basic

Sum of Squares from 1 to n Calculator

Σ k² = n·(n + 1)·(2n + 1) / 6.

Compute the closed-form sum of the first n positive squares: 1² + 2² + ⋯ + n² = n(n+1)(2n+1)/6. The classical Faulhaber identity, used in calculus (Riemann sums), discrete math, and physics moment-of-inertia derivations.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

Σₖ₌₁ⁿ k² = n(n+1)(2n+1) / 6.

In depth

Compute the closed-form sum of the first n positive squares: 1² + 2² + ⋯ + n² = n(n+1)(2n+1)/6. The classical Faulhaber identity, used in calculus (Riemann sums), discrete math, and physics moment-of-inertia derivations.