Partition Function p(n) Calculator

About this calculator

This calculator computes the integer partition function p(n), a classic object of study in number theory: the number of distinct ways to write n as a sum of positive integers, where order doesn't matter (so 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1 counts as 4 partitions, not more). The function grows explosively — p(100) already exceeds 190 million.

p(n) is famous for the Hardy–Ramanujan asymptotic formula that approximates it for large n, and for Ramanujan's remarkable congruences (like p(5n+4) always divisible by 5). This calculator returns the exact value, computed for any n up to 300.