Skip to content
ToolQivo

Permutation & Combination Calculator

nPr, nCr, factorials and counting with or without repetition.

Calculators Reviews Free · no sign-up

Which one do I need?

If reordering the same selection counts as a different result, it is a permutation — a PIN, a podium, a running order. If it does not, it is a combination — a hand of cards, a committee, a pizza's toppings.

Factorials

n!—
r!—
(n − r)!—

—

0! is 1 — there is exactly one way to arrange nothing.

Ratio

—

Quick Tool Overview

The Permutation & Combination Calculator returns nPr and nCr side by side, each with the formula and the substitution shown, plus the versions with repetition allowed and the plain factorial of n. The distinction is simply whether order matters.

What it does
Calculates permutations, combinations and factorials
You give it
A total n and a selection size r
You get back
nPr, nCr, the repetition variants and n factorial
Best for
Combinatorics homework, lottery odds and password space
Calculators Free, unlimited use No sign-up Runs in your browser

About the Permutation & Combination Calculator

Enter n and r to get the number of permutations and combinations side by side, each with the formula and the substitution shown. Versions with repetition allowed are calculated too, along with the plain factorial of n.

The distinction is simply whether order matters. A three-digit lock code is a permutation, because 1-2-3 is not the same as 3-2-1; a hand of three cards is a combination, because the order you were dealt them in changes nothing. Permutations always outnumber combinations for the same n and r, by exactly r factorial, and showing both together makes that relationship visible rather than something to memorise.

Key features of the Permutation & Combination Calculator

Both counts together

Permutations and combinations appear side by side, which makes the relationship between them visible.

The order rule explained

A three-digit lock code is a permutation because 1-2-3 differs from 3-2-1; a hand of three cards is a combination because the deal order changes nothing.

With and without repetition

All four counting cases are covered rather than only the two textbook ones.

Formula and substitution shown

Your numbers are printed inside the formula, so the working can be copied into an answer.

Factorial included

n! is calculated alongside, since it is the building block of both results.

How to use the Permutation & Combination Calculator

  1. 1

    Enter n

    The total number of items you are choosing from.

  2. 2

    Enter r

    How many you are selecting. It cannot exceed n unless repetition is allowed.

  3. 3

    Compare the results

    Permutations and combinations are shown together, with and without repetition, each with its formula.

Frequently asked questions

Order. A permutation counts arrangements where sequence matters, a combination counts selections where it does not. Picking three winners in order is a permutation; picking three winners who all get the same prize is a combination.

Reviews of the Permutation & Combination Calculator

What people who use the Permutation & Combination Calculator think of it. Reviews come from visitors and are posted as written.

No ratings yet

Yours would be the first.

  • 5 0 reviews rated 5 stars
  • 4 0 reviews rated 4 stars
  • 3 0 reviews rated 3 stars
  • 2 0 reviews rated 2 stars
  • 1 0 reviews rated 1 star

Write a review

Used this tool? Your rating helps the next person decide.

Your rating

Plain text only — links, email addresses and HTML are not accepted. Your name and review are shown publicly; nothing else is collected. See the privacy policy.

0 reviews

Newest first

No reviews yet

Be the first to rate the Permutation & Combination Calculator. It takes half a minute and no account.

Write the first review

More calculators