How to Calculate Percentage Increase
The Basic Formula
Percentage Increase = ((New Value - Original Value) / Original Value) ร 100
Step-by-Step Example
Problem: A product price increased from $80 to $100. What's the percentage increase?
Step 1: Find the increase amount: $100 - $80 = $20
Step 2: Divide by original value: $20 รท $80 = 0.25
Step 3: Multiply by 100: 0.25 ร 100 = 25%
Answer: The price increased by 25%
Step 1: Find the increase amount: $100 - $80 = $20
Step 2: Divide by original value: $20 รท $80 = 0.25
Step 3: Multiply by 100: 0.25 ร 100 = 25%
Answer: The price increased by 25%
Three Types of Calculations
1. Find Percentage Increase (most common)
When you know both the original and new values, and want to find the percentage change.
- Formula: ((New - Original) / Original) ร 100
- Example: From 50 to 65 โ ((65-50)/50)ร100 = 30% increase
- Use case: Comparing prices, measuring growth, tracking progress
2. Find New Value After Increase
When you know the original value and the percentage increase, and need to find the new value.
- Formula: Original ร (1 + Percentage/100)
- Example: $200 increased by 15% โ $200 ร 1.15 = $230
- Use case: Applying discounts, calculating tips, projecting growth
3. Find Original Value (Reverse Calculation)
When you know the final value after an increase, and need to find what the original value was.
- Formula: New Value / (1 + Percentage/100)
- Example: $120 after 20% increase โ $120 รท 1.20 = $100 original
- Use case: Working backwards from discounted prices, finding base salary
Percentage Increase vs Decrease
Increase (Positive)
- New value is higher
- Result is positive percentage
- Example: 100 โ 150 = +50%
- Indicates growth
Decrease (Negative)
- New value is lower
- Result is negative percentage
- Example: 100 โ 75 = -25%
- Indicates decline
Real-World Applications
- Business: Track sales growth, revenue changes, market share increases
- Finance: Investment returns, stock price changes, salary raises
- Retail: Price markups, seasonal increases, inflation adjustments
- Real Estate: Property value appreciation, rent increases
- Statistics: Population growth, survey result comparisons
- Personal: Weight loss/gain, savings growth, expense tracking
โ ๏ธ Common Mistakes to Avoid
- Dividing by the wrong number: Always divide by the ORIGINAL value, not the new value
- Forgetting to multiply by 100: The result is a decimal until you multiply by 100
- Confusing increase with final value: A 50% increase doesn't mean the new value is 50
- Not considering negatives: A negative result means decrease, not an error
Quick Reference Table
| Original | New | Change | % Increase |
|---|---|---|---|
| 100 | 110 | +10 | 10% |
| 100 | 125 | +25 | 25% |
| 100 | 150 | +50 | 50% |
| 100 | 200 | +100 | 100% |
| 100 | 300 | +200 | 200% |
| 50 | 75 | +25 | 50% |