Square Pyramidal Number Calculator

About this calculator

The nth square pyramidal number Pₙ = n(n+1)(2n+1)/6 is the sum of the first n perfect squares (1² + 2² + … + n²), representing the number of spheres that stack into a pyramid with a square base n layers tall — one layer of n² balls, the next of (n−1)², and so on down to a single ball on top.

These numbers are famous in number theory for the cannonball problem: the question of when a square pyramidal stack can be rearranged into a flat square array, which turns out to happen only for n=1 and n=24 (1+4+9+…+24² = 4900 = 70²), a result proved using elliptic curves. Mathematics educators use square pyramidal numbers to teach summation formulas, and puzzle enthusiasts encounter them in classic stacking problems. Enter n to get Pₙ.