The three formulas
Percent of: X% of Y = (X ÷ 100) × Y, so 15% of 200 is 30. Percent ratio: X is (X ÷ Y) × 100 percent of Y, so 30 is 15% of 200. Percent change: ((new − old) ÷ old) × 100, so going from 200 to 250 is a 25% increase. Nearly every percentage question you'll meet — tips, discounts, raises, returns — is one of these three in disguise.
Percent change isn't symmetric
A 25% drop followed by a 25% gain does not get you back to even: 200 falls to 150, then rises only to 187.50. The percentages are computed from different starting points. This asymmetry is why a 50% investment loss needs a 100% gain to recover, and why 'percentage points' and 'percent' aren't interchangeable — a rate going from 4% to 5% rose one percentage point, but 25 percent.
Mental shortcuts worth keeping
10% is just the number with the decimal moved left one place; 5% is half of that; 1% moves the decimal two places. Stack them: 15% of 80 = 8 + 4 = 12. And x% of y always equals y% of x — 8% of 25 feels hard, but 25% of 8 is obviously 2. Same answer, easier path.
How to use this calculator
Each of the three modes has its own pair of inputs and updates the moment you type. Use the first for 'what is X% of Y' (tips, discounts, tax), the second for 'X is what percent of Y' (test scores, progress bars), and the third for percent change between a starting and ending value (price moves, growth rates). There's nothing to submit — read the answer as you go.
Everyday uses of each mode
Mode one handles a 20% tip on a $54 bill (0.20 × 54 = $10.80) or 15% sales tax on a purchase. Mode two answers 'I scored 43 out of 50' (43 ÷ 50 × 100 = 86%). Mode three measures a stock going from $80 to $92 (a 15% gain) or a $1,200 rent rising to $1,320 (a 10% increase). Recognizing which of the three a problem is saves you from reaching for a formula you only half-remember.