Percentages are everywhere — price changes, salary raises, test scores, discounts, and investment returns. Yet many people confuse percent increase with percentage points, or forget that percentages can be misleading when the base number changes. This guide covers every percentage formula you'll ever need.
The Three Core Percentage Formulas
1. What is X% of Y?
Result = (X ÷ 100) × Y
What is 15% of $200? → (15 ÷ 100) × 200 = $30
2. X is what % of Y?
Result = (X ÷ Y) × 100
30 is what % of 200? → (30 ÷ 200) × 100 = 15%
3. Percent Change (X to Y)
Result = ((Y − X) ÷ |X|) × 100
From $80 to $100: ((100−80) ÷ 80) × 100 = +25%
Percentage Increase Formula
% Increase = ((New − Original) ÷ Original) × 100
Salary: $60,000 → $67,500
12.5% raise
Price: $25 → $31.25
25% increase
Followers: 10,000 → 12,500
25% growth
Stock: $100 → $143
43% gain
Percentage Decrease Formula
% Decrease = ((Original − New) ÷ Original) × 100
Sale: $120 → $84
30% off
Calories: 2,500 → 2,000
20% reduction
Stock: $200 → $160
20% decline
Subscribers: 50K → 42K
16% drop
Reverse Percentage: Find the Original Price
If you know the final price after a discount, how do you find the original price?
Original = Final Price ÷ (1 − Discount Rate)
Example: Item costs $85 after a 15% discount → $85 ÷ (1 − 0.15) = $85 ÷ 0.85 = $100 original price
Common Mistakes with Percentages
❌ Mistake 1: Percentage points vs. percent
If interest rates go from 2% to 4%, that's a 2 percentage point increase, but a 100% relative increase. These are very different. Politicians and media frequently confuse these intentionally or not.
❌ Mistake 2: Sequential discounts don't add up
A 20% discount followed by a 10% discount is NOT a 30% discount. After 20% off $100 → $80. After 10% off $80 → $72. That's 28% off, not 30%.
❌ Mistake 3: Percent increase ≠ reverse percent decrease
If a stock rises 50% then falls 50%, you DON'T break even. $100 → $150 → $75. You've lost 25%. To return to $100 from $75 requires a 33.3% gain.
Quick Reference: Common Percentage Calculations
10% of any number
Move decimal left 1
1% of any number
Move decimal left 2
25% of X
X ÷ 4
33.3% of X
X ÷ 3
50% of X
X ÷ 2
75% of X
X × 3 ÷ 4