๐ขPermutation & Combination Calculator
Calculate nPr and nCr, with or without repetition, using exact arithmetic and full factorial working.
Calculations use exact BigInt arithmetic, so large factorials remain precise. Runs entirely in your browser.
Free Permutation and Combination Calculator
Need to calculate nPr or nCr for a probability or combinatorics problem? Our free permutation and combination calculator computes both instantly from n and r, with the full factorial working shown step by step.
Choose whether order matters (permutations) or doesn't (combinations), and whether repetition is allowed โ covering all four standard combinatorics formulas in one tool. Large values of n are handled precisely using exact arithmetic, so results stay accurate even when factorials get enormous, switching to scientific notation only when a number is too large to display in full.
Whether you're solving a lottery-odds problem, a seating arrangement, a password combination count, or a stats homework question, this tool gives you the exact answer with the formula and working shown. No sign-up, no downloads, completely free. See the About page or the FAQ for more.
About the Permutation & Combination Calculator
Features
Four modes
nPr, nCr, and their with-repetition variants.
Exact large-number arithmetic
BigInt keeps factorials precise; huge results switch to scientific notation.
Step-by-step working
The factorial formula shown fully substituted.
Input validation
r > n without repetition is flagged, not silently wrong.
Frequently Asked Questions
What's the difference between a permutation and a combination?
A permutation counts arrangements where order matters; a combination counts selections where order doesn't matter.
How is nPr calculated?
Using n! / (nโr)!, the number of ordered ways to choose r items from n.
How is nCr calculated?
Using n! / (r!(nโr)!), the number of unordered ways to choose r items from n.
What does "with repetition" mean?
It allows the same item to be chosen more than once, which changes the formula (n^r for permutations, (n+rโ1)Cr for combinations).
What if r is greater than n?
Without repetition that's impossible (you can't choose more items than exist), so the calculator flags it as invalid rather than returning zero silently.
Can it handle large numbers like 20!?
Yes, exact arithmetic is used so large factorials remain precise; extremely large results switch to scientific notation for display.
Does it show the factorial working?
Yes, the formula is shown fully substituted with your n and r values, including the computed factorials.
Can n or r be zero?
Yes, both are valid: 0! = 1, so results involving zero are handled correctly (e.g. nC0 = 1).
Is my data stored?
No, everything runs client-side in your browser.
Is it free?
Yes, completely free with no sign-up or limits.