Percentage Changes and How to Calculate Them (2024)

What Is Percentage Change?

Percentage change is used for many purposes in finance, often to represent the price change of a stock over time, expressed as a percentage. The formula used to calculate this change as a percentage is a simple mathematical concept that varies slightly depending on whether the change is an increase or a decrease.

Read on to learn how to calculate percentage change.

How Percentage Changes Work

Percentage change can be applied to any quantity that you measure over time. In finance, the percentage change formula is often used to track the prices of both large market indexes and individual securities and compare the values of different currencies.

Balance sheets with comparative financial statements will generally include the prices of specific assets at different points in time along with the percentage changes over the accompanying time periods.For example, a company might use percentage change to illustrate revenue growth year over year (YOY) in its balance sheet.

Companies use percentage change to track and report trends in their revenues or profits. For instance, for the third quarter of 2020, Starbucks reported a 38% drop in net revenues over the same quarter in 2019 “due to adverse impact of COVID-19.” By the fourth quarter of 2020, despite store closures and reduced hours, net revenues were down 8% from the prior year. Subsequent quarterly reports show the slow recovery of Starbucks revenues—and positive percentage changes in net revenues—as the business disruptions caused by COVID-19 diminished.

Formula and Calculation of Percentage Change

To calculate apercentage increase, first work out the difference (increase) between the two numbers you are comparing:

$\begin{aligned}\text{Increase}=\text{New Number}-\text{Original Number}\end{aligned}$Increase=NewNumber−OriginalNumber​

Next,divide the increase by the original number and multiply the answer by 100:

$\begin{aligned}\text{Percentage Increase}=\left(\frac{\text{Increase}}{\text{Original Number}}\right)\times100.\end{aligned}$PercentageIncrease=(OriginalNumberIncrease​)×100.​

This expresses the change as a percentage—i.e., the percentage change.

To calculate apercentage decrease, first work out the difference (decrease) between the two numbers you are comparing.

$\begin{aligned}\text{Decrease}=\text{Original Number}-\text{New Number}\end{aligned}$Decrease=OriginalNumber−NewNumber​

Next,divide the decrease by the original number and multiply the answer by 100.

$\begin{aligned}\text{Percentage Decrease}=\left(\frac{\text{Decrease}}{\text{Original Number}}\right)\times 100\end{aligned}$PercentageDecrease=(OriginalNumberDecrease​)×100​

The result expresses the change as a percentage—i.e., the percentage change.

Uses of Percentage Change

Different industries, companies, or investments may all benefit from analyzing how the percentage of a value differs from one period to the next. Here is a list of uses of percentage change that span a variety of implementations:

• Measuring Investment Returns: The return on investment (ROI) for various assets, such as stocks, bonds, or mutual funds, is determined using percentage changes. This helps investors evaluate the success or performance of their assets over a certain time frame.
• Analyzing Price Movements: Investors examine the price movements of stocks, commodities, or other financial instruments using percentage changes. This helps in the identification of trends, volatility, and prospective trading opportunities.
• Evaluating Portfolio Success: Investors can assess the success of their total investment portfolio by computing the percentage changes of individual assets within a portfolio. They are able to make well-informed judgments about asset allocation and rebalancing thanks to this analysis.
• Comparing Financial Measures: Over time, financial measures like revenue growth, profits growth, or profit margins are compared and analyzed using percentage changes. This helps understand the financial performance and health of businesses.
• Assessing Volatility: The risk connected with investments is measured and assessed using percentage changes. Volatility, which is indicated by percentage fluctuations in asset values, helps investors in assessing future ups and downs and informing their risk-taking decisions.
• Setting Benchmarking: The performance of an investment or a portfolio is measured against a benchmark such as an index or a particular industry average, and this may be done by setting a percentage change target. Investors can use it to ascertain if their holdings are outperforming or underperforming the market.
• Managing Risk: When deciding on stop-loss levels or position sizes, percentage changes may be used to evaluate possible gains or losses based on percentage changes.
  

Example of Calculating Percentage Change

As an example of calculating percentage change, consider Grace, who bought shares of a stock at $35 per share on Jan. 1.On Feb. 1, the stock was worth $45.50 per share. By what percentage did Grace’s share value increase?

To answer this question, firstcalculate the difference in price between the new and old numbers.$45.50 - $35 = $10.50 more.To work out the increase as a percentage, divide the increase by the original (January) number:

$\begin{aligned}\frac{10.5}{35}=0.3\end{aligned}$3510.5​=0.3​
Finally, to get the percentage, we multiply the answer by 100.This simply means moving the decimal place two columns to the right.

$\begin{aligned}0.3\times100=30\end{aligned}$0.3×100=30​
Grace’s stock increased by 30%.

The Bottom Line

Percentage change is used to track the change in a number over time. That number can be anything from the price of a stock to the amount of money made by a business. It is often used on a company’s balance sheet to offer a quick indication of how performance has improved or declined from year to year or from yearly quarter to the same yearly quarter. It is also used to compare values among different currencies.

There are two formulas that express change as a percentage, one for an increase and one for a decrease, both of which will result in a positive number. You can also just use the formula for an increase. If you do, a positive result will indicate an increase, while a negative result will mean a decrease.