Geometric Mean Calculator
Calculate the geometric mean of positive numbers, ideal for growth rates and ratios.
About Geometric Mean Calculator
The geometric mean is the nth root of the product of n values. It represents the central tendency of multiplicative data such as growth rates, investment returns, and ratios. It is computed via logarithms to avoid overflow.
Formula
Geometric Mean
G = (x₁ × x₂ × ... × xₙ)^(1/n) = exp(mean(ln(values)))
- G
- Geometric mean
- n
- Number of values
- xᵢ
- Each positive value
Worked example
With the default values below, Geometric Mean Calculator returns Geometric Mean of 5.656854. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Values (comma separated)
- 2, 8, 4, 16
Results
- Geometric Mean
- 5.656854
- Count
- 4
- Product of Values
- 1,024.0000
Step by step
- 1Count of values= 4
- 2Sum of natural logarithms= 6.93147181
- 3Mean of logarithms= 1.73286795
- 4Geometric mean = exp(mean of logs)= 5.656854
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
When should I use geometric mean vs arithmetic mean?
Use geometric mean for multiplicative data: growth rates, interest rates, population growth, or any data spanning multiple orders of magnitude. Use arithmetic mean for additive data like test scores or heights.
Why use logarithms instead of computing the product directly?
For many values or large numbers, the product can overflow. Taking ln of each value, averaging those, then exponentiating gives the same result without overflow.