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Variance Calculator

Find the variance and standard deviation of a data set.

How it is calculated

Numbers can be separated by commas, spaces or semicolons; non-numeric entries are skipped and at least two values are needed. With mean x̄ and sum of squared deviations SS = Σ(x − x̄)²: population variance σ² = SS ÷ n, sample variance s² = SS ÷ (n − 1), and the standard deviations are their square roots. Use the population figures when your list is the whole group, and the sample figures when it is a sample drawn from a larger group. Variance is in squared units of the data; standard deviation returns to the original unit. Results show four decimals.

Worked example

Data 4, 8, 6, 5, 3, 7 (n = 6). Mean = 33 ÷ 6 = 5.5. Squared deviations: 2.25, 6.25, 0.25, 0.25, 6.25, 2.25, summing to 17.5. Population variance = 17.5 ÷ 6 = 2.9167. Sample variance = 17.5 ÷ 5 = 3.5000. Standard deviations: √2.9167 = 1.7078 and √3.5 = 1.8708.

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Common mistakes

  • Using the population figure for a sample, which understates the spread; the sample version divides by n − 1.
  • Comparing variances of data in different units or scales; use the standard deviation or the coefficient of variation.
  • Reading variance as a distance: it is in squared units, so 3.5 is not in the same unit as the data.
  • Typing a decimal comma in a list that is separated by commas, which splits 2,5 into two numbers; use a point for decimals.
  • Entering a single value; at least two are needed.

About this calculator

This calculator computes both population variance (σ²) and sample variance (s²) from a list of numbers, along with their square roots, the population and sample standard deviations. Population variance divides the sum of squared deviations from the mean by N, while sample variance uses Bessel's correction — dividing by n−1 instead of n — to produce an unbiased estimate when the data is only a sample of a larger population.

Variance measures how spread out values are around the mean, and it's foundational to statistics: it feeds into confidence intervals, ANOVA, regression analysis, and risk metrics in finance, where the standard deviation of returns is used as a proxy for volatility.

Statistics students working through coursework, data analysts and researchers summarizing a dataset, quality control engineers measuring process consistency, and finance professionals assessing investment risk all reach for this calculation.

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Comments (1)

  • Editorial team

    Variance has a useful property that standard deviation lacks: for independent quantities the variances add. If two unrelated steps in a process have variances of 3.5 and 2.9167, the combined variance is 6.4167, and only then do you take the square root, about 2.53, for the combined spread. Adding the two standard deviations instead would overstate it. What process or dataset are you combining?

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