Percentage Calculator
Three common percentage questions, answered as you type.
About Percentage Calculator
A percentage calculator answers the three common percent questions in one place: what is X% of Y, X is what percent of Y, and the percentage increase or decrease between two numbers. Enter your values and each answer updates instantly — right in your browser, nothing uploaded.
The three calculations, and how to tell them apart
Almost every percentage question is one of three. Finding a part: 15% of 240 is 0.15 × 240 = 36. Finding a rate: 36 out of 240 is 36 ÷ 240 = 0.15, so 15%. Finding a change: going from 240 to 288 is (288 − 240) ÷ 240 = 0.2, so a 20% increase. The arithmetic is trivial; picking the right one of the three is where mistakes happen.
The reliable trick is to identify which number is the base — the thing the percentage is of. In a change calculation the base is always the starting value, never the ending value or the difference. Divide by the base and you will get the right answer even when the wording is confusing.
Why a 50% rise and a 50% fall do not cancel
Take 100, add 50% to get 150, then take 50% off: you land on 75, not 100. This is not a trick, it is the base changing. The increase was 50% of 100; the decrease was 50% of 150. Percentages are always relative to whatever they are applied to, so the order matters and the two do not undo each other.
To reverse a 50% increase you need a 33.3% decrease. In general, to undo a rise of r you need a fall of r ÷ (1 + r). This is why a stock that drops 50% needs to gain 100% to break even, and why a shop can advertise 50% off and then a further 20% off and only be giving you 60% off in total, not 70%.
Percent versus percentage point
These are different units and conflating them produces genuinely misleading numbers. If an interest rate moves from 2% to 3%, that is a rise of one percentage point — and also a rise of 50 percent. Both statements are true and they describe the same event, which is exactly why the distinction matters.
The convention is to use percentage points when comparing two percentages, and percent when describing relative change. Whenever a headline reports a percentage of a percentage — unemployment, interest, tax rates, poll shares — check which is meant. A 1-point move reported as a 50% surge is technically accurate and rhetorically dishonest.
Working backwards from a total
Removing a percentage that is already included is where most real errors happen. If a price of 120 includes 20% tax, the tax is not 20% of 120. The 120 represents 120% of the pre-tax price, so divide: 120 ÷ 1.2 = 100, and the tax is 20. Taking 20% off 120 gives 24, which is wrong by four.
The same shape covers a discounted price you want to reverse, a gross figure you need net, or a total that includes a service charge. Divide by one plus the rate, never subtract the rate. The larger the percentage, the bigger the error from doing it the wrong way — at 50% the two methods differ by a third of the answer.
Frequently asked questions
- How do I calculate the percentage of a number?
- To find X% of Y, multiply Y by X and divide by 100 — so 15% of 60 is 60 × 15 ÷ 100 = 9. The calculator's first box does this instantly for any two numbers.
- How do I find what percent one number is of another?
- Divide the part by the whole and multiply by 100. Enter both numbers in the second box and it returns the percentage — for example, 15 is 25% of 60.
- How do I calculate percentage change?
- Subtract the old value from the new, divide by the old value, and multiply by 100. The third box does this automatically and shows whether it's an increase or a decrease.
- What's the difference between percentage change and percentage points?
- Percentage change is relative to the starting value; percentage points are the raw difference between two percentages. Going from 20% to 25% is a 5 percentage-point rise but a 25% increase.