Mean Calculator — Arithmetic, Geometric & Harmonic Mean
Enter a list of numbers and instantly get the arithmetic mean (average), geometric mean, and harmonic mean, plus the sum, count, minimum, and maximum.
Sum of all values divided by the count
- 1
Count values (n)
6 - 2
Sum all values
Σxᵢ (6 values) = 108 - 3
Arithmetic mean = sum ÷ n
108 ÷ 6 = 18
Come funziona questo calcolatore?
Arithmetic mean = sum ÷ count. Geometric mean = nth root of the product (for positive values). Harmonic mean = n ÷ sum of reciprocals (for non-zero values). The three satisfy H ≤ G ≤ x̄, with equality only when all values are the same. Enter your numbers separated by commas to get all three instantly.
Formula
How this is calculated
The three classical means each describe the "centre" of a dataset in a different way. The arithmetic mean x̄ = Σxᵢ / n is the everyday average — it minimises the sum of squared deviations and is appropriate for data where you want to share a total equally (e.g., average score, average price). It is sensitive to extreme outliers.
The geometric mean G = (x₁ × x₂ × … × xₙ)^(1/n) is the average of multiplicative quantities. It is computed as exp(mean of the natural logs) for numerical stability. Use it for growth rates, ratios, and any data where changes are proportional — for example, averaging annual percentage returns, or investment multipliers. It requires all values to be strictly positive.
The harmonic mean H = n / Σ(1/xᵢ) is the correct average for rates — situations where you travel at different speeds for equal distances, or process items at different rates. It is always ≤ the geometric mean ≤ the arithmetic mean (AM–GM–HM inequality), with equality only when all values are identical. It is undefined if any value is zero.
Domande frequenti
Use the geometric mean when combining values that multiply together — compounding investment returns, population growth rates, or any ratio-scale quantities. For example, if an investment grows by 50% in year 1 and falls by 33% in year 2, the geometric mean growth rate is (1.50 × 0.67)^(1/2) − 1 ≈ 0%, reflecting no net gain, while the arithmetic mean of 8.5% would be misleading.
If you travel the same distance at two different speeds, the average speed is the harmonic mean of the two speeds. For equal distances at 60 mph and 40 mph, the average speed is 2 / (1/60 + 1/40) = 48 mph, not the arithmetic average of 50 mph. The arithmetic mean would only be correct if you spent equal time at each speed.
The arithmetic mean handles any real numbers including negatives and zeros. The geometric mean requires all values to be strictly positive (logarithm is undefined at zero and imaginary for negatives). The harmonic mean requires all values to be non-zero. The calculator shows N/A for means that cannot be computed with your data.
Conosciuto anche come
TG we-Calculate Editorial Team. (2026). Mean Calculator — Arithmetic, Geometric & Harmonic Mean [Online calculator]. TG we-Calculate. https://we-calculate.com/it/calculator/mean-calculator
TG we-Calculate Editorial Team. "Mean Calculator — Arithmetic, Geometric & Harmonic Mean." TG we-Calculate. 2026. https://we-calculate.com/it/calculator/mean-calculator.
TG we-Calculate Editorial Team, "Mean Calculator — Arithmetic, Geometric & Harmonic Mean," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/it/calculator/mean-calculator
@misc{wecalculate_mean_calculator, title = {Mean Calculator — Arithmetic, Geometric & Harmonic Mean}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/it/calculator/mean-calculator}}, year = {2026}, note = {TG we-Calculate} }
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