How to use the sum of squares calculator
Find the sum of the squares of the first n whole numbers using the closed formula. Enter number of terms in the field above; the sum of squares 1² + … + n², average square are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “sum of squares formula”, “1 squared plus 2 squared”, “n(n+1)(2n+1)/6”, “calculate sum of squares”, “find sum of squares 1² + … + n²”.
Formula
Variables
- n — Number of terms
Worked example
With number of terms = 10, the calculator gives sum of squares 1² + … + n² ≈ 385; average square ≈ 38.5.
Frequently asked questions
What is the sum of squares calculator used for?
Find the sum of the squares of the first n whole numbers using the closed formula. It helps with questions such as “sum of squares formula”, “1 squared plus 2 squared”, “n(n+1)(2n+1)/6”.
What is the formula for the sum of squares calculation?
Sum of squares 1² + … + n² = n × (n+1) × (2 × n+1) / 6. Average square = [Sum of squares 1² + … + n²] / n. Here n is number of terms.
What inputs do I need for the sum of squares calculator?
You need number of terms. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the sum of squares calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the sum of squares result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.