Permutations and combinations

Calculate permutations and combinations with clear inputs and assumptions.

Your inputs stay in your browser. Displayed results are rounded to a maximum of 12 significant digits.

Method and assumptions

Method version 1.0.0 · Updated October 17, 2026

Calculate

Formula: Calculate permutations and combinations with clear inputs and assumptions.

Calculate permutations and combinations with clear inputs and assumptions.

n: n
r: r
mode: Calculation

Results are estimates where noted and depend on the entered assumptions.

Calculate with code

These short examples use the same inputs and core calculation as this tool. Adapt validation and formatting to your application.

JavaScript

const n = 5, r = 2;
const factorial = n => n <= 1 ? 1 : n * factorial(n - 1);
console.log(factorial(n) / factorial(n-r) / factorial(r)); // C(5,2) = 10

TypeScript

const factorial = (n: number): number => n <= 1 ? 1 : n * factorial(n - 1);
const n = 5, r = 2;
console.log(factorial(n) / factorial(n-r) / factorial(r)); // 10 combinations

Python

import math
n, r = 5, 2
print(math.comb(n, r), math.perm(n, r))  # 10 combinations, 20 permutations

Java

int n=5, r=2;
long combinations = 1; for (int i=1;i<=r;i++) combinations = combinations*(n-r+i)/i;
System.out.println(combinations); // 10

int n=5, r=2;
double combinations = Enumerable.Range(1,r).Aggregate(1.0,(v,i)=>v*(n-r+i)/i);
Console.WriteLine(combinations); // 10