Every everyday percent question is one of three shapes, and this page solves all of them side by side: a percent of a number (tips, tax, discounts), what percent one number is of another (test scores, market share), and percentage change (price rises, growth rates).
How to calculate percentages
A percent is just a fraction of 100 — the word comes from the Latin per centum, "by the hundred." To take 15% of 80, convert the percent to a decimal (15 ÷ 100 = 0.15) and multiply: 80 × 0.15 = 12. The same logic runs in reverse: if you know 12 is 15% of something, divide instead — 12 ÷ 0.15 = 80.
Worked examples
A $64 dinner with an 18% tip: 64 × 0.18 = $11.52. You scored 42 out of 60 on a test: (42 ÷ 60) × 100 = 70%. Your rent went from $1,400 to $1,540: (1,540 − 1,400) ÷ 1,400 × 100 = a 10% increase. For money-specific versions of these, see the tip, discount, and sales tax calculators.
The classic percentage mistakes
Two traps cause most percent errors. First, base confusion: a 50% increase followed by a 50% decrease does not return to the start (100 → 150 → 75), because each percent applies to its own current base. Second, percentage points vs percent: going from a 10% rate to a 12% rate is a rise of 2 percentage points, but a 20% relative increase. Headlines mix these up constantly.
Percent vs percentage change vs percentage difference
Percent change is directional and uses the old value as the base. Percentage difference — used when neither number is "first" — divides by the average of the two instead. If you need that symmetric comparison, the dedicated percentage change calculator computes both and explains which to use.
For information only.
Reverse percentages: undoing a percent change
The most common real-world variant: you know the after number and need the before. A $92 price tag after a 20% discount didn't start at $110.40 — divide instead of multiplying: 92 ÷ 0.80 = $115. Same for tax-inclusive receipts: a $54 total at 8% tax was 54 ÷ 1.08 = $50 before tax. The rule: to undo "+x%", divide by (1 + x/100); to undo "−x%", divide by (1 − x/100). Adding the percent back never returns you to the original, because the percent now applies to a different base.