Integer Partition Calculator

Count the number of integer partitions of n with optional constraints on maximum part size and distinctness.

Integer n

Max Part Size

Distinct Parts Only (0=No, 1=Yes)

Tab to move between fields

Partition Count

Unrestricted p(n)42

How to Use This Calculator

Enter the Integer n to compute its number of integer partitions.
Optionally set a Max Part Size to restrict the partition to parts at most that value.
Toggle Distinct Parts Only to count partitions where all parts must be different.
Review Partition Count under your constraints and the unrestricted p(n) for comparison.
Use the Conjugate Count to explore partition duality in combinatorics problems.

How the result changes with Integer n

Integer n: The integer to partition (max 200)
Max Part Size: Largest allowed part in the partition (set equal to n for unrestricted)
Distinct Parts Only (0=No, 1=Yes): Restrict to partitions where all parts are distinct

Identify Input Parameters
Integer n = 10, Max Part Size = 10, Distinct Parts Only (0=No, 1=Yes) = 0 = 3 input(s) provided
Calculate Partition Count
Partition Count
42 = 42
Calculate Unrestricted p
Unrestricted p
42 = 42

Engine last updated August 5, 2026. Checked against 6 independently-derived tests — how we verify calculators.

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