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CAGR Formula

The compound annual growth rate is the single constant rate that would grow a beginning value to its ending value over the period. It is the geometric mean return, which correctly accounts for compounding, and it is almost always lower than the arithmetic average return because volatility drags compound growth below the simple mean.

3 variables. Published May 26, 2026. By AI Fin Hub Research.

Formula
CAGR = (EndingValue / BeginningValue)^(1 / years) - 1

Variables

EndingValue

Ending value

The portfolio or investment value at the end of the period, after all gains, losses, and reinvested income.

BeginningValue

Beginning value

The starting value at the beginning of the period. The ratio of ending to beginning is the total growth multiple.

years

Number of years

The length of the period in years, which can be fractional. The reciprocal exponent annualizes the total growth into a per-year rate.

Step by step

  1. 1

    Divide the ending value by the beginning value to get the total growth multiple.

    Growing from 10,000 to 18,000 is a multiple of 1.8.

  2. 2

    Raise the multiple to the power of one divided by the number of years.

    Over 4 years: 1.8^(1/4) = 1.8^0.25 = 1.1583.

  3. 3

    Subtract 1 to convert the growth factor into a rate.

    1.1583 - 1 = 0.1583 = 15.83%.

  4. 4

    Note that CAGR is the geometric mean and will be below the arithmetic mean whenever returns vary.

    A path of +50% then -10% has arithmetic mean 20% but CAGR of only 16.2%.

Worked example

Four-year investment growth

Beginning value

10,000

Ending value

18,000

Years

4

Growth multiple = 18,000 / 10,000 = 1.8. CAGR = 1.8^(1/4) - 1. The fourth root of 1.8: sqrt(1.8) = 1.34164, sqrt(1.34164) = 1.15829. So CAGR = 1.15829 - 1 = 0.15829 = 15.83%.

CAGR of about 15.83%. A constant 15.83% annual return compounds 10,000 to 18,000 over four years. Verify: 10,000 x 1.15829^4 = 10,000 x 1.8 = 18,000. Because real returns vary year to year, this smooth rate hides the actual path, which is exactly why CAGR is paired with drawdown and volatility when describing performance.

Common variations

Money-weighted return (IRR): accounts for the timing and size of cash flows in and out, unlike CAGR which assumes a single lump sum.
Time-weighted return: chains period returns to remove the effect of cash-flow timing, the standard for comparing managers.
Annualized return from periodic returns: (product of (1 + r_i))^(N/n) - 1, the same geometric idea computed from a return series.

Run the numbers next

  • Calculators Drawdown-Recovery Markov Simulator

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Sources

  1. Investments , Bodie, Kane, Marcus, McGraw-Hill (2018)
  2. Global Investment Performance Standards (GIPS) , CFA Institute

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