Geometric Mean Calculator
Find the geometric mean of a set of positive numbers, ideal for rates and ratios.
Enter your data set. All values must be positive (greater than zero).
Geometric Mean
Count (n)
Product
Calculation Steps
What the Geometric Mean Measures
The geometric mean is a type of average that multiplies all the values together and then takes the n-th root of the product. Unlike the arithmetic mean, it is well suited to data that grows multiplicatively, such as rates of return, growth rates, and ratios. It always requires every value to be positive.
Formula
For a data set of n positive values, the geometric mean (GM) is defined as the n-th root of the product of all values:
- GM = (x₁ × x₂ × … × xₙ)^(1/n)
- Equivalently: GM = exp( (1/n) × Σ ln(xᵢ) )
Why Use Logarithms
Multiplying many values together can quickly overflow the limits of floating-point arithmetic. By summing the natural logarithms of each value and then exponentiating the average, this calculator computes the geometric mean accurately even for long lists or large numbers. The geometric mean is only defined when all values are positive.