Four different questions, one word
“Percentage” covers at least four distinct calculations, and most of the confusion around them comes from not noticing which one is being asked. This calculator separates them explicitly:
X% of Y finds a part from a whole — 20% of 250. X is what % of Y goes the other way, turning two known numbers into a percentage — 50 out of 250. X is Y% of what works backwards to a whole you do not know — if 50 is 20% of something, what is that something? And % increase or decrease compares two numbers to measure the change between them.
Picking the wrong one of those four is a far more common error than getting the arithmetic wrong, which is why the mode is a visible setting rather than something inferred.
Using this percentage calculator
Choose what you want to find in the customize panel — the four modes above — and the fields change to match. The answer updates as you type.
The page also offers a sentence mode, which reads the calculation as a plain question: “What is 20% of 250? It is 50.” For percentages specifically, that framing is worth using, because seeing the question written out makes it obvious when you have picked the mode that answers a different one.
The formulas, worked through
A percentage of a number: divide the percent by 100 and multiply. 20% of 250 is 0.20 × 250 = 50.
What percent one number is of another: divide the part by the whole and multiply by 100. 50 ÷ 250 × 100 = 20%.
Finding the whole: divide the part by the percent as a decimal. If 50 is 20% of a number, that number is 50 ÷ 0.20 = 250. This is the one people most often try to solve by adding a percentage back on, which does not work.
Percentage change: subtract, divide by the original, multiply by 100. Going from 200 to 250 is (250 − 200) ÷ 200 × 100 = 25% increase. The denominator is the trap here: dividing by the new value instead gives 20%, and both numbers look plausible.
The two traps worth knowing
Percentage changes do not cancel out. A 50% fall followed by a 50% rise does not get you back. 100 drops to 50; a 50% rise on 50 is 25, taking you to 75. To undo a 50% fall you need a 100% rise, because the second percentage is measured against a smaller base. The same asymmetry is why a stock that halves needs to double to recover.
Percent and percentage points are different units. If an interest rate moves from 4% to 5%, that is a rise of one percentage point — but a 25% increase in the rate. Both descriptions are true and they differ by a factor of 25, which makes this the single most exploited ambiguity in reporting on rates, taxes and poll numbers. When a figure is itself a percentage, always check which of the two is meant.
For percentages in specific settings, the discount calculator handles sale prices and stacked coupons, the GST calculator covers adding and removing tax, and the attendance calculator answers the “how many can I still miss” version.
FAQ
How do you find a percentage of a number?
Divide the percentage by 100 and multiply.
How do you work out what percent one number is of another?
Divide the part by the whole, then multiply by 100.
50 out of 250 is 50 ÷ 250 = 0.2, so 20%. The order matters: 250 out of 50 is 500%, which is a different question with a different answer.
How do you calculate percentage increase and decrease?
Take the difference, divide by the starting value, and multiply by 100.
Dividing by the new value instead is the usual mistake. 200 → 250 is a 25% increase (50 ÷ 200), not 20% (50 ÷ 250).
Why isn't a 50% drop undone by a 50% rise?
Because each percentage is taken from a different base. Fall 50% from 100 and you're at 50. Rise 50% from 50 and you're at 75, not 100.
To undo a 50% fall you need a 100% rise. This is why percentage losses hurt more than the same percentage gain helps.
What's the difference between percent and percentage points?
A rate going from 4% to 5% has risen by 1 percentage point, but by 25 percent. Both statements are true and they describe the same change.
Use points when comparing two percentages directly, and percent when describing the size of the move relative to where it started.