Harmonic Mean Calculator Formula
Understand the math behind the harmonic mean calculator. Each variable explained with a worked example.
Formulas Used
Harmonic Mean
harm_mean = 2 / (1/a + 1/b)Arithmetic Mean (for comparison)
arith_mean = (a + b) / 2Variables
| Variable | Description | Default |
|---|---|---|
a | Value 1 | 40 |
b | Value 2 | 60 |
recip_sum | Derived value= 1/a + 1/b | calculated |
How It Works
How to Compute the Harmonic Mean
Formula (for two values)
Harmonic Mean = 2 / (1/a + 1/b)
More generally for n values: HM = n / (1/v1 + 1/v2 + ... + 1/vn)
The harmonic mean gives more weight to smaller values. It is the correct average to use when the quantities are defined in relation to a common unit, such as speed over the same distance at different rates.
Worked Example
A car travels 100 km at 40 km/h and returns at 60 km/h. What is the average speed?
a = 40b = 60
- 01Reciprocal sum = 1/40 + 1/60 = 0.025 + 0.01667 = 0.04167
- 02Harmonic Mean = 2 / 0.04167 = 48
- 03The average speed is 48 km/h (not 50 as the arithmetic mean would suggest)
Ready to run the numbers?
Open Harmonic Mean Calculator