Quick guide
How to use this calculator
- Enter the integer n.
- Different orders of the same positive parts are treated as one partition.
- Read the partition number p(n).
Calculation method
Accumulate partitions by allowed part size
A dynamic program adds each possible positive part in increasing order, which counts every unordered partition once.
Worked example
Partition four
The partitions are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1.
p(4) = 5
Supported inputs
Precision and limits
Discrete domain
Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.
Exact integers
Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.
Maximum n
n is limited to 1,000 to keep the exact dynamic calculation responsive.