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Sum of Powers Squares Cubes and Fourth Powers Calculator

Σk² = n(n+1)(2n+1)/6; Σk³ = [n(n+1)/2]².

Calculates closed-form sums of squares, cubes, and fourth powers from 1 to n. Also includes sum of first n integers. Essential for discrete mathematics and proof writing.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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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 = n(n+1)/2; Σk² = n(n+1)(2n+1)/6; Σk³ = [n(n+1)/2]²; Σk⁴ = n(n+1)(2n+1)(3n²+3n−1)/30

In depth

Calculates closed-form sums of squares, cubes, and fourth powers from 1 to n. Also includes sum of first n integers. Essential for discrete mathematics and proof writing.