Percentage Change Calculator
Understanding the percentage change between two values is essential for financial analysis, tracking growth, or solving math problems. This percentage change calculator allows you to input an initial value and a final value to instantly see the difference expressed as a percentage. Whether you are tracking stock market portfolio performance, calculating a salary raise, or measuring population growth, this tool simplifies the math for you.
How this calculator works
Our tool follows a standard mathematical process to find the percentage difference:
- It determines the numeric difference between the Final Value and the Initial Value.
- It divides that difference by the absolute value of the Initial Value.
- It multiplies the result by 100 to generate a percentage.
A positive result indicates an increase, while a negative result shows a decrease.
Percentage Change Formula Explained
The mathematical formula used to determine the percentage change is straightforward but powerful. It is expressed as:
((New Value - Old Value) / |Old Value|) × 100%
First, subtract the old value from the new value to find the absolute difference. Next, divide this difference by the absolute value of the original number. Finally, multiply by 100 to convert the decimal into a percentage.
Common Uses for Percentage Change
- Finance: Tracking the growth or decline of stock prices, investment portfolios, and company revenue year-over-year.
- Shopping: Calculating the discount rate during sales to see exactly how much you are saving off the original price.
- Science: Determining the percent error in experiments by comparing observed values to accepted theoretical values.
- Demographics: Measuring population growth or migration statistics over specific time periods.
Examples
- Price Increase: If a product price goes from $50 to $75, the change is +50%.
- Weight Loss: If weight drops from 80kg to 70kg, the result is a -12.5% decrease.
- Investment: If you invest $1000 and it grows to $1100, that is a 10% gain.
? Frequently Asked Questions
The formula is ((New Value - Old Value) / |Old Value|) × 100%.
Yes, if the new value is smaller than the old value, the result will be negative, indicating a decrease.
Dividing by the old value standardizes the difference relative to where you started, providing a proportional measure of change.