Percentages are fundamental to everyday math: calculating discounts, tipping at restaurants, understanding sales tax, and comparing interest rates. This guide covers the four main percentage calculations.
Calculation 1: What is X% of Y?
Formula: (X / 100) x Y. Example: What is 15% of $80? (15 / 100) x 80 = $12.
Use cases: 20% tip on a $45 bill = $9. 10% off $50 = $5 off, pay $45.
Calculation 2: X is What Percent of Y?
Formula: (X / Y) x 100. Example: 15 is what percent of 200? (15 / 200) x 100 = 7.5%.
Use cases: You scored 85 out of 100 = 85%. You saved $3,000 out of a $10,000 goal = 30%.
Calculation 3: Discount and Markup
Discount: Original Price x (1 - Discount%). $100 x (1 - 0.20) = $80 (20% off).
Markup: Cost x (1 + Markup%). $60 x (1 + 0.25) = $75 (25% markup).
Note: Markup and discount are not the same. A 20% discount on $100 is $80, but a 20% markup on $80 is $96, not $100.
Calculation 4: Percentage Change
Formula: ((New - Old) / Old) x 100. Example: Price went from $50 to $65: ((65 - 50) / 50) x 100 = 30% increase.
Price went from $65 to $50: ((50 - 65) / 65) x 100 = -23.1% decrease.
Common Scenarios
- Sales tax: $50 x 1.08 = $54 (8% tax)
- Compound interest: $10,000 x (1.05)^10 = $16,288.95 (5% for 10 years)
- Sales discount stacking: 20% off then 10% off = 28% total off (not 30%)
For stacking discounts, calculate sequentially: $100 x 0.80 = $80, then $80 x 0.90 = $72. Total discount = 28%, not 30%.