Integer Partitions Calculator
Enter a number to count its integer partitions.
Result
How to use
- Enter your values in the fields above.
- Press Calculate to see your result instantly.
- Use the Share button to copy a link to your result.
About this calculator
A partition of a positive integer n is a way of writing it as a sum of positive integers where order doesn't matter — for example, 4 can be partitioned as 4, 3+1, 2+2, 2+1+1, or 1+1+1+1, giving p(4) = 5. This calculator computes p(n) using a dynamic-programming recurrence (or Euler's pentagonal number theorem for larger n), counting all such distinct sums.
Mathematicians and combinatorics students use partition counts as a foundational topic in number theory, and the underlying recurrence appears in computer science too — competitive programmers implement partition-counting algorithms for problems involving coin-change combinations, generating functions, and other combinatorial counting tasks.
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