A permutation is an ordered arrangement of r elements chosen from a set of n. The order of elements matters: AB and BA are different permutations.
Permutation Calculator
Calculate P(n,r) and permutations with repetition. Formula, steps, and BigInt result.
Permutations without and with repetition with exact results.
A permutation is a count of ordered arrangements of r elements chosen from n, where order matters. Without repetition, P(n,r) = n! / (n-r)!. With repetition, PR(n,r) = nʳ. The tool uses BigInt for exact results even for large values.
Enter n and r, then choose the permutation mode.
- Enter n (total available elements) and r (positions to fill).
- Select 'Without repetition' for P(n,r) or 'With repetition' for PR(n,r).
- Check the result, the applied formula, and the calculation steps.
Sources and references for this tool
These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
- Permutations — NIST Digital Library of Mathematical FunctionsNIST — Definitions for simple and repetition permutations.
- Factorial — Wolfram MathWorldWolfram MathWorld — Context on factorial and super-exponential growth relevant to P(n,r).
- BigIntMDN Web Docs — API used for permutations of large n and r without overflow.