What is X% of Y?
e.g. what is 15% of 200?
X is what percent of Y?
e.g. 30 is what percent of 200?
Percentage change
e.g. from 50 to 75, what's the change?
Find the whole
e.g. 30 is 15% of what number?
Last updated 3 September 2026
How each one works
- X% of Y — multiply Y by X, then divide by 100. 15% of 200 is (15 × 200) ÷ 100 = 30.
- X is what percent of Y — divide X by Y, then multiply by 100. 30 out of 200 is (30 ÷ 200) × 100 = 15%.
- Percentage change — subtract the original from the new value, divide by the original, then multiply by 100. From 50 to 75 is ((75 − 50) ÷ 50) × 100 = 50% increase.
- Find the whole — divide the known part by the percentage as a decimal. If 30 is 15% of a number, the number is 30 ÷ 0.15 = 200.
The four questions people actually ask
Almost every percentage problem is one of four shapes, and knowing which one you are in solves most of the confusion. What is 15% of 240? Multiply: 240 × 0.15 = 36. 36 is what percent of 240? Divide and multiply by 100: 36 ÷ 240 = 15%. 36 is 15% of what? Divide by the decimal: 36 ÷ 0.15 = 240. What is the change from 240 to 276? Take the difference over the original: 36 ÷ 240 = a 15% increase.
The one that catches people out is the third — working backwards to the original. The instinct is to add 15% back on, which gives the wrong answer every time, because the percentage was calculated against the larger unknown figure rather than the smaller known one.
Percentage change and percentage points
These are different things and mixing them up produces genuinely misleading statements. If an interest rate moves from 4% to 6%, that is a rise of two percentage points, but a 50% increase in the rate. Both are true. A headline that picks whichever sounds more dramatic is technically accurate and practically deceptive.
The other asymmetry worth internalising: increases and decreases of the same percentage do not cancel. A price rising 20% then falling 20% does not return to where it started — $100 becomes $120, then $96. The second percentage applies to a different base, so you end up 4% down. The same arithmetic explains why a 50% investment loss needs a 100% gain to break even.
Common questions
What is the formula for percentage change?
Subtract the original value from the new value, divide by the absolute value of the original, then multiply by 100. A positive result is an increase and a negative result is a decrease.
Why is percentage change based on the original number?
Because a change is always relative to where you started. Going from 50 to 75 is a 50% increase, but going from 75 back down to 50 is a 33.3% decrease, not 50%, since the starting point is different each time.
Is my data saved anywhere?
No. Every calculation runs in your browser and nothing is sent anywhere or stored.
How do I find the original number from a percentage?
Divide rather than add back. If 36 is 15% of an unknown figure, the original is 36 ÷ 0.15 = 240. Adding 15% to 36 gives 41.40, which is wrong because the percentage was measured against the larger original number.
What is the difference between a percentage point and a percentage increase?
A rate moving from 4% to 6% has risen by two percentage points, but that is also a 50% increase in the rate itself. Both statements are correct and describe the same change, which is why the distinction matters when reading statistics.
Why does a 20% rise then a 20% fall not return to the start?
Each percentage is applied to a different base. A 100 price rising 20% becomes 120, and 20% of 120 is 24, so it falls to 96. The second percentage is measured against the larger figure, leaving you 4% below where you began.