CAGR

Compound Annual Growth Rate (CAGR) is the single annualized growth rate that would take a metric from its beginning value to its ending value over a stated number of years, assuming the growth compounded steadily (i.e., geometrically) each year rather than happening in one lump sum or unevenly. It answers the question "if this had grown at the same percentage rate every year, what would that rate have been?" It is not the average of the year-over-year growth rates; it is the single compounding rate implied by only the first and last data points.

This page covers CAGR as a calculation method: how to compute it, when it is an appropriate summary statistic, and where it breaks down. It does not cover money-weighted return methods (IRR/XIRR), which are the correct tool when a stream of interim contributions or withdrawals occurred during the period; CAGR's formula assumes exactly one inflow at the start and one outflow at the end, with nothing added or removed in between. It also is not a volatility or risk measure -- it says nothing about how bumpy the path between the two endpoints was -- and does not by itself distinguish nominal growth from inflation-adjusted (real) growth; that adjustment has to be made to the input values before applying the formula, not to the CAGR output afterward. It also does not apply when the beginning value is zero or negative, since a negative base raised to a fractional power is not a real number.

Use CAGR when you have two point-in-time values of the same metric (revenue, market size, subscriber count, portfolio value) measured in the same units and currency, no cash was added or withdrawn in between, and you want one comparable annualized growth figure -- for example, comparing a company's 5-year revenue CAGR against a competitor's, comparing an industry's historical market-size CAGR against its forecast CAGR, or annualizing a fund's multi-year return. Avoid it, or supplement it with year-by-year figures, when: interim contributions/withdrawals occurred (use XIRR/IRR instead), you need to communicate volatility or downside risk (CAGR alone hides both), or the two periods being compared span different lengths or different parts of an economic cycle, which can make otherwise-similar CAGRs misleading.

1. Identify the beginning value (V0) and the ending value (Vn) of the same metric, in the same currency and units (e.g., both in constant/real terms, or both nominal -- do not mix).
2. Confirm no interim cash was added to or withdrawn from the underlying asset during the period; if it was, use a money-weighted method (IRR/XIRR) instead, since plain CAGR will misstate the return.
3. Count n, the number of years (compounding periods) between the two values -- this is the difference between the end year and the start year, not the number of data points (e.g., 2021 to 2026 is n=5, not n=6).
4. Divide the ending value by the beginning value to get the total growth multiple (Vn / V0).
5. Raise that multiple to the power of 1/n (the nth root).
6. Subtract 1 from the result and multiply by 100 to express it as a percentage.
7. Sanity-check the result against the plain year-over-year figures if you have them: CAGR should fall somewhere within the range those individual years cover, and a CAGR far outside that range usually signals a units, currency, or period-count error.

Illustrative example only -- all figures below are hypothetical inputs chosen to demonstrate the arithmetic, not a sourced estimate for any real company or market.

A hypothetical company's revenue was $10,000,000 in year 0 (2021) and $21,600,000 in year 5 (2026). n = 2026 - 2021 = 5.
Growth multiple = 21,600,000 / 10,000,000 = 2.16.
2.16 ^ (1/5) = 1.16657 (the 5th root of 2.16).
CAGR = 1.16657 - 1 = 0.16657, or approximately 16.66% per year.

Why the smoothing matters: a second hypothetical company starts at the same $10,000,000 and ends at the same $21,600,000 five years later, but along a much bumpier path -- $10.0M, then +40% to $14.0M, then -35.7% to $9.0M, then +66.7% to $15.0M, then +20% to $18.0M, then +20% to $21.6M. Its year-by-year growth swings from -35.7% to +66.7%, yet because it shares the same beginning value, ending value, and n, its CAGR is also exactly 16.66%. CAGR cannot distinguish the smooth path from the volatile one; that is its main limitation, not a flaw in the arithmetic.

Not yet available.

• Corporate Finance Institute, "CAGR (Compound Annual Growth Rate)" -- formula, worked example, and common uses.
• Wikipedia, "Compound annual growth rate" -- formula notation and the calculation-error caveat when used for forecasting.
• U.S. Securities and Exchange Commission, Investor.gov glossary entry: "Compound Annual Growth Rate (CAGR)" -- official investor-education definition.