Harmonic Mean Calculator
Calculate Harmonic Average
Calculate the harmonic 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 Harmonic Mean?
The harmonic mean is the reciprocal of the arithmetic mean of reciprocals. It's used for rates and ratios.
H = n / Σ(1/xᵢ)
For [2, 4, 8]:
H = 3 / (1/2 + 1/4 + 1/8) = 3.43
Features
- Step-by-step calculations
- Add/remove numbers easily
- Edit numbers inline
- Arithmetic mean comparison
- Geometric mean comparison
- Mean inequality verification
- Bulk import numbers
- Copy results
- Quick examples
Mean Types
Best for rates and ratios
Best for growth rates
Best for simple averages
H ≤ G ≤ A (always true)
When to Use
When traveling same distance at different speeds
Financial ratios averaging
Work rates, production rates
Parallel resistance calculations
Use Cases
- Average speed calculations
- Financial ratio analysis
- Physics and engineering
- Statistics and data analysis
- Computer science algorithms
- Economics and finance
- Quality control
- Scientific research
Applications
Real-World Applications:
Calculate average speed for round trips
Average P/E ratios and financial metrics
Calculate parallel resistance
Analyze rates and ratios in datasets
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