Tetrahedral Number Calculator

About this calculator

The nth tetrahedral number Teₙ = n(n+1)(n+2)/6 counts the objects (like cannonballs or oranges) that can be stacked into a triangular pyramid n layers deep — it's the running sum of the first n triangular numbers (1, 3, 6, 10, …), the same way triangular numbers are the running sum of the first n integers.

These figurate numbers connect visual geometry to algebra and are a staple of combinatorics education for illustrating summation identities and Pascal's triangle relationships (Teₙ is the entry in the 4th diagonal of Pascal's triangle). They also appear in the classic “cannonball stacking” puzzles studied in recreational and number theory. Enter n to get Teₙ.