The compound annual growth rate (CAGR) shows the rate of return of an investment over a certain period of time, expressed in annual percentage terms. Below is an overview of how to calculate it both by hand and by using Microsoft Excel.
What is CAGR?
But first, let's define our terms. The easiest way to think of CAGR is to recognize that over a number of years, the value of something may change – hopefully for the better – but often at an uneven rate. The CAGR provides the one rate that defines the return for the entire measurement period. For example, if we were presented with yearend prices for a stock like:
 2015: $100
 2016: $120
 2017: $125
From yearend 2015 to yearend 2016, the price appreciated by 20% (from $100 to 120). From yearend 2016 to yearend 2017, the price appreciated by 4.17% (from $120 to 125). On a yearoveryear basis, these growth rates are different, but we can use the formula below to find a single growth rate for the whole time period.
CAGR requires three inputs: an investment’s beginning value, its ending value and the time period (expressed in years). Online tools, including Investopedia’s CAGR calculator, will give the CAGR when entering these three values. The formula is:
Plugging in the above values we get [(125 / 100)^(1/2)  1] for a CAGR of 11.8%. Despite the fact that the stock's price increased at different rates each year, its overall growth rate can be defined as 11.8%.
Tips & Tricks for Calculating CAGR
One mistake that's easy to make in figuring CAGR is to incorrectly count the time period For instance, in the above example, there are three calendar years. But since the data is presented as yearend prices, we really we only have two completed years. That's why the equation reads 1/2, not 1/3.
Now, let's say we had a stock whose annual price data was presented in percentage, instead of dollar, terms:
 2015: 10%
 2016: 15%
 2017: 4%
In this case, the data is being shown from the beginning of the year, as in, the entire yearly return in 2015 (10%), the entirely yearly return in 2016 (15%), and the entire yearly return in 2017 (4%). So when calculating CAGR, we would actually be working with a time period of three years.
We would need to convert these percentages into actual beginning and ending values. This is a good opportunity to use a spreadsheet, since it's easy to add a helper column to convert the percentages into values.
Calculating CAGR in Excel
The math formula is the same as above: you need ending values, beginning values and a length measured in years. Although Excel has a builtin formula, it is far from ideal, so we will explain that last.
Financial modeling best practices require calculations to be transparent and auditable. The trouble with piling all of the calculations into a formula is that you can't easily see what numbers go where, or what numbers are user inputs or hardcoded.
The way to set this up in Excel is to have all the data in one table, then break out the calculations line by line. For example, let's derive the compound annual growth rate of a company's sales over 10 years:
The CAGR of sales for the decade is 5.34%.
A more complex situation arises when the measurement period is not in even years. This is a nearcertainty when talking about investment returns, compared to annual sales figures. The solution is to figure out the total completed years, and add them to the partial year (called the stub year).
Let's take the same figures, but have them be stock prices:
Pros and Cons of the CAGR
The CAGR is superior to other calculations, such as average returns, because it takes into account the fact that values compound over time.
On the down side, CAGR dampens the perception of volatility. For instance, let's say you have an investment that's posted these changes over three years:
 2015: 25% gain
 2016: 40% loss
 2017: 54% gain
That's actually a 5% CAGR, but the yearoveryear volatility in those returns is huge. The reality is many investments experience significant shortterm ups and downs, and by smoothing them out, so to speak, the CAGR might give a numerically accurate, but emotionally misleading, impression of performance. It's like a map that tells correctly informs you your destination is only five miles away, without indicating the bumpy condition of the road.
CAGR is also subject to manipulation depending on the measurement period, which is ultimately (and often arbitrarily) selected. A CAGR can be shifted to avoid a negative year in the stock market (such as 2008), or to include a year of strong performance (such as 2013).
The Bottom Line
The CAGR helps identify the steady rate of return of an investment over a certain period of time. It assumes the investment compounds over the period of time specified, and it is helpful for comparing investments with similar volatility characteristics.
For more information on CAGR, check out What are the main differences between compound annual growth rate (CAGR) and internal rate of return (IRR)? and Why is the compound annual growth rate (CAGR) misleading when assessing longterm growth rates?.
And for more about using Microsoft's spreadsheet software, check out our Guide to Excel for Finance.

What is the formula for calculating net present value (NPV) in Excel?
Net present value is used to estimate the profitability of projects or investments. Here's how to calculate NPV using Microsoft ... Read Answer >> 
What formula calculates interest on interest?
Find out about compounding interest, what it measures, and how to calculate the amount of compound interest accrued using ... Read Answer >> 
What is the formula for calculating return on investment (ROI) in Excel?
Find out more about return on investment (ROI) and the formula used for calculating return on investment for a company in ... Read Answer >> 
Calculate your portfolio's investment returns
Learn the basic principles underlying the data and calculations used to perform personal rates of return on investment portfolios. Read Answer >>

Managing Wealth
Morgan Stanley On the Trends in Asset Management (MS)
Learn about trends in the asset management industry and future prospects for its growth, according to a May 2016 Morgan Stanley report. 
Investing
5 Stock Market Metrics Explained
Learn how to evaluate a company's performance using metrics such as ROE, EPS and P/E ratio. 
Investing
How to calculate your investment return
How much are your investments actually returning? The method of calculation can make a significant difference in your true rate of return. 
Investing
Wearable Tech Market to Surpass $72B by 2021
The adoption of IoT technology and smart mobile devices worldwide will drive the wearable tech market expected to grow at a CAGR of 18.9% through 2021. 
Investing
Why Amazon's Stock May Continue To Outperform Alibaba's
Amazon's stock will probably outperform Alibaba over the next few years. Here's why. 
Investing
Continuous compound interest
Different frequency in compound interest results in different returns. Check out how continuous compounding accelerates your return. 
Personal Finance
Schedule Loan Repayments With Excel Formulas
Learn how to calculate all the particulars of a loan using Excel, and find out how to set up a schedule of repayment for a mortgage or any other loan. 
Retirement
The Magic Numbers Of Retirement
Don't forget these numbers when planning for your golden years. 
Retirement
Using Compounding to Boost Retirement Savings
Allowing growth on your investments to compound over time gives you immense returns when saving for retirement. 
Investing
The Effective Annual Interest Rate
The effective annual interest rate is a way of restating the annual interest rate so that it takes into account the effects of compounding.

Sequential Growth
Sequential growth is the measure of a company's financial performance ... 
Compound Interest
Compound Interest is interest calculated on the initial principal ... 
Compound Return
The compound return is the rate of return that represents the ... 
Growth Rates
Growth rates are the percentage change of a variable within a ... 
Periodic Interest Rate
The periodic interest rate is the interest rate charged on a ... 
MAR Ratio
MAR ratio measures returns adjusted for risk used to compare ...