TickerLeague

Compound annual growth rate (CAGR) explained

Plain-English guide to CAGR — formula, the difference from arithmetic average return, the link to the Rule of 72, and why CAGR is the right way to compare multi-year performance.

The formula in one line

The compound annual growth rate (CAGR) is the constant year-over-year rate that takes an initial value to a final value over a given number of years: CAGR = (End ÷ Start)^(1 ÷ Years) − 1. CAGR is a geometric mean — it accounts for the compounding effect of returns being earned on top of returns.

Project compounded growth on contributions and returns with the investment growth calculator or model pure compound interest with the compound interest calculator.

Why CAGR ≠ arithmetic average return

Suppose a portfolio gains 50% in year one and loses 50% in year two. The arithmetic average is 0%. The CAGR is (0.75)^(1/2) − 1 ≈ −13.4%. The portfolio is actually down 25% over the two years (1.5 × 0.5 = 0.75), and CAGR captures that — the arithmetic mean does not.

For long-horizon comparisons CAGR is the only honest annualized number. Using arithmetic averages systematically overstates compound performance, especially for volatile assets where the gap between arithmetic and geometric mean grows with volatility.

The Rule of 72 link

For any constant CAGR r, the time it takes to double your money is approximately 72 ÷ r years. At a 6% CAGR money doubles in roughly 12 years; at 9% in 8 years; at 12% in 6 years. The Rule of 72 is a quick mental shortcut for the exact log formula ln(2) ÷ ln(1 + r) — see the Rule of 72 calculator for both versions side by side.

Real-world reference points

  • S&P 500 since 1928: roughly 9–10% CAGR with dividends reinvested.
  • U.S. inflation, very long-run average: roughly 3% CAGR.
  • 30-year Treasury bond returns since 1980: roughly 6–7% CAGR.
  • Long-run U.S. nominal GDP growth: roughly 5–6% CAGR.

Browse multi-decade total-return CAGRs across individual stocks on the best stocks since IPO ranking.

What CAGR hides

CAGR collapses an entire return path into a single number. Two assets can have the same CAGR but very different journeys — one a steady glide, the other 70% drawdowns interspersed with 200% recoveries. CAGR does not measure volatility, drawdown depth, or sequence-of-returns risk. Pair it with those metrics for a complete picture.

Related concepts and tools

For a per-stock CAGR over any holding period, open any company hub and use the "What if you invested" tile.