Calculate a compound annual growth rate from two values, or compare the arithmetic and geometric mean of a list of yearly returns.
How to Use the Average Return Calculator
Use the toggle to pick a mode. Beginning & Ending Value asks for just those two numbers plus a holding period and works out a single compound annual growth rate. List of Yearly Returns instead wants each year's percentage return entered separately — add or remove rows with the buttons below the list — and returns both an arithmetic mean and a geometric mean side by side.
Those two averages answer different questions, and the gap between them is the actual point of this mode. Arithmetic mean just adds up the yearly returns and divides by how many there are — treat each year like flipping a coin, and this is the expected value. Geometric mean instead compounds the years together and finds the single flat rate that would have produced the same ending balance. Whenever returns bounce around, the geometric mean always comes in lower.
Arithmetic Mean = (r₁ + r₂ + ... + rₙ) ÷ n
Geometric Mean = [(1 + r₁) × (1 + r₂) × ... × (1 + rₙ)]^(1/n) − 1The default three years — 8%, −4%, 15% — arithmetic-average to 6.33%, but the geometric mean comes out to 6.04%. That's not a rounding quirk; it's what actually happened to a dollar invested across those three years, and it will always sit at or below the simple average whenever there's any volatility at all.
The effect gets dramatic fast with bigger swings. A portfolio that gains 50% one year and loses 50% the next averages 0% arithmetically — sounds like a wash — but $100 that grows to $150 and then falls 50% ends the second year at $75. That's a real 25% loss wearing a 0% average as a disguise, and it's the single biggest reason "average return" is a phrase worth being suspicious of whenever the underlying yearly numbers aren't shown alongside it.