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Sum of Squares Calculator

Paste your numbers to compute the sum of squares.

How it is calculated

Paste your numbers separated by commas, spaces, semicolons or line breaks (one value is enough). The tool computes the sum of squared deviations from the mean, not the sum of the raw squares:

mean = Σx / n and SS = Σ(x − mean)²

It also shows the count, the mean, and the sample variance SS / (n − 1), all to four decimals. With a single value the variance is shown as 0. Any entry that is not a number makes the whole input invalid. If you need the raw sum Σx² instead, use the shortcut identity Σx² = SS + (Σx)² / n.

Worked example

Data: 4, 8, 6, 5, 3, 2, 8, 9. There are 8 values adding to 45, so the mean is 5.625. The deviations are −1.625, 2.375, 0.375, −0.625, −2.625, −3.625, 2.375 and 3.375. Their squares add up to 45.8750, which is the sum of squares. The sample variance is 45.875 / 7 = 6.5536. As a cross-check, Σx² = 299 and 299 − 45² / 8 = 45.875.

Try this example →

Common mistakes

  • Expecting Σx² (squares of the raw values). This tool measures spread around the mean, so for 4, 8, 6, 5, 3, 2, 8, 9 it gives 45.875, not 299.
  • Using a decimal comma such as 2,5 in the list. Commas separate values here, so it becomes two numbers; write 2.5.
  • Reading the variance as a population variance. It divides by n − 1, the sample version; divide the SS by n yourself for the population figure.
  • Leaving a label or unit in the data, such as "5kg", which makes the input invalid.
  • Comparing SS between datasets of different sizes. SS grows with n, so compare variances instead.

About this calculator

The sum of squares — formally SS = Σ(xᵢ − x̄)², the sum of each data point's squared distance from the mean — is one of the most foundational quantities in statistics, because it measures total spread while squaring keeps positive and negative deviations from canceling each other out. Dividing it by n or n−1 produces variance, and its square root gives standard deviation, while in regression and ANOVA it splits into explained and residual components that drive hypothesis tests.

This calculator takes a pasted list of numbers and returns the sum of squares alongside the count, mean, and sample variance in one step. Statistics students checking homework by hand, quality-control analysts running Six Sigma calculations, and researchers doing a quick sanity check before running a full analysis in dedicated software use it to skip the repetitive by-hand arithmetic.

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Comments (1)

  • Editorial team

    A tiny test case helps when you doubt a result: the list 2, 4, 6 has a mean of 4, a sum of squares of 8, and a sample variance of 4, so a standard deviation of 2. Take the square root of the variance shown to get the standard deviation for any list. What are you using the figure for, a variance, an ANOVA table or a regression?

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