Percentage Calculator
Choose the question you are trying to answer, enter the two numbers, and get the result with the working shown.
Last updated
15% of 200
30
Working
- Calculation
- (15 × 200) ÷ 100
- Result
- 30
- Remaining after taking this out
- 170
How this calculator works
Percentage means "per hundred". Every percentage question is really the same operation viewed from a different angle: you have a part, a whole, and a rate, and you know two of them.
Finding X% of Y multiplies the whole by the rate. Finding what percentage X is of Y divides the part by the whole. Percentage change divides the difference by the original value — and the choice of which value is "original" is what makes the answer asymmetric.
That asymmetry causes most percentage mistakes. Going from 100 to 125 is a 25% increase, but going from 125 back to 100 is a 20% decrease. The rupee difference is the same; the base is not.
The same trap appears with discounts and taxes. Adding 18% GST and then removing 18% does not return you to the starting figure, because the second 18% is calculated on a larger number.
The formula
X% of Y
result = (X × Y) ÷ 100
X is what percent of Y
percentage = (X ÷ Y) × 100
Percentage change from X to Y
change = ((Y − X) ÷ |X|) × 100
The denominator is always the starting value. Swap the two numbers and you get a different percentage, even though the difference is identical.
Worked example: the three questions on the same numbers
Take the numbers 15 and 200, and apply each of the three calculations.
| 15% of 200 | 30 |
|---|---|
| 15 is what percent of 200 | 7.5% |
| Change from 15 to 200 | +1,233.33% |
| Change from 200 to 15 | −92.5% |
| 100 increased by 25% | 125 |
| 125 decreased by 25% | 93.75 |
The last two lines are the point. A 25% rise followed by a 25% fall does not return you to where you started, because the fall is calculated on the larger number. This is why a stock that drops 50% needs a 100% gain to recover.
Things worth knowing
- Percentage change is not symmetric. Up 25% then down 25% leaves you below where you began.
- Percentage points and percentages are different. A rate rising from 6% to 8% is a rise of two percentage points, but a 33% increase.
- A 50% loss requires a 100% gain to recover. The larger the loss, the more disproportionate the recovery needed.
- Percentage change from zero is undefined, because there is nothing to compare against. Report the absolute change instead.
- When comparing growth rates over different periods, convert them to a common annual basis first — a 20% rise over two years is not the same as 20% a year.