Numarly

Factorial Calculator

Calculate factorial (n!) of a number

What is it?

The factorial of a non-negative integer n, written n!, is the product of all positive integers less than or equal to n. It's fundamental to permutations, combinations, and probability calculations.

Formula

n! = n × (n−1) × (n−2) × ... × 2 × 1

Formula Explanation

Factorial counts the number of ways to arrange n distinct items in a sequence: there are n choices for the first position, (n−1) remaining choices for the second, and so on down to 1 — multiplying all these choices together gives n!.

Example Calculation

5! = 5 × 4 × 3 × 2 × 1 = 120.

How to Use

  1. Enter a non-negative whole number.
  2. Click Calculate Factorial.
  3. View the factorial result.

Benefits

  • Instantly computes exact factorial values without manual multiplication.
  • Correctly handles the special case of 0! = 1.
  • Flags inputs beyond safe precision limits instead of returning a wrong answer.

Use Cases

  • Calculating permutations and combinations for probability problems.
  • Counting the number of ways to arrange a set of items.
  • Evaluating terms in Taylor series or other calculus expansions.

What Your Result Means

The result is the exact number of ways to arrange n distinct items in order. Factorials grow extremely quickly — even relatively small values of n produce enormous results.

Tips

  • Remember that 0! = 1 by definition, not 0.
  • Factorials grow faster than exponential functions, so results become huge very quickly.
  • Use factorials together with the Permutation or Combination calculators for counting problems.

Common Mistakes

  • Assuming 0! equals 0 instead of the correct value, 1.
  • Trying to compute the factorial of a negative number, which is undefined.
  • Expecting precise results beyond 170!, where JavaScript's number precision breaks down.

FAQs

What is 0!?

0! is defined as 1 by mathematical convention, which keeps formulas involving factorials (like permutations and combinations) consistent.

Why is there a limit of 170?

Factorials grow extremely fast — 171! exceeds the maximum value JavaScript can represent precisely as a number, so results beyond 170! would be inaccurate.

Where are factorials used?

Factorials are used in permutations, combinations, probability theory, and series expansions in calculus.

Can I calculate the factorial of a decimal number?

This calculator only supports non-negative whole numbers — factorials of non-integers require the more advanced Gamma function.

How fast do factorials grow?

Very fast — 10! is already 3,628,800, and 20! exceeds 2.4 quintillion, illustrating how quickly factorial values expand.

Results are exact for n up to 170; beyond that, JavaScript number precision is insufficient.

Last updated: July 25, 2026