CAGR Calculator

The compound annual growth rate is the geometric mean of a return series, expressed as the single constant rate that would carry a beginning value to an ending value across n periods. The nth root appears in the formula because investment growth is multiplicative rather than additive: a holding that gains 20 percent and then loses 20 percent finishes at 0.96 of its starting value, not back at par, so averaging the two annual figures arithmetically overstates the outcome. Raising the ending-to-beginning ratio to the power 1/n strips out the sequence of returns and reports only the compounded average. Useful reference points are roughly 10 percent nominal and 6.5 to 7 percent real for large-cap US equities over the last century, about 5 percent for long-term investment grade bonds, and 3 to 5 percent for US house prices before rental income. The metric is path-blind, which is both its strength and its main weakness. Two portfolios ending at the same value have identical CAGR even if one moved in a straight line and the other fell 60 percent in the interim, so CAGR says nothing about drawdown or volatility and should be paired with standard deviation or maximum drawdown. It is also acutely sensitive to endpoint selection: shifting a start date across a market peak can swing a reported figure by several percentage points. Because the formula admits only two cash flows, portfolios with contributions or withdrawals require internal rate of return or a time-weighted return instead.

The mathematics behind CAGR long predates the acronym. Compound interest tables were published in Europe from the early seventeenth century, notably by Richard Witt in 1613, and Jacob Bernoulli examined the limit of ever more frequent compounding in 1683, work that produced the constant e. The geometric mean itself was known to Greek mathematicians, but its application to sequences of investment returns became standard only once mutual funds and pension portfolios needed a defensible way to summarize multi-year performance rather than quoting a simple average of yearly gains. The modern discipline arrived with performance reporting standards. In 1987 the Financial Analysts Federation and the Institute of Chartered Financial Analysts, later merged into the CFA Institute, issued the Performance Presentation Standards to stop investment managers from advertising flattering arithmetic averages and cherry-picked periods. Those rules were extended internationally as the Global Investment Performance Standards, first released in 1999 and revised repeatedly since, which require geometrically linked and time-weighted returns. In parallel, market research firms and equity analysts adopted CAGR as shorthand for revenue, earnings, and market-size growth, which is why the term now appears as often in industry forecasts and investor presentations as it does in portfolio statements.