Factorial Calculator

Name: Factorial Calculator
Author: Jitendra Kumar

Calculate n factorial with exact output for readable results, scientific notation for large values, digit count, trailing zeros, and setup checks.

Last Updated: May 2026

Non-negative whole number (n)

Enter an integer from 0 to 10,000.

10!

3,628,800

Approximation

3.628800e+6

Digits

Trailing zeros

Step	Value
Definition	n! = n x (n - 1) x ... x 2 x 1
Substitution	10! = 10 x 9 x 8 x ... x 3 x 2 x 1
Special cases	0! = 1 and 1! = 1
Arrangement meaning	There are 3,628,800 ways to arrange 10 distinct items in a line.
Growth check	7 digits

Exact result

3,628,800

Definition

Factorial multiplies all positive integers from n down to 1. The empty product convention makes 0! equal 1.

Counting

n! counts the linear arrangements of n distinct objects, so each added item multiplies the total by one more choice.

Growth

Factorials grow very quickly. This calculator switches to compact notation when the full integer is too long for a readable result card.

Trailing Zero Check

Term	Contribution
floor(10 / 5)	2

Whole-Number Factorial Notice

This calculator is for ordinary factorials of non-negative whole numbers. Extensions such as the gamma function are related but are not used for decimal or negative inputs here.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

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Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

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Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

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How to Use the Factorial Calculator

Enter a non-negative whole number n. The calculator accepts values from 0 to 10,000.

Review the main factorial result, scientific notation, digit count, and trailing-zero breakdown. Use the exact-result box when the integer is compact enough to display.

Step 1: Enter n
Use a non-negative whole number.
Step 2: Read n factorial
The highlighted card shows n!, using compact notation when needed.
Step 3: Check the scale
Use the digit count and scientific notation to understand very large factorials.
Step 4: Audit trailing zeros
The trailing-zero table shows the powers of 5 that create ending zeros.

How This Factorial Calculator Works

For a whole number n, the calculator applies n! = n x (n - 1) x ... x 2 x 1. The special cases 0! = 1 and 1! = 1 are handled directly.

Exact integers are displayed when they are short enough to read. Larger factorials are summarized with scientific notation and digit count.

Trailing zeros are counted by adding floor(n/5), floor(n/25), floor(n/125), and so on, because each factor of 5 pairs with a factor of 2 to make a factor of 10.

Factorial Guide

Core Factorial Rules

Concept	Formula	Use
Factorial definition	n! = n x (n - 1) x ... x 2 x 1	Multiply every positive integer up to n.
Zero factorial	0! = 1	The empty-product convention used in counting formulas.
Recursive rule	n! = n x (n - 1)!	Useful for step-by-step expansion.
Arrangements	n distinct objects -> n! orders	Counts linear arrangements with no repetition.
Trailing zeros	floor(n/5) + floor(n/25) + ...	Counts factor pairs of 2 and 5 at the end of n!.

Factorial Examples

Input	Expansion	Result
0!	1	Special case
5!	5 x 4 x 3 x 2 x 1	120
10!	10 x 9 x ... x 1	3,628,800
12!	12 x 11 x ... x 1	479,001,600
100!	Product of integers 1 through 100	158 digits

When Factorials Appear

Factorials appear in permutations, combinations, probability formulas, series expansions, and counting problems where each step has one fewer available choice than the step before it.

Keep the research moving with Permutation & Combination Calculator, Fundamental Counting Principle Calculator, Integer Calculator, and Long Multiplication Calculator.

Frequently Asked Questions

The factorial of a non-negative whole number n is the product of all positive integers from n down to 1.

0! is defined as 1 by the empty-product convention, which keeps permutation and combination formulas consistent.

This calculator accepts non-negative whole numbers only. Decimal and negative inputs are outside ordinary factorial arithmetic.

Factorials become very large quickly, so compact scientific notation and digit counts are easier to read for large inputs.

Trailing zeros come from factors of 10. Since factors of 2 are plentiful in factorials, the calculator counts factors of 5 using floor(n/5) + floor(n/25) and so on.