Enter a set of numbers into the Mean Calculator and get back the arithmetic mean, geometric mean, and harmonic mean all at once. Type your values into the data set field separated by commas, and the tool returns all three averages along with the count, sum, minimum, and maximum of your dataset.
Arithmetic Mean
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Geometric Mean
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Harmonic Mean
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Count (n)
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Sum
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Minimum
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Maximum
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The arithmetic mean is the most common type of average. It is calculated by summing all values in a dataset and dividing by the total count of values. For example, the arithmetic mean of 2, 4, and 6 is (2+4+6)/3 = 4.
The geometric mean is calculated by multiplying all values together and then taking the nth root, where n is the count of values. For example, the geometric mean of 2, 8, and 32 is the cube root of (2×8×32) = cube root of 512 = 8. It requires all values to be positive.
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of a dataset. It is best used when averaging rates or ratios, such as speeds, prices per unit, or price-to-earnings ratios. It gives more weight to smaller values than the arithmetic mean.
The arithmetic mean adds all values and divides by the count, while the geometric mean multiplies all values and takes the nth root. The geometric mean is always less than or equal to the arithmetic mean. Use the arithmetic mean for additive data and the geometric mean for multiplicative or exponential data like growth rates.
A data set is a collection of individual values or observations used for statistical analysis. Each number in the set represents a single data point. Measures of central tendency like the mean describe what a typical value in that set looks like.
For any set of positive numbers, the relationship holds that harmonic mean ≤ geometric mean ≤ arithmetic mean. The harmonic mean penalizes large values more heavily by working with reciprocals, making it the most conservative of the three averages.
The arithmetic mean works with any real numbers, including negatives and zeros. However, the geometric mean requires all values to be strictly positive, and the harmonic mean requires all values to be non-zero. This calculator will alert you if your data set is incompatible with geometric or harmonic mean calculations.
In Excel, use =AVERAGE(range) for the arithmetic mean, =GEOMEAN(range) for the geometric mean, and =HARMEAN(range) for the harmonic mean. Replace 'range' with your cell range, for example =AVERAGE(A1:A10). This calculator gives you all three results simultaneously without any spreadsheet setup.