Geometric Mean Calculator
Calculate Geometric Average
Calculate the geometric mean with detailed step-by-step solutions and comparison to other means.
Numbers
Import Numbers
All numbers must be positive. Supports comma, space, or newline separated values.
What is Geometric Mean?
The geometric mean is the nth root of the product of n numbers. It's ideal for calculating average growth rates and ratios.
G = ⁿ√(x₁ × x₂ × ... × xₙ)
For [2, 8, 32]:
G = ³√(2 × 8 × 32) = ³√512 = 8
Features
- Step-by-step calculations
- Add/remove numbers easily
- Edit numbers inline
- Arithmetic mean comparison
- Harmonic mean comparison
- Mean inequality verification
- Growth rate calculation
- Bulk import numbers
- Copy results
Mean Types
Best for growth rates and ratios
Best for simple averages
Best for rates and speeds
H ≤ G ≤ A (always true)
When to Use
Average compound growth over time
Average return on investments
Average of ratios or percentages
Price indices, stock indices
Use Cases
- Investment return calculations
- Population growth analysis
- Financial analysis
- Statistics and data analysis
- Economics and business
- Biology and ecology
- Computer science algorithms
- Scientific research
Applications
Real-World Applications:
Calculate average investment returns over time
Price indices and inflation calculations
Population growth and bacterial cultures
Analyze multiplicative data and ratios
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