Percentage Change Calculator
Enter the original and new value to calculate percentage increase or decrease.
Percentage Change — Formula & Guide
Formula
% Change = ((New Value − Old Value) / |Old Value|) × 100
Positive = increase • Negative = decrease.
Example: price $80 → $100
((100 − 80) / 80) × 100 = +25%
Example: temperature 40°C → 32°C
((32 − 40) / 40) × 100 = −20%
Frequently Asked Questions
What is a 50% increase from 80?
80 × (1 + 0.50) = 80 × 1.50 = 120. Percentage change formula: ((120−80)÷80)×100 = 50%.
Price went from $40 to $52 — what percentage increase is that?
((52−40)÷40)×100 = (12÷40)×100 = 30% increase.
How do I calculate year-over-year growth?
YoY % = ((This Year − Last Year) ÷ Last Year) × 100. Revenue last year: $2M; this year: $2.4M → ((2.4−2)÷2)×100 = 20% YoY growth.
Percentage Change vs Percentage Difference
% Change is directional — one value is the reference (old value).
% Difference is symmetric — no reference; just the gap between two values.
Related Calculators
How Percentage Change Works
Percentage change measures relative change between two values: ((New − Old) / |Old|) × 100. A positive result is an increase; negative is a decrease. If a stock goes from $50 to $65: ((65−50)/50) × 100 = 30% increase. If it drops from $65 to $50: ((50−65)/65) × 100 = −23.1% decrease. Note the asymmetry: a 30% gain is not undone by a 30% loss — you need a 43% gain to recover from a 30% loss, because the base changes.
Percentage change is used for stock returns, GDP growth rates, population changes, price inflation, and test score comparisons. Always state the direction (increase/decrease). A common error is comparing absolute changes — a 1-point drop in a 2% interest rate is a 50% change, not a 1% change. Compounded percentage change over multiple periods requires multiplying factors: two 10% gains = (1.1 × 1.1 − 1) × 100 = 21% total gain, not 20%.
Percentage Change Examples
| Scenario | Old | New | % Change |
|---|---|---|---|
| Price increase | $80 | $100 | +25% |
| Price decrease | $100 | $80 | −20% |
| Revenue growth | $500K | $650K | +30% |
| Job cuts | 1200 | 900 | −25% |
| Temperature drop | 20°C | 15°C | −25% |
When to Use Percentage Change
Percentage change measures how much a quantity has grown or declined relative to its original value, making it indispensable for comparing changes across different scales. A price increase from $40 to $50 and an increase from $4000 to $5000 both represent a 25% increase, even though the absolute dollar difference is vastly different. This relative perspective is why investors track portfolio performance in percentage terms rather than dollar amounts, why economists report GDP growth as a percentage, and why retailers advertise discounts as percentages. A positive percentage change indicates growth; a negative value (often shown with a minus sign or parentheses) indicates decline. When comparing two percentage changes across different time periods or different items, be aware that percentage changes are not additive: a 50% increase followed by a 50% decrease does not return you to the original value but leaves you 25% below it, because the second percentage applies to a larger base. Always specify the reference (base) period when reporting percentage changes to prevent ambiguous interpretation of the direction and magnitude of the change.
Percentage Change Reference Table
| Old value | New value | Change | % Change |
|---|---|---|---|
| 50 | 75 | +25 | +50% |
| 100 | 85 | −15 | −15% |
| 200 | 250 | +50 | +25% |
| 1,000 | 600 | −400 | −40% |
