Add the squares of a list of numbers, or of the first n natural numbers, with mean square and root mean square.
Sum of squares
How to use this tool
A list takes priority; otherwise the first n natural numbers are used.
The headline figure is the sum of the squares.
It is the sum divided by the count.
It gives the typical magnitude of the values.
Formula & worked example
2² + 3² + 4² = 29, and the squares of 1 to 10 sum to 385.
Limitations — read this before you rely on it
The first-n mode caps at n = 1,000,000 to keep results exact in floating point. Lists are computed in double precision.
Frequently asked questions
Each number is squared and the squares are added: for 2, 3, 4 that is 4 + 9 + 16 = 29.
1² + 2² + … + n² = n(n + 1)(2n + 1) / 6. For n = 10 that gives 385.
The square root of the average square — a single figure for the typical size of the values, used in signal and error analysis.
No. Squaring the sum of 2, 3, 4 gives 81; the sum of squares is 29. They are different quantities.
In variance, regression and ANOVA, where squared deviations measure spread and fit.