Sum of Squares Calculator

The sum of squares (SS) measures the total variability within a dataset. The statistical sum of squares is calculated by summing the squared differences between each value and the dataset mean. It is a foundational quantity used in computing variance, standard deviation, and in ANOVA tests.

The statistical sum of squares (SS) is the sum of squared deviations from the mean: SS = Σ(xᵢ − x̄)². The algebraic sum of squares is simpler — it's just the sum of each value squared: Σ(xᵢ²). Both have different uses in statistics and algebra.

First, find the mean of your dataset. Second, subtract the mean from each value to get the deviation. Third, square each deviation. Finally, add all the squared deviations together. The result is the statistical sum of squares.

The sum of squares is the building block for variance and standard deviation — two of the most widely used measures of data spread. It is also central to ANOVA (Analysis of Variance), regression analysis, and many hypothesis testing procedures.

Yes. If all values in your dataset are identical, the deviation from the mean is zero for every observation, making the statistical sum of squares exactly zero. This indicates there is no variability in the data.

Yes. This calculator supports negative numbers, decimals, and integers. Simply separate your values with commas, spaces, or line breaks, and the calculator will parse them correctly — invalid entries like letters or symbols are automatically ignored.

You can enter as few as 2 values and as many as several hundred. For very large datasets, a deviation breakdown table is shown so you can inspect each observation's contribution to the total sum of squares.

The statistical sum of squares formula is SS = Σ(xᵢ − x̄)², where xᵢ is each individual value and x̄ is the mean of all values. The algebraic sum of squares formula is simply Σ(xᵢ²) — the sum of each value squared without subtracting the mean.