Percentage Change Calculator

About Percentage Change Calculator

The Percentage Change Calculator is a tool that determines the relative change (increase or decrease) between an original value and a new value, expressed as a percentage of the original value. This calculation is commonly used in finance, business, statistics, and everyday situations to quantify changes over time or between different states.

How to Calculate Percentage Change

The percentage change is calculated using the following formula:

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

Where:

(New Value - Original Value) is the absolute change between the two values
|Original Value| is the absolute value of the original value
The result is multiplied by 100 to convert to a percentage
A positive result indicates an increase, while a negative result indicates a decrease

Example Calculations

Example 1: Percentage Increase

Calculate the percentage change from 100 to 125:

Find the difference between the new and original values:

125 - 100 = 25

Divide the difference by the original value:

25 / 100 = 0.25

Multiply by 100 to get the percentage:

0.25 × 100 = 25%

The percentage change from 100 to 125 is a 25% increase.

Example 2: Percentage Decrease

Calculate the percentage change from 80 to 60:

Find the difference between the new and original values:

60 - 80 = -20

Divide the difference by the original value:

-20 / 80 = -0.25

Multiply by 100 to get the percentage:

-0.25 × 100 = -25%

The percentage change from 80 to 60 is a 25% decrease.

Applications of Percentage Change

Financial Analysis

Calculating percentage changes in stock prices, revenue, profit margins, and other financial metrics to analyze business performance over time.

Price Changes

Determining the percentage discount on a sale item or the percentage increase due to inflation or price adjustments.

Economic Indicators

Analyzing percentage changes in GDP, unemployment rates, consumer spending, and other economic metrics to assess economic health.

Health and Fitness

Tracking percentage changes in weight, body measurements, or fitness performance to monitor progress towards health goals.

Percentage Change vs. Percentage Difference

It's important to understand the distinction between percentage change and percentage difference:

Percentage Change	Percentage Difference
Compares a new value to a baseline value	Treats both values equally
Uses the original/baseline value as the denominator	Uses the average of two values as the denominator
Can be positive (increase) or negative (decrease)	Always gives a positive percentage
Asymmetric: change from A to B differs from change from B to A	Symmetric: difference between A and B equals difference between B and A
Used when tracking changes from one value to another	Used when comparing independent values

Special Cases

Case 1: Original Value is Zero

When the original value is zero, the standard percentage change formula would result in division by zero, which is undefined. In such cases:

If both original and new values are zero, the percentage change is 0%
If the original value is zero and the new value is non-zero, the percentage change is technically infinite or undefined

Case 2: Change from Negative to Positive

When calculating percentage change between negative and positive values, the formula still applies but may yield unexpected results. For example, a change from -10 to +10 would be calculated as:

(10 - (-10)) / |-10| = 20 / 10 = 2 = 200%

Note:

When reporting percentage changes, especially in business or financial contexts, it's important to clearly specify the direction of change (increase or decrease) alongside the percentage value to avoid any ambiguity.