Combination & Permutation Calculator

Combination & Permutation Calculator lets you compute nPr (permutations) and nCr (combinations) for any total count n and selection size r. Enter your two numbers and get both results instantly — no installation, no uploads, everything runs locally in your browser.

What is the Combination & Permutation Calculator and Why is it Useful?

In combinatorics, a permutation counts the number of ways to arrange r items out of n when order matters, calculated as P(n, r) = n! / (n - r)!. A combination counts the number of ways to choose r items out of n when order does not matter, calculated as C(n, r) = n! / (r! × (n - r)!). This tool computes both values side by side from the same n and r inputs, which is handy for students, statisticians, lottery odds calculations, probability problems, and anyone working with counting principles.

Key Features

• Both Permutations and Combinations at Once: Enter n and r once and instantly see both P(n, r) and C(n, r), so you don't need two separate tools.
• Built to Avoid Overflow Errors: Instead of computing raw factorials (which silently break down as Infinity ÷ Infinity for large n), the calculator multiplies out only the necessary terms, so it stays accurate for much larger inputs.
• Input Validation: The tool checks that n and r are non-negative whole numbers and that r does not exceed n, showing a clear message instead of a confusing result if something is off.
• Large Number Warning: If a result grows beyond what a browser's number type can represent exactly (above 2^53 − 1), the tool flags the value as approximate rather than presenting it as exact.
• Fully Offline and Private: All math happens directly in your browser session. Nothing you type is sent to a server.

How to Use This Tool?

1. Enter the total number of elements in the n field.
2. Enter the number of elements to choose in the r field.
3. Click Calculate. The tool instantly displays both the permutation P(n, r) and the combination C(n, r).
4. If r is greater than n, or either value is negative or not a whole number, an inline message explains what to fix.

Why Choose Our Client-Side Tool?

Most online calculators send your inputs to a server to compute the answer. This tool computes nPr and nCr entirely in your browser using JavaScript, so there are no network requests, no tracking of your inputs, and no delay waiting for a server response. It is free, requires no sign-up, and works the same way offline once the page has loaded.

Frequently Asked Questions (FAQ)

What is the difference between a permutation and a combination?

A permutation cares about order — arranging 3 people in a line gives a different result for ABC versus BCA. A combination ignores order — picking the same 3 people as a group counts only once. This tool calculates both for the same n and r.

What happens if r is greater than n?

You cannot choose more items than exist in the set, so the tool shows a validation message instead of returning a result.

Can this tool handle large numbers like n = 100?

Yes, up to the point where the exact integer value would exceed JavaScript's safe integer limit (2^53 − 1). Beyond that the tool still shows a result but flags it as an approximation, since no browser-based calculator can represent every digit of extremely large factorials with full precision.

Is repetition (with replacement) supported?

No. This calculator computes the standard permutations and combinations without repetition (each of the n items can be selected at most once in a given arrangement or subset).