# Permutation Calculator

Calculate permutations with or without repetition, plus circular arrangements, with formulas and optional steps

> Canonical page: https://elysiatools.com/en/tools/permutation-calculator

- **Category:** Math & Numbers

- **Keywords:** permutation, arrangement, combinatorics, calculator, math

## Overview

The Permutation Calculator is a fast and accurate math utility designed to compute the number of possible arrangements for a given set of items. Whether you are solving combinatorics problems, determining password combinations, or calculating seating arrangements, this tool supports permutations with repetition, without repetition, and circular arrangements, complete with step-by-step formulas.

## Inputs

- **Total Items** (number)
- **Selected Items** (number)
- **Permutation Type** (select)
- **Show Formula** (checkbox)
- **Show Steps** (checkbox)

## When to use

- When you need to find the exact number of ordered arrangements for a subset of items from a larger pool.
- When solving probability or combinatorics assignments that require showing the underlying mathematical formulas and steps.
- When calculating possible combinations for passwords, lock codes, or scheduling scenarios where order matters.

## How it works

- Enter the total number of items available in your set.
- Specify the number of items you want to select and arrange.
- Choose the permutation type: without repetition, with repetition, or circular.
- Toggle the options to show the formula and calculation steps, then view the final computed result.

## Use cases

- Determining the number of possible outcomes for race podiums (1st, 2nd, and 3rd place).
- Calculating the total number of possible PIN codes or passwords given a specific character set and length.
- Figuring out seating arrangements for guests around a circular dining table.

## Frequently asked questions

### What is the difference between a permutation and a combination?

In a permutation, the order of the items matters (e.g., a lock code). In a combination, the order does not matter (e.g., selecting a team).

### What does 'without repetition' mean?

It means once an item is selected from the pool, it cannot be chosen again. This is common in race rankings or seating arrangements.

### How are circular permutations calculated?

Circular permutations account for arrangements in a circle where there is no fixed starting point. The formula used is typically (n-1)! for arranging n items.

### Can I see the math behind the result?

Yes, by checking the 'Show Formula' and 'Show Steps' boxes, the calculator will output the exact mathematical formula and steps used to reach the answer.

### Is there a limit to the numbers I can input?

The tool currently accepts inputs up to 100 for both the total items and selected items to prevent browser performance issues with massive factorials.

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