📊 Harmonic Mean Calculator
Calculate harmonic mean
How to Use This Calculator
Enter Positive Numbers
Type positive numbers separated by commas (e.g., 10, 20, 40). All values must be positive.
Click Calculate Harmonic Mean
Get harmonic mean plus comparison with geometric and arithmetic means.
View Results
See harmonic, geometric, and arithmetic means for comparison.
Formula
HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
Example: 10, 20, 40
HM = 3 / (1/10 + 1/20 + 1/40)
= 3 / (0.1 + 0.05 + 0.025) = 3 / 0.175
= 17.143
About Harmonic Mean Calculator
The Harmonic Mean Calculator computes the harmonic mean, which is ideal for rates, speeds, and situations where reciprocals matter more than absolute values. It's the reciprocal of the arithmetic mean of reciprocals.
When to Use This Calculator
- Average Speed: When distances are equal
- Rates: Pipes filling tanks, productivity rates
- Reciprocal Data: When reciprocals are important
Why Use Our Calculator?
- ✅ Instant Results: Calculate harmonic mean instantly
- ✅ Comparison: Shows all three means
- ✅ Educational: Learn when to use harmonic mean
- ✅ Completely Free: No registration required
Frequently Asked Questions
When should I use harmonic mean?
Use harmonic mean for rates, speeds, and reciprocal data. Example: average speed when traveling equal distances at different speeds.
Is harmonic mean always less than arithmetic mean?
Yes! For positive numbers, HM ≤ GM ≤ AM (harmonic ≤ geometric ≤ arithmetic).