Percentage calculations come up constantly — discounts, tips, tax, grade calculations, growth rates. Here are the formulas and practical applications.
The three basic percentage questions
1. What is X% of Y?
Result = Y × (X / 100)Example: What is 20% of 150? → 150 × 0.20 = 30
2. X is what percent of Y?
Percent = (X / Y) × 100Example: 30 is what percent of 150? → (30 / 150) × 100 = 20%
3. Percent change from X to Y
Change = ((Y - X) / X) × 100Example: Price went from $80 to $100 → ((100 - 80) / 80) × 100 = 25% increase
Common real-world uses
Shopping discounts
A $200 item with 30% off:
Discount = $200 × 0.30 = $60
Final price = $200 - $60 = $140Stacked discounts don’t add up the way you’d expect:
- 20% off + 10% off ≠ 30% off
- $100 → 20% off = $80 → 10% off = $72 (28% total, not 30%)
Tips
Standard tipping:
- 15% tip on $45: $45 × 0.15 = $6.75
- 20% tip on $45: $45 × 0.20 = $9.00
Quick mental math: 10% is easy (move the decimal). Double it for 20%, or add half for 15%.
Tax calculations
$85 item + 8.5% tax:
Tax = $85 × 0.085 = $7.23
Total = $85 + $7.23 = $92.23Grade calculations
Scored 42 out of 50:
(42 / 50) × 100 = 84%Growth rates
Revenue grew from $50K to $65K:
((65000 - 50000) / 50000) × 100 = 30% growthPercentage pitfalls
Percentage points vs percent
“Interest rates rose from 3% to 5%”
- That’s a 2 percentage point increase
- But a 66.7% increase (relative change)
Media often conflates these, which can be misleading.
Working backward
“The price dropped 20%, then went up 20% — back to the original, right?”
Wrong:
- $100 → 20% off = $80
- $80 → 20% up = $96
You need a 25% increase to recover from a 20% decrease.
Small base numbers
“Sales increased 200%!” sounds impressive, but if sales went from 1 to 3, it’s not very meaningful. Always consider the base number.
A percentage calculator handles all these scenarios — plug in your numbers, pick the calculation type, and get the answer instantly.