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

Similarly, to calculate a percentage decrease, determine the difference (decrease) between the two numbers you are comparing.

$\begin{array}{c}{\displaystyle \text{Decrease}=\text{Original Number}-\text{New Number}}\end{array}$

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

$\begin{array}{c}{\displaystyle \text{Percentage Decrease}=\left(\frac{\text{Decrease}}{\text{Original Number}}\right)\times 100}\end{array}$

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

Uses of Percentage Change

Investors, companies, and entire industries can benefit from analyzing how prices or other measures rise or fall from one period to the next. Here are some ways that investors can use percentage change calculations to their advantage:

• Measuring individual investment returns: The return on investment (ROI) for various assets, such as stocks, bonds, or mutual funds, is expressed in terms of percentage changes. This helps investors evaluate the performance of their assets over a particular time frame and compare them to other possible investments.
• Evaluating portfolios: In addition to computing the percentage changes of individual assets within a portfolio, investors can compute the change for their entire portfolio. This can be useful in determining whether their current asset allocation is delivering the returns they need or whether they should consider rebalancing.
• Analyzing price movements: Percentage changes in the prices of stocks, commodities, or other financial instruments can also help identify trends, volatility, and potential trading opportunities.
• Comparing against benchmarks: Investors can check the percentage changes in their investments against the percentage changes in the appropriate stock index or other benchmark to see whether their holdings are outperforming or underperforming the market. If they are significantly underperforming the benchmark, it can be worth asking why.
• Managing risk: Investors who use stop-loss orders to protect themselves from steep declines in the value of an investment can set their targets based on percentage changes.

Example of Calculating Percentage Change

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

To answer this question, first calculate the increase in price between the new and old numbers: $45.50 – $35 = $10.50. Then divide the increase by the original price:

$\begin{array}{c}{\displaystyle \frac{10\mathrm{.}5}{35}=0\mathrm{.}3}\end{array}$
Finally, to get the percentage, multiply the answer by 100 (or simply move the decimal point two spaces to the right).

$\begin{array}{c}{\displaystyle 0\mathrm{.}3\times 100=30}\end{array}$
Grace’s stock increased by 30%.