# Mastering Percentage Change: Formula, Examples, and Applications

**Formula:**`percentageChange = ((newValue oldValue) / oldValue) × 100`

## Understanding Percentage Change

Percentage change is a key concept that helps us understand shifts in data over time. Whether you're analyzing your finances, tracking company performance, or making monthly budget adjustments, calculating percentage change provides insightful metrics on how much values have increased or decreased relative to their original figures.

## Formula Breakdown

Let's dive into the formula for percentage change:

`percentageChange = ((newValue oldValue) / oldValue) * 100`

This simple formula uses basic arithmetic to give you the percentage change between two values. Let's break down the parts:

**newValue (measured in relevant units like USD for finances):**The value you're comparing against the original.**oldValue (measured in the same units as newValue):**The initial value you're comparing to.

By subtracting the old value from the new value, you find the difference. Dividing this difference by the old value gives you a ratio that is then multiplied by 100 to convert it to a percentage.

## Real Life Examples

### Financial Example

Imagine you invested **$1000** in a stock last year, and today it’s worth **$1200**. Calculating the percentage change helps you understand how much your investment has grown.

`percentageChange = ((1200 1000) / 1000) * 100`

Here, the percentage change would be 20%. This means your investment increased by 20% compared to its original value.

### Distance Example

Consider a runner who improves their time from 20 minutes to run 5 kilometers to 18 minutes. Let’s calculate the percentage decrease in time.

`percentageChange = ((18 20) / 20) * 100`

In this case, the percentage change would be 10%. This means the runner's time decreased by 10%.

## Data Validation

When using this formula, it’s essential to ensure the oldValue isn't zero, as dividing by zero is undefined and would lead to errors. Always validate that:

`newValue`

and`oldValue`

are valid numbers.`oldValue`

is not zero to avoid division errors.

## Summary

The percentage change formula is a valuable tool for various analytical insights. By accurately calculating increases or decreases in values over time, you can make informed decisions whether in finance, fitness, business, or any other field of study.

## FAQ

### Why is the old value used as the denominator?

The old value serves as the baseline measurement. Dividing by the old value normalizes the change relative to the original value, giving you a percentage that accurately represents the size of the change.

### What does a negative percentage change indicate?

A negative percentage change indicates a decrease in value compared to the original. For example, if your expenses dropped from $500 last month to $400 this month, the result would be a negative percentage change.

### Can I use this formula for multiple values?

Yes, the formula can be scaled to compare multiple sets of values. However, it remains most effective for paired comparisons where a clear 'old' and 'new' value exist.

Tags: Finance, Mathematics, Investments, Runner Time