Sum of Squares Calculator
Enter a whole number n and this tool returns the sum of the first n squares, 1^2 + 2^2 + ... + n^2, using the identity n(n+1)(2n+1)/6. For n = 10 the sum is 385.
What this calculator does
The Sum of Squares Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Enter a whole number n and this tool returns the sum of the first n squares, 1^2 + 2^2 + ... + n^2, using the identity n(n+1)(2n+1)/6. For n = 10 the sum is 385. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Sum of Squares Calculator
The Sum of Squares Calculator adds up the squares of every whole number from 1 to n. It applies the closed-form identity n(n+1)(2n+1)/6, so you get the total without squaring and adding each term by hand.
Formula & Mathematical Calculation
Sum = f(n (sum of first n squares))
Calculated according to standard math formulas implemented in the calculator core.
Calculation Example
Enter n = 10 and click Calculate. The tool evaluates 10 x 11 x 21 / 6, and the Sum box shows 385, meaning 1^2 + 2^2 + ... + 10^2 = 385.
Key Benefits
- Computes 1^2 + 2^2 + ... + n^2 from a single whole-number input
- Uses the exact n(n+1)(2n+1)/6 identity instead of adding each term one at a time
- Spells out the worked identity in the interpretation line beneath the result
How to Use this Calculator
-
Enter n
Type a non-negative whole number in the 'n (sum of first n squares)' field. -
Calculate
Click the Calculate button to run the sum. -
Read the Sum
Read the total in the Sum box; the line below restates the n(n+1)(2n+1)/6 identity for your value.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Sum of Squares Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.