Percentage Change Calculator: Calculate Increase & Decrease
A percentage change calculator computes the relative difference between an original value and a new value, expressing the change as a percentage using the formula: percent change = (new value - original value) / original value × 100%, where positive results indicate increases (growth) and negative results indicate decreases (decline). This essential financial and statistical tool calculates price changes, sales growth, population changes, stock market movements, salary adjustments, economic indicators, business metrics, and any scenario requiring measurement of relative change over time, enabling comparison of growth rates, tracking performance trends, analyzing market fluctuations, and making data-driven decisions across finance, business, economics, science, and everyday applications where understanding proportional change is critical.
📈 Interactive Percentage Change Calculator
Calculate percentage increase, decrease, and find values
Percentage Change Calculator
Calculate: % Change = (New - Original) / Original × 100%
Percentage Increase Calculator
Calculate: % Increase = (New - Original) / Original × 100% (positive only)
Percentage Decrease Calculator
Calculate: % Decrease = (Original - New) / Original × 100% (positive only)
Find New Value from % Change
Calculate new value given original and percent change
Find Original Value from % Change
Calculate original value given new value and percent change
Understanding Percentage Change
Percentage change measures the relative difference between an old value and a new value. It shows how much something has increased or decreased as a proportion of the original amount, making it easy to compare changes of different magnitudes.
Percentage Change Formula
General Percentage Change Formula:
\[ \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\% \]
Interpretation:
Positive result (+) = Increase/Growth
Negative result (-) = Decrease/Decline
Zero (0) = No change
Types of Percentage Change
Percentage Increase
Percentage Increase Formula:
\[ \text{Percentage Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\% \]
Used when: New Value > Original Value
Always positive
Example: Price increase, salary raise, population growth
Percentage Decrease
Percentage Decrease Formula:
\[ \text{Percentage Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100\% \]
Used when: New Value < Original Value
Always positive (absolute value)
Example: Discount, weight loss, population decline
Step-by-Step Examples
Example 1: Calculating Percentage Increase
Problem: A stock price increased from $50 to $75. Calculate the percentage increase.
Given:
Original Value = $50
New Value = $75
Step 1: Find the change
Change = 75 - 50 = $25
Step 2: Divide by original
\( \frac{25}{50} = 0.5 \)
Step 3: Multiply by 100
0.5 × 100% = 50%
Answer: +50% increase
Interpretation: The stock price increased by 50%.
Example 2: Calculating Percentage Decrease
Problem: A product's price dropped from $200 to $150. Calculate the percentage decrease.
Given:
Original Value = $200
New Value = $150
Step 1: Find the change
Change = 200 - 150 = $50
Step 2: Divide by original
\( \frac{50}{200} = 0.25 \)
Step 3: Multiply by 100
0.25 × 100% = 25%
Answer: -25% decrease
Interpretation: The price decreased by 25%.
Example 3: Finding New Value
Problem: A salary of $40,000 increased by 15%. What is the new salary?
Given:
Original = $40,000
Percentage Increase = 15%
Method 1: Add the increase
Increase amount = 40,000 × 0.15 = $6,000
New = 40,000 + 6,000 = $46,000
Method 2: Multiply by factor
New = 40,000 × (1 + 0.15) = 40,000 × 1.15 = $46,000
Answer: $46,000
Percentage Change Examples Table
| Original | New | Change | % Change | Type |
|---|---|---|---|---|
| 100 | 150 | +50 | +50% | Increase |
| 100 | 75 | -25 | -25% | Decrease |
| 50 | 100 | +50 | +100% | Doubled |
| 100 | 50 | -50 | -50% | Halved |
| 80 | 88 | +8 | +10% | Increase |
| 200 | 180 | -20 | -10% | Decrease |
Common Percentage Changes Reference
| % Change | Multiplier | If Original = 100 | Description |
|---|---|---|---|
| +10% | 1.10 | 110 | Increases to 110% of original |
| +25% | 1.25 | 125 | Increases by one quarter |
| +50% | 1.50 | 150 | Increases by half |
| +100% | 2.00 | 200 | Doubles |
| -10% | 0.90 | 90 | Decreases to 90% of original |
| -25% | 0.75 | 75 | Decreases by one quarter |
| -50% | 0.50 | 50 | Halves |
Real-World Applications
Finance and Business
- Stock market: Calculate price changes, returns on investment
- Sales analysis: Track revenue growth, compare periods
- Profit margins: Measure profitability changes
- Budget variance: Compare actual vs planned spending
- Interest rates: Analyze rate changes over time
- Market share: Track competitive position changes
Economics and Statistics
- Inflation: Measure price level changes
- GDP growth: Calculate economic expansion/contraction
- Unemployment rate: Track labor market changes
- Population growth: Demographic trend analysis
- Exchange rates: Currency value fluctuations
- Consumer price index: Cost of living changes
Personal Finance
- Salary increases: Calculate raise percentages
- Savings growth: Track account balance changes
- Expense tracking: Monitor spending changes
- Investment returns: Portfolio performance
- Debt reduction: Track loan paydown progress
- Budget adjustments: Income/expense variations
Retail and Shopping
- Discounts: Calculate sale savings
- Price comparisons: Compare old vs new prices
- Markup/markdown: Retail pricing strategies
- Tax calculations: Pre/post-tax price changes
- Tip calculations: Service charge percentages
Advanced Formulas
Finding New Value
Calculate New Value from % Change:
\[ \text{New Value} = \text{Original} \times \left(1 + \frac{\text{% Change}}{100}\right) \]
For increase: use positive %
For decrease: use negative %
Example: 100 with +20% → 100 × 1.20 = 120
Finding Original Value
Calculate Original Value from % Change:
\[ \text{Original Value} = \frac{\text{New Value}}{1 + \frac{\text{% Change}}{100}} \]
Example: New = 120, Change = +20%
Original = 120 / 1.20 = 100
Multiple Percentage Changes
Sequential Changes
Important: Changes Don't Add Directly!
