CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Factorial Calculator

Calculate n factorial exactly for a non-negative integer.

Counting & Combinatorics

Enter a non-negative integer

Exact n!
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Exact count

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Understand the subject

What does factorial mean?

A <strong>factorial</strong> counts the ways to put distinct objects into every available position. Each filled position leaves one fewer choice.

Use it when all distinct objects are arranged and every position matters.

The relationship

The counting rule

See the structure

Choices shrink as positions fill

Worked example

Check the rule with a small case

Five books can be arranged in 5! = 5 × 4 × 3 × 2 × 1 = 120 orders.

Interpret with care

Choose the right counting model

Factorial is for distinct objects. Repeated objects, circular layouts, or partial selections use different models.

Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.

Quick guide

How to use this calculator

  1. Enter a non-negative integer n.
  2. Read the exact product n!.
  3. Use the definition note to distinguish 0! from an empty result.

Calculation method

Multiply the integers from 1 through n

For n greater than zero, n! is the product 1×2×⋯×n. The empty product convention defines 0! as 1.

Worked example

Factorial of 5

Multiply every positive integer no greater than five.

5! = 5×4×3×2×1 = 120

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.