Percentage Change Calculator

Calculate the percentage increase or decrease between two values. Find how much something has changed in percentage terms.

Original Value

New Value

About Percentage Change Calculator

Understanding Percentage Change

Percentage change is a way of expressing the difference between an old value and a new value as a proportion of the old value, multiplied by 100. It tells you how much something has increased or decreased in relative terms, making it easy to compare changes across different scales.

The formula is straightforward: Percentage Change = ((New Value − Original Value) / |Original Value|) × 100. A positive result indicates an increase, while a negative result indicates a decrease. The absolute value in the denominator ensures correct calculations even when the original value is negative.

Quick Examples:

From 50 to 75: ((75 − 50) / 50) × 100 = +50%
From 200 to 150: ((150 − 200) / 200) × 100 = −25%
From 80 to 160: ((160 − 80) / 80) × 100 = +100%

Real-World Applications

Percentage change is one of the most widely used mathematical concepts in everyday life. In business, it tracks revenue growth, profit margins, and market share shifts. Investors rely on it to evaluate stock performance, compare portfolio returns, and assess inflation-adjusted gains.

Scientists use percentage change to measure experimental outcomes, such as the effectiveness of a treatment compared to a control group. Economists apply it to GDP growth rates, unemployment changes, and consumer price indices. Even in personal finance, understanding percentage change helps you evaluate salary raises, price discounts, and loan interest rate adjustments.

Common Use Cases:

Stock price movements and investment returns
Year-over-year revenue or sales growth
Inflation and cost-of-living adjustments
Population growth and demographic shifts
Scientific measurement comparisons

Common Mistakes to Avoid

One of the most frequent errors is confusing the base value. Always divide by the original (starting) value, not the new value. Swapping these gives an incorrect result. For example, going from 100 to 150 is a 50% increase, but going from 150 to 100 is a 33.3% decrease — not 50%.

Another common mistake is assuming that equal percentage changes in opposite directions cancel out. A 50% increase followed by a 50% decrease does not return you to the original value. If you start at 100, a 50% increase gives 150, and a 50% decrease of 150 gives 75 — a net loss of 25%.

Watch Out For:

Using the wrong base value in the denominator
Assuming percentage changes are symmetrical
Dividing by zero when the original value is 0
Confusing percentage change with percentage points

Tips for Accurate Calculations

When working with percentage change, always clearly identify which value is the original and which is the new value. The context usually makes this obvious — the earlier value in time is typically the original. If you are comparing two values without a clear time-based relationship, consider using percentage difference instead.

For sequential percentage changes (such as year-over-year growth), compound the changes rather than adding them. To find the overall change over multiple periods, multiply the individual growth factors: (1 + r₁) × (1 + r₂) × ... × (1 + rₙ) − 1, where each r is expressed as a decimal.

Pro Tips:

Convert percentages to decimals before compounding
Use absolute value in the denominator for negative bases
Round results to 2 decimal places for clarity
State the direction (increase/decrease) alongside the number

Frequently Asked Questions

What is the difference between percentage change and percentage difference?

Percentage change measures the increase or decrease from an original value to a new value, using the original as the base. Percentage difference compares two values without treating either as the original, using the average of both as the base. Use percentage change when one value clearly comes before the other in time.

Can percentage change be greater than 100%?

Yes. A percentage change greater than 100% means the new value is more than double the original. For example, if a stock price goes from $10 to $25, that is a 150% increase. There is no upper limit to percentage increase, though percentage decrease is capped at 100% (when the value drops to zero).

How do I calculate percentage change when the original value is zero?

Percentage change is undefined when the original value is zero because the formula requires dividing by the original value. In practice, you can describe the change in absolute terms or use a small baseline value if appropriate for your context.

What does a negative percentage change mean?

A negative percentage change indicates a decrease from the original value. For example, if revenue dropped from $500 to $400, the percentage change is −20%, meaning revenue decreased by 20% compared to the original amount.

How is percentage change used in finance?

In finance, percentage change is used to measure stock price movements, revenue growth, inflation rates, and portfolio performance. It allows investors to compare returns across investments of different sizes on a common scale, making it one of the most important metrics in financial analysis.

What is the formula for percentage change?

The formula is: Percentage Change = ((New Value − Original Value) / |Original Value|) × 100. The absolute value of the original is used in the denominator to handle negative original values correctly. A positive result indicates an increase, while a negative result indicates a decrease.

Additional Resources

Khan Academy: Percent Change Math is Fun: Percentage Change Wikipedia: Relative Change and Difference

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