How it works
The geometric mean is the nth root of the product of n numbers. It is the right average for quantities that multiply together, such as growth rates, investment returns and ratios.
For returns, the calculator converts each percent to a growth factor (10% becomes 1.10), takes the geometric mean of the factors and subtracts 1. This is the constant rate that would produce the same total growth, the same idea as CAGR.
The geometric mean is always less than or equal to the arithmetic mean. The gap widens as the numbers become more spread out, which is why the arithmetic average overstates the real return of a volatile investment.
Formula
GM = (x₁ × x₂ × … × xₙ)^(1/n) · Average return = ((1 + r₁)(1 + r₂)…(1 + rₙ))^(1/n) − 1
Questions people ask
Why not just average the returns?
Because returns compound. A +50% year followed by a −50% year averages 0% arithmetically, but $100 becomes $75. The geometric average of −13.4% per year reflects that loss.
Can I use zero or negative values?
Not as plain values: the geometric mean needs positive numbers. Negative percent returns are fine in returns mode as long as each is above −100%.
What is the harmonic mean?
It is n divided by the sum of reciprocals, and is the right average for rates such as speeds over equal distances. For positive data, harmonic ≤ geometric ≤ arithmetic.