Geometric Mean Calculator
Calculate the geometric mean of positive numbers, ideal for growth rates and ratios.
Inputs
Positive numbers only.
Geometric Mean
5.656854
Count
4
Product of Values
1,024.0000
Step by step
Count of values
= 4
Sum of natural logarithms
ln(2) + ln(8) + ln(4) + ln(16)
= 6.93147181
Mean of logarithms
6.93147181 / 4
= 1.73286795
Geometric mean = exp(mean of logs)
exp(1.73286795)
= 5.656854
How it works
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
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.