This calculator computes the harmonic mean, ideal for reciprocal relationships and requiring positive numbers only. For standard averages, use our arithmetic mean calculator; for multiplicative relationships, our geometric mean calculator; or for varying importance levels, our weighted mean calculator. Compare different types of means →
Harmonic Mean Calculator
Harmonic Mean Formula
n = count of numbers
x₁, x₂, etc. = individual values
Result
Understanding Harmonic Mean
Practical Example: Average Speed
You travel:
- 60 miles at 30 mph
- 60 miles at 50 mph
Total distance is 120 miles. Using two different speeds for equal distances means the harmonic mean more accurately represents the true average speed than the arithmetic mean.
Detailed Computation:
- Time(1) = 60 / 30 = 2.0 hours
- Time(2) = 60 / 50 = 1.2 hours
- Total time = 3.2 hours
- Harmonic Mean Speed = 120 miles / 3.2 h = 37.5 mph
Notice how the slower speed significantly affects the average.
When to Use Harmonic Mean
Speed & Travel
- • Round-trip speeds
- • Variable speed segments
- • Transportation rates
- • Delivery times
Production
- • Manufacturing rates
- • Work completion times
- • Processing speeds
- • Output per hour
Pricing
- • Price per unit
- • Cost comparisons
- • Rate averaging
- • Value metrics
Common Questions
When should I use harmonic mean vs. arithmetic mean?
Use Harmonic Mean for:
- Speeds over equal distances
- Production rates (units/time)
- Price per unit comparisons
- Any per-unit measurements
Use Arithmetic Mean for:
- Simple totals or counts
- Direct measurements
- Temperatures, grades
- General averages
What data limitations should I know about?
The calculator cannot handle:
- Zero values (division by zero)
- Negative numbers
- Non-numeric data
These limitations exist because harmonic mean involves taking reciprocals (1/x) of values.
Why is my result smaller than expected?
The harmonic mean emphasizes smaller values among rates or speeds. Even one small rate can pull the overall average down more than one large rate can pull it up. This is accurate for scenarios like averaging travel speeds or production rates where slow segments significantly affect total performance. This makes it perfect for:
- Accurately representing average speeds
- True production rate calculations
- Realistic performance metrics