Harmonic Mean Calculator
This calculator computes the harmonic mean of a set of positive numbers. It’s especially useful when averaging rates, ratios, or quantities like speed, density, or efficiency. Just enter your values, and the calculator returns the harmonic mean instantly.
Calculate the Harmonic Average of Numbers
Harmonic Mean Formula
$$\text{Harmonic Mean} = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}}$$
Explanation:
To compute the harmonic mean, divide the number of values n by the sum of the reciprocals of all values. This mean gives more weight to smaller numbers and is ideal for averaging rates.
Harmonic Mean – Calculation Example
Values: 4, 5, 10
- Compute reciprocals → 1/4 + 1/5 + 1/10 = 0.25 + 0.2 + 0.1 = 0.55
- n = 3
- 3 / 0.55 ≈ 5.45
Result: Harmonic mean ≈ 5.45
The harmonic mean is commonly used in finance (e.g., P/E ratios), physics (e.g., average speed), and data science when smaller values have greater impact. Unlike arithmetic mean, it penalizes high outliers and is the best choice when averaging values expressed as “per unit.”