Percentage Change: Formula, Examples, and Applications

Percentage change measures how much a value has increased or decreased relative to its original value. It expresses the difference as a percentage of the starting value, making it easy to compare changes across different scales.

For example, a $10 increase on a $100 investment (10%) feels very different from a $10 increase on a $1,000 investment (1%), even though the absolute change is the same. Percentage change gives us a standardized way to understand these differences.

The percentage change formula is:

**Percentage Change = ((New Value - Original Value) / |Original Value|) × 100**

Breaking it down: - **New Value** — the value after the change - **Original Value** — the value before the change - **|Original Value|** — the absolute value of the original (ensures the denominator is always positive) - **× 100** — converts the decimal to a percentage

The result tells you: - **Positive result** = percentage increase - **Negative result** = percentage decrease

A percentage increase occurs when the new value is larger than the original value.

**Step-by-step process:** 1. Subtract the original value from the new value (difference = new - original) 2. Divide the difference by the absolute value of the original 3. Multiply by 100

**Example — Investment Growth:** You invested $5,000, and it grew to $6,500. - Difference: $6,500 - $5,000 = $1,500 - $1,500 ÷ $5,000 = 0.30 - 0.30 × 100 = 30% increase

Your investment grew by 30%.

A percentage decrease occurs when the new value is smaller than the original value.

**Example — Price Drop:** A laptop originally priced at $1,200 is now selling for $900. - Difference: $900 - $1,200 = -$300 - (-$300) ÷ $1,200 = -0.25 - (-0.25) × 100 = -25% - The price decreased by 25%

**Example — Population Decline:** A town's population fell from 50,000 to 45,000. - Difference: 45,000 - 50,000 = -5,000 - (-5,000) ÷ 50,000 = -0.10 - (-0.10) × 100 = -10% - The population declined by 10%.

Year-over-year growth compares a metric from one period to the same period one year earlier. It smooths out seasonal variations and provides a clearer picture of long-term trends.

**Example — Company Revenue:** A company earned $2 million in Q1 2025 and $2.4 million in Q1 2026. - Difference: $2.4M - $2M = $0.4M - $0.4M ÷ $2M = 0.20 - 0.20 × 100 = 20% YoY growth

YoY growth is widely used in finance, e-commerce, and business reporting to measure performance over time.

These two concepts are frequently confused but mean very different things.

**Percentage Point Change** is the arithmetic difference between two percentages. **Percentage Change** is the relative change.

**Example:** An interest rate rises from 5% to 7%. - Percentage point change: 7% - 5% = **2 percentage points** - Percentage change: ((7 - 5) ÷ 5) × 100 = **40% increase**

Confusing these can lead to serious misunderstandings in financial reporting and data analysis. Always check which measure is being used.

**Finance and Investing** Track stock price movements: "AAPL rose 2.3% today." Calculate portfolio returns and compare investment performance across different asset sizes.

**Business and Sales** Measure month-over-month or year-over-year revenue growth. Analyze customer acquisition costs and conversion rate improvements.

**Economics and Government** Track inflation rates, GDP growth, unemployment changes. Economic indicators are almost always reported as percentage changes.

**Health and Science** Measure changes in patient outcomes, drug efficacy, and experimental results. Clinical trials commonly report percentage improvements.

**Marketing and Analytics** Analyze campaign performance: "Click-through rate increased by 15% after the redesign." Compare A/B test results.

**1. Using the wrong denominator** Always divide by the original (old) value, not the new value. This is the most common error.

**2. Confusing percentage change with absolute change** A change from 1% to 2% is a 1 percentage point change, but a 100% increase. Make sure you report the right measure.

**3. Dividing by zero** If the original value is zero, percentage change is undefined. In practice, this means you cannot calculate a meaningful percentage improvement if you started from zero.

**4. Ignoring negative values** The absolute value in the denominator (|Original Value|) prevents division by a negative number. Always use absolute value to get a meaningful result.

**5. Misinterpreting direction** A negative result means a decrease, but people sometimes report it as a positive "decrease of X%" rather than saying "decreased by X%." Both can be correct, but clarity is essential.

| Original | New | Change | Formula Applied | |---|---|---|---| | 100 | 150 | +50% | ((150-100) ÷ 100) × 100 | | 200 | 120 | -40% | ((120-200) ÷ 200) × 100 | | 50 | 75 | +50% | ((75-50) ÷ 50) × 100 | | 1,000 | 1,200 | +20% | ((1200-1000) ÷ 1000) × 100 | | 80 | 60 | -25% | ((60-80) ÷ 80) × 100 | | 5 | 7 | +40% | ((7-5) ÷ 5) × 100 |

Use our [Percentage Calculator](/calculators/math/percentage-calculator/) to calculate percentage change and other percentage operations instantly.