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Variance Calculator

Enter a set of numbers, pick whether you have whole population data or sampled data, and press Calculate to see the variance, the standard deviation, and the mean.

About this calculator

The variance calculator has a text field for the values and a Data type selector with two options: Whole population data and Sampled data. Press Calculate and the results appear in cards below the button: Variance, Standard deviation, and Mean.

The calculation runs only when the button is pressed. Each result card can be sent to the clipboard with Copy, which writes the result and its unit, and Clear resets the form.

Whole population data or sampled data

Which formula is used depends on the data type you pick. With whole population data, the variance is the sum of the squared differences from the mean divided by the count of values. With sampled data, that same sum is divided by one less than the count of values.

Variance formula

Both versions start the same way: find the mean, subtract it from each value, square the differences, and add them up. What changes is the divisor. For a whole population, written as the variance symbol sigma squared, the sum is divided by the number of values. For a sample, written as s squared, the sum is divided by the number of values minus one.

The worked examples show this directly: the squared differences add to 8 for the values 1 3 5 and to 9.68 for the values 1.2, 3.4, 5.6, giving the expressions σ² = 8 / 3 ≈ 2.66666666666667, s² = 8 / 2 = 4, and s² = 9.68 / 2 = 4.84.

Standard deviation and mean formula

The mean is the sum of the values divided by the count of values. The standard deviation is the square root of the variance.

For example, entering 1.2, 3.4, 5.6 as sampled data returns Variance: 4.84; Standard deviation: 2.2; Mean: 3.4.