Harmonic Mean Calculator
Calculate the harmonic mean of four positive values. The harmonic mean is ideal for averaging rates and ratios.
How to Use the Harmonic Mean Calculator
- Enter four positive values.
- Click Calculate to see the harmonic and arithmetic means.
- The sum of reciprocals is also shown for reference.
Referência Rápida
| De | Para |
|---|---|
| 40, 60 (speeds) | HM = 48 km/h |
| 2, 3, 6 | HM = 3 |
| 1, 1, 1, 1 | HM = 1 |
| 1, 2, 4, 8 | HM ≈ 2.13 |
| HM ≤ GM ≤ AM | Always true |
Casos de Uso
- •Computing average speed over equal distances at different speeds.
- •Calculating the F1-score (harmonic mean of precision and recall).
- •Averaging P/E ratios in financial analysis.
Fórmula
Harmonic mean = n / Σ(1/xᵢ). For positive values, HM ≤ GM ≤ AM (AM–GM–HM inequality).
Perguntas Frequentes
What is the harmonic mean?
The reciprocal of the average of reciprocals. It gives more weight to smaller values.
When should I use it?
When averaging rates (e.g., speeds over equal distances) or ratios like P/E ratios.
Is HM always ≤ AM?
Yes, for positive values the harmonic mean is always less than or equal to the arithmetic mean.