Percentage Calculator
Free online percentage calculator. Calculate percentages, increases, decreases. Accurate and easy to use.
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Percentage Calculator — Three Calculator Modes, One Answer Each
This percentage calculator covers the three questions people actually arrive with, and it will not let you submit a calculation that has no meaning. There are three modes: X% of Y (find the part), X as a % of Y (find the rate), and percent change (compare two values). Switching modes swaps the labels and the hint text, so you always know which question you are answering.
Percentages cause more confusion than any other basic arithmetic because the same symbol means three different things depending on direction. "What is 15% of 240?" is a multiplication. "240 is what percent of 1600?" is a division and gives a completely different number. Confusing the two is the single most common source of wrong answers, and picking the right mode is the whole job.
The Three Modes Explained
Mode 1 — X% of Y
Finds the portion. Multiply the rate by the whole and divide by 100. 15% of 240 = 36.
Use it for discounts, tax, tips, and estimating a share of a budget.
Mode 2 — X as a % of Y
Finds the rate. Divide the part by the whole and multiply by 100. 240 as a % of 1600 = 15%.
This is Mode 1 in reverse, and the number you get is not the number you put in. Mode 1 takes a percentage and returns a value; Mode 2 takes two values and returns a percentage.
Mode 3 — % change
Compares a new value against an old one. 240 from 200 = +20%.
The result is signed and coloured, so a drop is immediately distinguishable from a rise.
The One Rule That Prevents Every Percent Change Mistake
Percent change is measured against the original value, never against the new one. Going from 200 to 240 is a 20% increase, and 240 to 200 is a decrease of 16.67%, not 20%. The two figures are not symmetric, which surprises people:
| From | To | Percent change |
|---|---|---|
| 200 | 240 | +20% |
| 240 | 200 | −16.67% |
| 100 | 150 | +50% |
| 150 | 100 | −33.33% |
A 50% loss needs a 100% gain to recover. This is not a flaw in the arithmetic; it is what "percentage" means, and it is why finance teams avoid quoting percentage changes without the underlying values.
Everyday Percentages, Worked Through
| Situation | Mode | Result |
|---|---|---|
| A £60 jacket is 25% off | X% of Y | Discount is £15, you pay £45 |
| 18% service charge on a £240 meal | X% of Y | Charge is £43.20, total £283.20 |
| You got 41 of 50 questions right | X as a % of Y | 82% |
| Salary rose from £28,000 to £31,500 | % change | +12.5% |
| You need 12% of 850 units to hit target | X% of Y | 102 units |
| How much of £3,200 is left after 35% spent? | X% of Y | Spent £1,120, remaining £2,080 |
| Test score rose from 62 to 78 | % change | +25.81% |
The last row is the one worth memorising. A jump from 62 to 78 is a large real-world improvement, but because the original value is smaller, the percentage looks larger than the "50 marks" gained. Percentage change and absolute change tell different stories, and professionals quote both.
Related Calculators
Most percentage questions turn into another calculation once you have the number:
- Percentage Increase Calculator — the reverse operation, going from a base value and a percentage to a new value.
- Percentage Difference — compares two values as a difference rather than a change, which is the right measure for two equally important figures.
- Averaging Calculator — mean, median and range across a set of scores or samples.
- Discount Calculator — chained sale percentages plus VAT, which is where mental arithmetic fails most often.
- Compound Interest Calculator — when a percentage applies repeatedly rather than once, compounding makes the result diverge sharply.
- Fraction to Percentage — for when the source data is a fraction rather than a decimal.
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