The difference between “how many ways can I arrange these?” and “how many ways can I choose these?” trips up a lot of students and developers alike — permutations and combinations answer two subtly different questions, and this calculator makes the distinction concrete with real numbers.
What Is the Permutation & Combination Calculator?
A calculator that takes a total item count (n) and a selection size (r), then computes both nPr (permutations, where order matters) and nCr (combinations, where it doesn’t) using exact BigInt arithmetic so results stay precise no matter how large the factorials get.
How to Use It
- Open the tool at /tools/permutation-combination-calculator.
- Enter n (total items) and r (items chosen).
- Read off nPr and nCr instantly, along with the formula used for each.
Key Features
- Exact BigInt arithmetic, avoiding the precision loss regular JavaScript numbers hit once factorials exceed roughly 18!.
- Both nPr and nCr shown side-by-side, making the order-matters vs. order-doesn’t-matter distinction visible at a glance.
- Step-by-step formula display, showing exactly how each result was derived.
- Input validation, flagging when r is greater than n (an undefined case).
When to Use This Tool
- Probability and statistics homework, checking arrangement and selection counts.
- Combinatorics in coding interviews, verifying nCr/nPr calculations for algorithm problems.
- Lottery or raffle odds calculations, where combinations determine the total possible outcomes.
Try It Now
Open Permutation & Combination Calculator directly, or press ⌘K and type the tool name from anywhere on the site.
Part of the Math & Numbers collection on WebdevToolbox — free, browser-based developer tools with no login required.