Geometric Mean Return Calculator
The geometric mean return is the true compound average of a series of returns: the steady rate that reproduces the same cumulative growth. It is the right average for reporting realised investment performance because it accounts for compounding. Enter your period returns as percentages and the calculator returns the geometric mean, the arithmetic mean for comparison, and the total cumulative growth. The geometric mean is always at or below the arithmetic mean.
Geometric mean formula
Growth factor each period = 1 + return
Product = multiply all growth factors
Geometric mean = product^(1/n) - 1
Cumulative growth = product - 1
Returns are entered as percentages and converted to decimals. The number of periods n is how many returns you enter.
Worked example
Returns 10, -5, 20, 8 percent (n = 4):
- Product = 1.10 * 0.95 * 1.20 * 1.08 = 1.354320.
- Geometric mean = 1.354320^(1/4) - 1 = 0.078789, or 7.88 percent.
- Arithmetic mean = (10 - 5 + 20 + 8) / 4 = 8.25 percent.
Geometric mean return: frequently asked questions
What is the geometric mean return?
The geometric mean return is the constant per-period return that would produce the same cumulative growth as the actual sequence of returns. It is the compound average. For returns over n periods, it equals the nth root of the product of (1 + each return), minus 1.
Why is it usually lower than the arithmetic mean?
Because volatility drags compound growth. The geometric mean is always less than or equal to the arithmetic mean, with equality only when every period return is identical. The gap widens as returns become more variable, which is why the geometric mean better reflects realised long-run growth.
How do I enter the returns?
Enter each period's return as a percentage, separated by commas. For example, 10, -5, 20 means plus 10 percent, minus 5 percent, then plus 20 percent. The calculator converts them to growth factors, multiplies them, takes the nth root, and subtracts one.
What happens if a return is -100 percent?
A return of minus 100 percent means the value went to zero in that period, so the cumulative product is zero and the geometric mean is minus 100 percent: the investment was wiped out and cannot recover through later returns. The calculator reflects this, since a single zero growth factor zeroes the whole product.
Official sources
- U.S. Securities and Exchange Commission, Investor.gov: Rate of Return.
- U.S. Securities and Exchange Commission, Investor.gov: Compound Interest.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.