This geometric mean calculator computes the geometric average of a list of numbers - useful for investment returns, growth rates, and comparing values of different weights.
Geometric mean calculator
What is the geometric mean?
The geometric mean is the nth root of the product of n numbers. Unlike the arithmetic mean, it only works for positive numbers (or percentage returns above -100%).
geometric\ mean = \sqrt[n]{x_1 \times x_2 \times ... \times x_n}The geometric mean is especially useful for:
- Investment returns - averaging percentage gains/losses over time
- Growth rates - population, revenue, or other compound growth
- Ratios and rates - comparing values with different units or scales
Why use geometric mean for returns?
Imagine a stock with these annual returns: -50%, +30%, +20%. The arithmetic mean gives 0%, but you'd actually have $78 for every $100 invested.
The geometric mean correctly shows -7.95% average annual return, accounting for compounding.
Using the calculator
Enter numbers separated by commas, spaces, or new lines. Use the Percentages mode for investment returns (enter -50, 30, 20 and it handles the conversion). Results update instantly.
The calculator also shows the harmonic mean and arithmetic mean for comparison.
