Percentage formulas
- X% of Y = Y × X ÷ 100 (15% of 80 = 12)
- X as a percent of Y = X ÷ Y × 100 (30 is 25% of 120)
- Percentage change = (new − old) ÷ old × 100
- Price after X% off = price × (1 − X÷100); after X% markup = price × (1 + X÷100)
Percent vs percentage points
If an interest rate rises from 3% to 4%, that is a rise of 1 percentage point — but a 33.3% increase in the rate itself. News reports usually quote rates, polls and market share changes in percentage points.
Stacked discounts
20% off followed by another 10% off is not 30% off. 0.8 × 0.9 = 0.72, so the total discount is 28%. Run the last calculator twice to check.