Mean Calculator – Arithmetic, Geometric & Harmonic
Choose arithmetic, geometric or harmonic mean for a list of numbers. Compare results and try an equal-distance speed example.
Last updated · View algorithm, constants and default inputs (JSON)
Numbers (separated by comma, semicolon or space)
About this calculator
There are several kinds of mean, and each suits different data. The arithmetic mean fits additive quantities, the geometric mean fits growth rates and ratios, and the harmonic mean fits rates such as speed over a fixed distance.
Choose the calculation that matches your task
This tool offers arithmetic, geometric and harmonic mean choices. Select the definition appropriate to the data and follow its input rules. For an arithmetic-only summary with minimum and maximum values, use the average calculator.
Worked example
calculated with the default values below
Mean to highlight Arithmetic mean · Numbers (separated by comma, semicolon or space) 4, 8, 15, 16, 23, 42 Arithmetic mean 18.0000 · Geometric mean 13.9655 · Harmonic mean 10.4995 · Sum 108.0000 · Count 6
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
x̄ = Σx ÷ n; G = e^(Σ ln(x) ÷ n); H = n ÷ Σ(1 ÷ x)
- x̄
- arithmetic mean
- G
- geometric mean
- H
- harmonic mean
- x
- entered values
- n
- value count
Parses up to 10,000 finite values separated by commas, semicolons or whitespace; empty items are rejected. Geometric mean is undefined for nonpositive values; harmonic mean is undefined when reciprocal sum is zero or undefined.
Frequently asked questions
How does the calculator handle separators and empty entries?
Use commas, semicolons or spaces between finite numbers. A missing value such as “1,,2” or a trailing separator is rejected instead of being silently treated as zero.
How do I calculate a harmonic mean?
For n nonzero values, H = n ÷ (1/x₁ + … + 1/xₙ), provided the reciprocal sum is nonzero. Choose harmonic mean to highlight it. For equal distances travelled at 40 and 60 km/h, H = 2 ÷ (1/40 + 1/60) = 48 km/h. For equal time intervals, use the arithmetic mean instead.
When should I choose geometric or arithmetic mean?
Use arithmetic mean for equally weighted additive values. This tool calculates geometric mean only for positive values; for 2 and 8, it is √(2 × 8) = 4. Growth rates must first be converted to positive growth factors. Zero or negative inputs leave geometric mean undefined.