Most percentage questions are variations of three relationships: finding a part, finding the percentage, or finding the whole. Identifying the unknown first makes the arithmetic much easier.
Reading-time estimate: 200 words per minute for the article and source names, rounded up. Navigation and related cards are excluded.
Match a question to the calculator mode
| Question | Mode and inputs | Output / interpretation |
|---|---|---|
| 15% of 240 | What is X% of Y?; X=15, Y=240 | 36 is the part |
| 30 out of 200 | X is what % of Y?; X=30, Y=200 | 15% is the share |
| Price after a 20% increase is 96 | Original before X% increase; X=20, Y=96 | 80 was the original price |
| Sale price after a 20% decrease is 64 | Original before X% decrease; X=20, Y=64 | 80 was the original price |
Reverse percentages and invalid denominators
To undo a 20% discount, divide the sale price by 0.80. Adding 20% to 64 instead gives 76.80, which does not recover the original 80. The denominator must reflect the share that remains. The formula in the “Find the original whole” section is a manual reference, not a separate calculator mode.
A zero whole cannot be used for “X is what % of Y?”. A 100% decrease cannot recover a unique original value; a −100% increase also gives a zero divisor. The tool rejects these cases. Other signed inputs are algebraically accepted: check whether a negative price or a discount above 100% has a sensible meaning for your task. Keep intermediate precision and round a currency result at the end.
Find a percentage of an amount
Convert the percentage to a decimal by dividing by 100, then multiply by the whole amount.
15% of 240 = 15 ÷ 100 × 240 = 36Find what percent one number is of another
Divide the part by the whole, then multiply by 100. The whole cannot be zero.
30 is what percent of 200? 30 ÷ 200 × 100 = 15%Find the original whole
When a part and its percentage are known, divide the part by the decimal form of the percentage.
36 is 15% of what number? 36 ÷ 0.15 = 240Discount and markup examples
A 20% discount on $80 is $16, leaving a sale price of $64. A 20% markup on an $80 cost adds $16, producing $96. Markup and margin are not interchangeable because they use different bases.
- Discounted price = original × (1 − discount rate)
- Marked-up price = cost × (1 + markup rate)
Why equal increases and decreases do not cancel
Reducing 100 by 20% gives 80. Increasing 80 by 20% adds only 16, producing 96. The second percentage uses a smaller base.