Geometric Mean Calculator

Typical Use Cases

• Average Annual Investment Return: John's mutual fund net asset value grew by +8%, +12%, -5%, and +10% over the past 4 years. The arithmetic mean is 6.25%, but the actual annualized return requires the geometric mean—about 5.98%. This number reflects the true rate at which his money grew.
• Multi-Period Price Increases: A raw material's price changed by 3%, 5%, and -2% (a decrease) over three consecutive years. When we need to know the "average" magnitude of the total price increase over three years, the geometric mean is more reasonable than the arithmetic mean.
• Scientific Experimental Data: When measuring indicators that grow exponentially, such as biological concentrations or pH levels, the geometric mean better represents the central tendency.

What is it? / Concept Explanation

The geometric mean is the Nth root of the product of a set of positive numbers (where N is the count of numbers). For a straightforward example: the geometric mean of 2 and 8 is √(2×8) = 4, whereas their arithmetic mean is 5. The geometric mean is ideal for handling data with "multiplicative" relationships, such as ratios, percentages, and growth rates, while the arithmetic mean is suited for additive relationships. In statistics, this concept describes the central tendency of a dataset. It is particularly "honest" when