Permutation & Combination Calculator

Order matters in a permutation but not in a combination. Arranging 3 books on a shelf is a permutation (ABC differs from CBA); choosing 3 books to take on a trip is a combination (the same 3 books, in any order, count once). That is why nPr is always greater than or equal to nCr for the same n and r.

Permutations use nPr = n! / (n − r)!, and combinations use nCr = n! / (r! × (n − r)!), where n is the total number of items and r is how many you choose. Both formulas are shown alongside the results.

Both n and r must be whole numbers with 0 ≤ r ≤ n. nP0 and nC0 both equal 1 (one way to choose nothing), and nCn equals 1 (one way to take everything). n is capped at 170, because beyond that a result overflows what a browser can represent at all. Results are exact only while they stay at or below 2^53 (about 9 × 10^15); larger values are floating-point approximations, accurate to roughly 15–16 significant digits rather than to the exact integer.

No. The calculation runs entirely in your browser using JavaScript. The numbers you type stay on this page and are never uploaded anywhere.