Geometric Mean Calculator

The geometric mean is the n-th root of the product of n values. Unlike the arithmetic mean, which adds the values, it multiplies them, which makes it the right average for quantities that compound or are expressed as ratios.

Use it for growth rates, investment returns, ratios, percentages and index numbers, anything that multiplies from one period to the next. For example, averaging yearly growth factors with the geometric mean gives the true compound growth rate.

The geometric mean relies on multiplying the values and taking a root, which is only defined for positive numbers. A zero would force the result to zero and a negative value would make the root undefined, so the calculator requires every value to be greater than zero.

Convert each change to a growth factor before entering it. A rise of 5 percent becomes 1.05 and a fall of 10 percent becomes 0.90. The geometric mean of those factors is the average growth factor per period.

It is computed as the exponential of the average of the natural logarithms of the values. This is mathematically identical to the n-th root of the product but stays accurate even for long lists, where the raw product could overflow.