Math

Harmonic Mean Calculator

Find the harmonic mean of up to three numbers.

Calculated Output

Harmonic mean 3.429

Formula: HM = n ÷ Σ(1/xᵢ)

Step-by-Step Breakdown

1. Values used:

2. Value 1 = 2

3. Value 2 = 4

4. Value 3 = 8

6. Harmonic mean = 3.429

Did this calculator solve your problem today?

The math behind it

HM = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ). Always ≤ the arithmetic mean.

2, 4, 8 → 3 ÷ (0.5+0.25+0.125) = 3.43.

When to use?

Averaging speeds over equal distances, or P/E ratios.