How to Calculate Percentage Change
Guide · Updated
Percentage change measures how much a value has increased or decreased relative to its starting amount, expressed as a percentage. The formula is ((New Value – Old Value) ÷ Old Value) × 100. This metric is essential in finance, investing, sales, and data analysis to compare growth rates, price movements, and performance changes.
The Percentage Change Formula
Percentage change is calculated using a single, consistent formula that works for both increases and decreases:
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
The result is always expressed as a percentage. A positive result indicates an increase; a negative result indicates a decrease. The key is that the denominator is always the original (starting) value, not the new value—this ensures the change is measured relative to where you started.
This formula works universally across investment returns, salary changes, population growth, inventory adjustments, and almost any scenario where you need to measure relative change.
| Calculation | Formula | Example |
|---|---|---|
| Percentage of a number | part ÷ whole × 100 | 25 ÷ 200 × 100 = 12.5% |
| Percentage change | (new − old) ÷ old × 100 | (120 − 100) ÷ 100 = +20% |
| Percentage increase | old × (1 + p/100) | 100 × 1.20 = 120 |
| Percentage decrease | old × (1 − p/100) | 100 × 0.80 = 80 |
| Percentage points | new% − old% | 30% − 25% = 5 points (not 20%) |
Worked Examples
Example 1: Stock Price Increase Suppose a stock was worth $80 per share last month and is now worth $100. What is the percentage change? • Old Value = $80 • New Value = $100 • Percentage Change = ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% The stock has increased by 25%.
Example 2: Sales Decrease Your company's monthly sales were $50,000 last quarter and have dropped to $42,500 this quarter. What is the percentage change? • Old Value = $50,000 • New Value = $42,500 • Percentage Change = ((42,500 − 50,000) ÷ 50,000) × 100 = (−7,500 ÷ 50,000) × 100 = −15% Sales have decreased by 15%.
Example 3: Population Growth A city had a population of 250,000 in 2010 and 275,000 in 2020. What is the percentage change? • Old Value = 250,000 • New Value = 275,000 • Percentage Change = ((275,000 − 250,000) ÷ 250,000) × 100 = (25,000 ÷ 250,000) × 100 = 10% The population grew by 10% over the decade.
The Most Common Mistake: Percentage Change vs. Percentage Points
Many people confuse percentage change with percentage points, which are two entirely different measurements. This mistake frequently occurs in news reporting and casual conversation.
If an interest rate rises from 5% to 10%, that is a 5 percentage point increase (10 − 5 = 5). But the percentage change is ((10 − 5) ÷ 5) × 100 = 100%. The rate has doubled, meaning a 100% change relative to where it started. Similarly, if unemployment falls from 8% to 4%, that is a 4 percentage point decrease, but a 50% decrease in the rate itself ((4 − 8) ÷ 8) × 100 = −50%).
Percentage points are absolute differences between two percentages. Percentage change is the relative change, measured against the starting value. Always clarify which you mean when communicating: 'The rate increased by 5 percentage points' or 'The rate increased by 100 percent.'
When to Use Percentage Change
Percentage change is the standard metric for comparing growth, decline, and performance across different scales. It's used in profit margin calculations (to measure how much profit has grown relative to the base), investment returns (to evaluate how much your money has grown), discount calculations (to understand the size of a sale), and sales tax scenarios (to add a percentage to a base price). Our collection of free calculators—including the percentage calculator, discount calculator, sales tax calculator, and profit margin calculator—automates these calculations for you.
In business and finance, percentage change enables fair comparisons. A $1,000 increase means something very different if it's from a $10,000 base versus a $1,000,000 base. Percentage change automatically scales the change to the starting value, making it a universal measure of relative growth.
Tips and Quick Checks
To verify your calculation, remember that a 100% increase means you've doubled the original value. If you started with $100 and ended with $200, that's a 100% increase. Similarly, a 50% decrease means you've cut the value in half: $100 down to $50.
If the new value is less than the old value, the result will be negative. For example, a drop from 80 to 40 is a −50% change. Conversely, if the new value is greater, the result is positive. This is correct—negative percentages simply mean the value has declined, while positive percentages mean it has grown.
For quick mental math: divide the absolute change by the original value and multiply by 100. If the numbers are tricky, use a calculator to avoid rounding errors, especially in professional or financial contexts.
Frequently asked questions
What's the difference between percentage change and percentage points?
Percentage points are absolute differences between two percentages (e.g., 5% to 10% is +5 points). Percentage change is the relative change in the original value ((10−5)÷5×100 = 100%). Always clarify which you mean when discussing percentage changes.
Can percentage change be negative?
Yes. A negative percentage change indicates a decrease in value. For example, if a price drops from $100 to $75, the percentage change is −25%. Negative results are correct and show decline.
Why is the old value the denominator, not the new value?
The percentage change is always measured relative to the starting point. Using the old value as the denominator shows how much the value changed as a fraction of where it began. This makes percentage change a consistent, comparable metric across different scenarios.
How do I calculate percentage change over multiple years?
For a compound annual growth rate (CAGR), use a different formula: CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Number of Years) − 1. For a single jump across years, use the standard percentage change formula with the first year as 'old' and the last year as 'new.'
Is percentage change the same as growth rate?
In simple scenarios, yes. Percentage change measures the relative change from one period to another, which is equivalent to the growth rate. However, in more complex analyses (like compound growth over many years), growth rate often refers to a specific calculated rate like CAGR rather than a simple percentage change.
Can I use percentage change with negative starting values?
Technically yes, but it can be misleading. If you start with a negative value (e.g., −$100 debt), the interpretation becomes counterintuitive. In such cases, it's often clearer to discuss absolute change rather than percentage change, or to specify the context carefully.
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Sources & references
This guide is general information to help you understand the topic and use the tools — it is not professional (financial, medical, legal, or tax) advice. Verify anything important before relying on it. See our Disclaimer.