Harmonic Mean Calculator
Find the harmonic mean of positive values, ideal for averaging rates and ratios.
Harmonic Mean
48.0000
Harmonic Mean vs Value 1
公式
## How to Compute the Harmonic Mean ### Formula (for two values) **Harmonic Mean = 2 / (1/a + 1/b)** More generally for n values: **HM = n / (1/v1 + 1/v2 + ... + 1/vn)** The harmonic mean gives more weight to smaller values. It is the correct average to use when the quantities are defined in relation to a common unit, such as speed over the same distance at different rates.
计算示例
A car travels 100 km at 40 km/h and returns at 60 km/h. What is the average speed?
- 01Reciprocal sum = 1/40 + 1/60 = 0.025 + 0.01667 = 0.04167
- 02Harmonic Mean = 2 / 0.04167 = 48
- 03The average speed is 48 km/h (not 50 as the arithmetic mean would suggest)
常见问题
When should I use the harmonic mean?
Use it when averaging rates or ratios measured over the same base quantity, such as speeds over equal distances or price-to-earnings ratios.
Why is the harmonic mean always the smallest of the three Pythagorean means?
For any set of positive unequal values, Harmonic Mean <= Geometric Mean <= Arithmetic Mean. The harmonic mean is pulled toward the smaller values because it averages reciprocals.
Can the harmonic mean handle zero values?
No. A zero value causes a division by zero in the reciprocal, making the harmonic mean undefined.
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