Example: +10% followed by -10% does NOT equal 0%
Calculation:
Start: 100
After +10%: 100 × 1.10 = 110
After -10%: 110 × 0.90 = 99
Net result: -1% (not 0%!)
Formula: Multiply all factors: 1.10 × 0.90 = 0.99 = -1%
Common Mistakes to Avoid
⚠️ Frequent Errors
- Wrong denominator: Always use original value, not new value
- Decimal error: Remember to multiply by 100 for percentage
- Sign confusion: Increase is positive, decrease is negative
- Adding changes: Sequential changes multiply, don't add
- Reverse calculation error: Different formulas for increase vs decrease
- Zero original: Cannot calculate if original value is zero
- Percentage of percentage: 50% of 50% ≠ 25%, it's 25%
- Rounding too early: Keep decimals until final answer
Tips for Accurate Calculations
Best Practices:
- Identify original and new: Determine which is starting value
- Check direction: Increase (positive) or decrease (negative)
- Use formulas correctly: Original always in denominator
- Verify reasonableness: Does answer make sense?
- Show your work: Document calculation steps
- Use multipliers: For quick mental math (1.25 = +25%)
- Double-check signs: Positive = up, negative = down
- Consider context: Ensure interpretation matches scenario
Quick Reference Multipliers
| To Calculate | Multiply Original By | Example (Original = 100) |
|---|---|---|
| +5% | 1.05 | 105 |
| +10% | 1.10 | 110 |
| +20% | 1.20 | 120 |
| +50% | 1.50 | 150 |
| -5% | 0.95 | 95 |
| -10% | 0.90 | 90 |
| -20% | 0.80 | 80 |
| -50% | 0.50 | 50 |
Frequently Asked Questions
How do you calculate percentage change?
Formula: (New - Original) / Original × 100%. Example: Price changes from $50 to $60. (60-50)/50 × 100% = 10/50 × 100% = 20% increase. Positive result = increase, negative = decrease. Always divide by original value, not new. Multiply by 100 to convert decimal to percentage. This shows relative change compared to starting amount.
What's the difference between percentage change and percentage difference?
Percentage change compares new to original: (New-Original)/Original × 100%. Has direction (positive/negative). Percentage difference compares two values without reference point: |V1-V2|/Average × 100%. Always positive, no direction. Use change when tracking over time; use difference when comparing two separate values without clear original. Change shows growth/decline; difference shows how far apart values are.
How do you calculate percentage increase?
Same as percentage change when result is positive: (New-Original)/Original × 100%. Example: Salary $40,000 to $45,000. (45000-40000)/40000 × 100% = 5000/40000 × 100% = 12.5% increase. Quick method: Find multiplier (45000/40000 = 1.125), subtract 1 (0.125), multiply by 100 (12.5%). Always positive value indicating growth.
How do you calculate percentage decrease?
Formula: (Original-New)/Original × 100% (note order reversed for positive result). Example: Price drops $100 to $80. (100-80)/100 × 100% = 20/100 × 100% = 20% decrease. Or use standard formula and take absolute value. Express as positive number with "decrease" label. Common in discounts, weight loss, population decline. Result shows proportion of original that was lost.
Can percentage change exceed 100%?
Yes for increases! Percentage increase can be any positive value. 100% = doubled, 200% = tripled, etc. Example: $50 to $150 = (150-50)/50 × 100% = 200% increase. Common in growth scenarios (stock prices, business expansion). Decreases limited to -100% maximum (reaching zero). Cannot go below -100% because values can't be negative in most contexts. Over 100% means more than doubling original value.
How do you reverse a percentage change?
To find original from new value: Original = New / (1 + %Change/100). Example: New = $120 after 20% increase. Original = 120 / 1.20 = $100. For decrease, use negative: New = $80 after 20% decrease. Original = 80 / 0.80 = $100. Cannot simply subtract percentage—must divide by multiplier. This reverses the change calculation mathematically.
Key Takeaways
Percentage change is a fundamental metric for measuring relative differences between values over time or across conditions. Understanding how to calculate, interpret, and apply percentage changes is essential for financial analysis, business decisions, data comparison, and everyday calculations involving growth, decline, and variation.
Essential principles to remember:
- Formula: (New - Original) / Original × 100%
- Original value always goes in denominator
- Positive result = increase, negative = decrease
- Percentage increase can exceed 100%
- Percentage decrease maximum is -100%
- Sequential changes multiply, don't add
- Use multipliers for quick calculations (1.20 = +20%)
- New value = Original × (1 + %Change/100)
- Cannot calculate if original is zero
- Context determines interpretation
Getting Started: Use the interactive calculator at the top of this page to calculate percentage change, increase, decrease, find new values, or find original values. Enter your numbers and receive instant results with detailed step-by-step explanations showing exactly how the change was calculated and what it means in practical terms.