The three percentage calculations everyone needs
Most percentage confusion comes from mixing up which question you're actually asking.
- X% of Y: 'What is 15% of $80?' → (15/100) × 80 = $12. Used for tips, tax, discounts.
- X is what % of Y: '15 out of 60 is what percent?' → (15/60) × 100 = 25%. Used for test scores, ratios, market share.
- % change from X to Y: 'Price went from $80 to $100 — how much did it increase?' → ((100−80)/80) × 100 = +25%. Used for price changes, growth rates, salary comparisons.
Common percentage mistakes
The biggest one: confusing percentage points with percent change. An interest rate rising from 4% to 6% is a 2 percentage point increase but a 50% increase in rate. These sound very different for good reason — they measure different things.
A price that went up 25% and then came back down 25% is not back to its original level. Up 25% then down 25%: $100 × 1.25 × 0.75 = $93.75. Percentages are multiplicative, not additive.