This online Sum of Squares Calculator performs calculation of the sum of squares of a set of arbitrary real numbers or the sum of squares of a set of consecutive integer numbers. Enter the set of numbers in the input field of the calculator and click the “Calculate” button. You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators. In case of a set of consecutive integer numbers enter the first and last numbers separated by the minus sign.
Sum of squares formula
This online tool calculates the sum of squares \(S\) of a set of \(n\) arbitrary real numbers:
$$S = { x }_{ 1 }^2+{ x }_{ 2 }^2+…+{ x }_{ n }^2.$$
In case of a set of \(n\) consecutive integer numbers \(1,2,…n\) we use the following formula for the sum of squares:
$$S = \sum_{k=1}^nk^2 = \frac{n(n + 1)(2n + 1)}{6}.$$
In case of a set of consecutive integer numbers starting from \({ n }_{ 1 }\) through \({ n }_{ 2 }\) we use the following formula for the sum of squares:
$$S = \frac{{ n }_{ 2 }({ n }_{ 2 } + 1)(2{ n }_{ 2 } + 1)}{6} – \frac{{ n }_{ 1 }({ n }_{ 1 } – 1)(2{ n }_{ 1 } – 1)}{6}.$$
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