Harmonic Mean Calculator

About Harmonic Mean

The harmonic mean is the reciprocal of the arithmetic mean of reciprocals. It is particularly useful when dealing with rates, speeds, or other quantities where the reciprocal has meaning.

Formula:

For numbers x₁, x₂, ..., xₙ:
H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)

Properties:

• Always less than or equal to the arithmetic mean
• Useful for averaging rates and speeds
• Cannot include zero values (division by zero)
• Gives lower weight to larger values

Applications:

• Average speed over different segments
• Circuit calculations (parallel resistors)
• Financial ratios
• Population density calculations

Example:

If a car travels 60 km/h for half the distance and 40 km/h for the other half, the average speed is the harmonic mean: 48 km/h, not the arithmetic mean of 50 km/h.