How to Calculate Percentages (Of, Change, Reverse)
Three jobs show up everywhere: **what percent** one number is of another, **percent of** a value (discount/tip), and **percent change** between old and new. Pick the right base (denominator)—most errors are wrong-base errors.
Core formula
Percent = (part ÷ whole) × 100 · Change% = ((new − old) ÷ old) × 100Step by step
1. Percent of a number
Convert percent to decimal: 15% → 0.15. Multiply: 0.15 × 80 = 12.
2. What percent is X of Y?
(X ÷ Y) × 100. Example: 45 is what % of 180? → 45/180 = 0.25 → 25%.
3. Percent change
(new − old) ÷ old × 100. 80→100: (20/80)×100 = 25% increase (not 20%).
Percent of vs percent change
These are different questions—do not swap formulas.
- Percent of: Part relative to a whole (tip on bill, tax on subtotal).
- Percent change: Growth or drop relative to starting value.
- Percentage points: Rate 4% → 5% is +1 point, not +25% change unless you mean relative change.
- Reverse: If 12 is 15% of unknown, unknown = 12 ÷ 0.15.
Use our calculators
Common mistakes
- Using new value as base for percent change
- Adding percents without matching bases
- Confusing points with percent change
FAQ
Increase then decrease same %?
You won’t return to start—bases differ (e.g. +10% then −10%).
Tip before or after tax?
Pick a convention; pre-tax tips are common in the US.