Calculators
Harmonic Mean Calculator
Calculate the harmonic mean from a set of positive numbers locally in your browser. The harmonic mean is n ÷ (1/x₁ + 1/x₂ + ... + 1/xₙ), useful for rates and ratios.
Find the harmonic mean of positive values.
Enter positive numbers separated by newlines, commas, semicolons, or spaces. The harmonic mean is calculated as the count of values divided by the sum of their reciprocals. For example, the harmonic mean of 10, 20, and 40 is 3 ÷ (1/10 + 1/20 + 1/40) = 3 ÷ 0.175 ≈ 17.14. All calculations run locally in your browser; your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is the harmonic mean calculated?
Divide the number of values by the sum of their reciprocals: n / Σ(1/x). For 10, 20, and 40, this is 3 / 0.175, approximately 17.142857.
When should I use a harmonic mean for speed?
Use it for speeds over equal distances. Traveling one kilometer at 30 km/h and one kilometer at 60 km/h gives an average speed of 40 km/h. For equal times, use an arithmetic mean instead.
Can I enter zero or negative numbers?
This calculator accepts strictly positive finite numbers only. Zero has no finite reciprocal and negative values are outside the supported dataset definition.
How does it compare with other means?
For positive values, the harmonic mean is no greater than the geometric mean, which is no greater than the arithmetic mean. All three are equal when every value is the same.
Are my numbers uploaded?
No. Up to 10000 values are processed locally in your browser. Results use approximate floating-point arithmetic and display 12 significant digits.