Geometric Mean Calculator
Calculate the geometric mean of up to 6 positive values. The geometric mean is the appropriate average for growth rates, returns, and any multiplicative quantities.
The geometric mean is the nth root of the product of n values.
Formula: GM = (x₁ × x₂ × ... × xₙ)^(1/n)
Or equivalently: GM = exp((1/n) × Σ ln(xᵢ))
When to Use
- Averaging growth rates or returns over time
- Averaging ratios or proportions
- Data spanning several orders of magnitude
Mean Inequality: For positive values: Harmonic Mean ≤ Geometric Mean ≤ Arithmetic Mean
Equality holds only when all values are identical.