Ordering people
If you want to arrange 5 people in a line, 5! gives the number of possible full-order arrangements. That is one of the simplest and most common uses of factorial.
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Factorial Calculator
Calculate exact factorial values for non-negative whole numbers. Review digit count, trailing zeros, and how factorial connects to permutations, combinations, probability, and discrete math workflows.
Factorial Calculator
Use this free factorial calculator to compute exact values of n! for any non-negative whole number. It is useful for permutations, combinations, probability, combinatorics, and discrete math problems. The tool also shows digit count, trailing zeros, and quick links into the Permutations Calculator, Combinations Calculator, and the wider Math & Statistics Calculators category.
Calculate n! instantly
Enter any non-negative whole number to compute its exact factorial and a few useful counting insights.
Useful for
Combinatorics and counting
Helpful for arrangements, selections, series, and discrete-math formulas.
Factorial is defined here for non-negative whole numbers only.
Exact factorial value
3,628,800
Factorial grows extremely fast, so exact integer handling is important for larger values.
Digit count
7
Trailing zeros
2
Permutation link
10! appears in nPr formulas
Combination link
10C2 = 45
Calculation steps
- 1Start with n = 10
- 2Apply the definition n! = n × (n - 1) × (n - 2) × ... × 1
- 3Multiply all integers from 1 through 10
- 4The exact factorial result is 3,628,800
- 5This result contains 7 digits and 2 trailing zeros
How factorial connects to other tools
Factorial is a building block for permutations and combinations. That means it often sits behind ranking problems, card-hand counts, event-odds calculations, and many discrete-math formulas. After calculating n!, continue with the Permutations Calculator or Combinations Calculator when you want to move from raw factorial growth into real counting scenarios.
What this factorial calculator does
This tool computes exact factorial values for non-negative integers and adds practical context such as trailing zeros and digit count. It is built for students, analysts, and anyone working through combinatorics or discrete mathematics problems.
How factorial works
Factorial multiplies a whole number by every positive integer below it until reaching 1. That product grows extremely quickly, which is why factorial appears in formulas that count arrangements, selections, and other rapidly expanding outcome spaces.
Factorial formula explained
Standard factorial
n! = n × (n - 1) × (n - 2) × ... × 1
Special identity
0! = 1
n!
Product of all positive integers from n down to 1.
0!
Defined as 1 to keep counting formulas consistent.
nPr
Permutation formulas rely on factorial terms.
nCr
Combination formulas also use factorial terms.
Factorial calculator examples
Counting card arrangements
Large counting problems like shuffling a deck use factorial-based math because every card order matters. Even moderate factorial values grow surprisingly fast.
Probability and combinatorics
Factorial often appears behind permutations, combinations, binomial coefficients, and many event-counting formulas before probabilities are simplified into percentages or ratios.
If you want to move from a factorial result into a real selection or arrangement problem, continue with the Permutations Calculator for order-sensitive counts or the Combinations Calculator when order does not matter. For event-likelihood work after counting, the Probability Calculator is the natural next step.
Why factorial matters
Factorial is one of the core building blocks of counting math. It turns up whenever arrangements, selection counts, or fast-growing outcome spaces are involved.
Trailing zeros insight
Trailing zeros in n! come from factors of 10, which are created by 2 × 5 pairs. Because factors of 2 are plentiful, counting factors of 5 tells you how many zeros appear at the end.
Math & statistics workflow
Factorial sits upstream of several other math tools. It often leads naturally into permutations, combinations, probability, and later into sampling or distribution problems.
Related tools
Frequently asked questions
It multiplies a whole number by every positive integer below it. For example, 5! means 5 × 4 × 3 × 2 × 1. Factorials are widely used in combinatorics, probability, permutations, series expansions, and discrete mathematics.
Explore This Tool in Context
Factorial Calculator is part of the Math & Statistics Calculators collection. If you want a broader view of similar workflows, open the Math & Statistics Calculators category page or browse all QuickTools categories.
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