Harmonic mean calculator
Enter a list of positive numbers, such as speeds over equal distances. You get the harmonic mean, which is the count divided by the sum of the reciprocals, plus the geometric and arithmetic means for comparison.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter your positive numbers.
- Read the harmonic mean. The geometric and arithmetic means are listed for comparison.
How it works
Harmonic mean = n / Σ(1/x). Zero and negative numbers are rejected because their reciprocals break the average. Results show up to 12 significant digits.
Worked example
Speeds of 40 and 60 km/h over equal distances:
- 1/40 + 1/60 = 3/120 + 2/120 = 5/120
- 2 / (5/120) = 48 km/h
Tips
- Use the harmonic mean for equal distances or equal amounts of work, and the arithmetic mean for equal times.
- All values must be in the same unit.
Frequently asked questions
What is the harmonic mean?
The number of values divided by the sum of their reciprocals, n / (1/x₁ + … + 1/xₙ). It is the average that suits rates.
How do I average speeds correctly?
If you cover equal distances at 40 and 60 km/h, the average speed is the harmonic mean, 48 km/h, not 50. The slower leg takes more time, so it counts more.
How does it relate to parallel resistors?
Resistors in parallel combine as 1 / (1/R₁ + 1/R₂ + …), which is the harmonic mean divided by the number of resistors. For 40 and 60 ohms that is 48 / 2 = 24 ohms.
How does it compare with the other means?
For positive numbers that are not all equal, harmonic mean < geometric mean < arithmetic mean. For 40 and 60 they are 48, about 48.99 and 50.