Percentage Calculator
Seven calculations, each with the working shown. Runs entirely in your browser.
Working
The three mistakes that cause most wrong answers
A rise then an equal fall does not return you to the start
Take 100, add 50 per cent to get 150, then take 50 per cent off. The result is 75, not 100. The reason is that each percentage is measured against a different number: the rise was 50 per cent of 100, and the fall was 50 per cent of 150. Percentages are always relative to whatever they are applied to, and that base changes as you go.
The same logic explains why a 20 per cent fall needs a 25 per cent rise to recover, and why a stock that halves must double to break even.
Reversing a discount means dividing, not adding back
An item costs 80 after 20 per cent off. The original was 80 ÷ 0.8 = 100. Adding 20 per cent to 80 gives 96, which is wrong, because that 20 per cent is being taken of 80 rather than of the original 100. This is the single most common error in everyday percentage arithmetic, and the Reverse mode above does it correctly.
Percentage points are not per cent
If a rate moves from 20 per cent to 25 per cent, that is a rise of five percentage points and also a rise of 25 per cent, because five is a quarter of twenty. Both statements are true and they mean different things. Reporting the second while the reader assumes the first is how an ordinary change gets presented as a dramatic one.
Worked examples
| Question | Method | Answer |
|---|---|---|
| What is 15% of 240? | 240 × 0.15 | 36 |
| 18 is what per cent of 45? | 18 ÷ 45 × 100 | 40% |
| Increase 250 by 12% | 250 × 1.12 | 280 |
| From 80 to 100, what changed? | (100 − 80) ÷ 80 × 100 | +25% |
| 80 after 20% off, original? | 80 ÷ 0.8 | 100 |
| Bill 64.50, tip 15% | 64.50 × 0.15 | 9.68, total 74.18 |
How to use it
Choose a calculation and fill in the boxes. The answer and the working update as you type, so the method is visible rather than being hidden behind a result. Values are shown to a sensible number of decimal places; the working uses the exact figures.
Questions
Why is a 50 per cent rise followed by a 50 per cent fall not back where it started?
Because each percentage is taken of a different number. Starting at 100, a rise of 50 per cent gives 150; a fall of 50 per cent is then 50 per cent of 150, which is 75, not 100. The rise was measured against 100 and the fall against 150.
What is the difference between percentage points and per cent?
A move from 20 per cent to 25 per cent is a rise of five percentage points, and also a rise of 25 per cent, because five is a quarter of twenty. Both are correct and they describe different things. Mixing them up is how a modest change gets reported as a dramatic one.
How do I work out the original price before a discount?
Divide rather than adding the percentage back. A price of 80 after 20 per cent off came from 80 ÷ 0.8, which is 100. Adding 20 per cent to 80 gives 96, which is the wrong answer, and it is the most common mistake in percentage arithmetic.
Does the order of two percentage changes matter?
No, for the final figure. Applying a 10 per cent discount then a 20 per cent tax gives the same total as tax then discount, because multiplication does not care about order. The amounts attributed to each step differ, which matters when they have to be itemised.
Is anything sent to a server?
No. The arithmetic runs inside your browser and this tool has no backend, so nothing you type is transmitted, logged or stored.
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