating two 10% rises as a single 20% rise, when the multiplier is 1.1² = 1.21.
• Reading a rise of two percentage points as a rise of 2 per cent.