Calculators
Permutation and Combination Calculator & Word Generator
Calculate permutations and combinations with or without repetition. See exact formulas, step-by-step arithmetic, and generate custom word combinations.
What the result means
The tool evaluates permutations and combinations using exact integer arithmetic without floating-point inaccuracies. Permutations apply when sequence order matters, such as rank orders or sequential passphrases. Combinations apply when order does not matter, such as lottery numbers or group selections. When repetition is prohibited, selecting r elements from n choices reduces available candidates with each draw, calculated via factorials. When repetition is permitted, each position draws from all n candidates, calculated as n to the power of r for permutations or the multiset coefficient for combinations. In list mode, words or items are parsed, and candidate combinations are generated incrementally with strict display thresholds to maintain local browser performance and prevent interface memory exhaustion.
Related tools
Guides
Questions
What is the difference between permutations and combinations?
Permutations count arrangements where the order matters (e.g. 1-2-3 is different from 3-2-1). Combinations count selections where order does not matter (e.g. 1-2-3 and 3-2-1 are the same group).
How does repetition change the total number of permutations?
Without repetition, each choice reduces the available options (e.g. 20 × 19 × 18 × 17 = 116,280). With repetition allowed, every position has the full n choices, resulting in n to the r power (20^4 = 160,000).
Can this tool generate actual word lists or passphrases?
Yes. Switch to Word / Items mode, enter your list of words or phrases, choose whether order and repetition matter, and view or download the generated combinations.