CAGR Explained: Formula, Examples and When to Use It

When someone says an investment grew "12 percent a year", what do they mean? If the growth was steady, it is easy. But real investments bounce around, and it is possible to describe the same history in several ways. The compound annual growth rate, or CAGR, is the honest one: it is the steady yearly rate that would take you from the starting value to the ending value in the time given.

The formula

CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1

Multiply by 100 for a percentage. If an investment grew from 10,000 to 25,000 in 8 years, the ratio is 2.5. The eighth root of 2.5 is 1.1214, so the CAGR is 12.14 percent. Check it: 10,000 × 1.1214^8 = 25,000.

You need only three numbers: where you started, where you ended and how long it took. It does not matter what happened in between.

Why not just average the yearly returns?

The arithmetic average of yearly returns hides the effect of losses. Start with 100. It rises 50 percent to 150 in year one, then falls 50 percent to 75 in year two. The average of +50 and −50 is 0 percent, which sounds like you broke even, but you have lost a quarter of your money. The CAGR is (75 ÷ 100)^(1 ÷ 2) − 1 = −13.4 percent a year, which matches reality.

The bigger the swings, the larger the gap between the average return and the CAGR. Serious performance reporting uses compound rates for this reason.

Comparing investments fairly

CAGR puts different investments on the same footing.

• Fund A: 5,000 to 8,000 in 5 years, a CAGR of 9.86 percent
• Fund B: 5,000 to 7,000 in 3 years, a CAGR of 11.87 percent

Fund A made more money in total, but Fund B grew faster per year. Which is better depends on how long you can leave the money invested and what you can do with it afterwards. Just remember to compare over similar periods, since the start and end dates can flatter or hurt a result.

CAGR beyond investing

The same idea describes any quantity that grows over time.

• Revenue: monthly sales from 20,000 to 35,000 in two years is a CAGR of about 32 percent.
• Website traffic: visitors from 3,000 to 12,000 in 18 months (1.5 years) is a CAGR of about 152 percent a year.
• Population, prices, users: any start-and-end comparison over a period.

For periods that are not whole years, use decimals: 18 months is 1.5 years.

Setting targets with CAGR

The formula can be turned around. To double your money in 10 years, you need a CAGR of 2^(1/10) − 1 = 7.18 percent. To triple it in 15 years, you need about 7.6 percent. These checks show how realistic a goal is. A plan that needs 25 percent a year for a decade is very unlikely; one that needs 6 percent is plausible.

Limits of CAGR

• It assumes no deposits or withdrawals. If you added or removed money, use a money-weighted return (IRR).
• It says nothing about risk or the path taken. Two investments can share a CAGR and have very different swings.
• It depends on your chosen start and end dates. Cherry-picked dates can make anything look good.
• It looks backwards; it does not predict.
• It needs positive values. If the ending value is zero or negative, the rate is not defined.

CAGR, ROI and real returns

ROI is the total gain relative to cost, while CAGR turns that total into a yearly rate, so with no interim cash flows annualized ROI and CAGR are the same number. To see what a return means for your buying power, subtract inflation: a 6 percent CAGR with 3 percent inflation is about 2.9 percent in real terms.

Try it

The CAGR Calculator shows the growth rate, total growth and growth multiple for any start value, end value and time, with the formula filled in. The ROI Calculator gives the total return and its annualized form. See what a rate does with regular deposits in the Compound Interest Calculator, and adjust for inflation with the Inflation Calculator. For the ROI side of the story, read how to calculate ROI.