Calculators
Sum of Squares Calculator
Calculate the sum of squared values and squared deviations from the mean for signed data privately in your browser.
Distinguish raw and centered sums of squares.
The raw sum of squares is Σx²: square each value and add the squares. The centered sum of squares is Σ(x − mean)²: subtract the arithmetic mean before squaring. For 1, 2, 3, the mean is 2, the raw sum is 14, and the centered sum is 2. Negative values have positive squares; all-zero data returns zero. A single value has centered sum zero. Divide the centered sum by n for population variance or by n − 1 for sample variance when n is at least two. Both sums have squared input units. Enter up to 10000 finite signed numbers separated by spaces, commas, semicolons or newlines. Scientific notation is supported; thousands separators are not. Use consistent units. Calculations use scaled browser floating-point arithmetic, display 12 significant digits, and reject results outside the supported numeric range. Tiny differences relative to large values may lose precision. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I calculate the sum of squares?
Square every value and add the results: Σx². For 1, 2, 3, the sum is 1 + 4 + 9 = 14.
What is the centered sum of squares?
Subtract the arithmetic mean from each value, square each difference, and add them. For 1, 2, 3, the mean is 2 and the centered sum is 1 + 0 + 1 = 2.
How does this relate to variance?
Population variance is the centered sum divided by n. Sample variance divides it by n − 1 and requires at least two values. The raw sum of squares does not subtract the mean.
Can I enter negative numbers?
Yes. Enter 1 to 10000 finite signed numbers with spaces, commas, semicolons or newlines between them. Use decimal points without thousands separators. Scientific notation is accepted.
What units and precision do results use?
Both sums have squared input units. Results use floating-point arithmetic and display up to 12 significant digits. Extreme magnitudes can exceed the numeric range or lose small differences. No data is uploaded.