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Factorial Calculator.

Calculate n! exactly for a bounded non-negative integer.

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Use Cases

Combinatorics and Probability

Calculate the number of ways to arrange or choose items, which often involves factorials. Useful for permutations, combinations, and probability problems.

Example: Number of ways to arrange 5 books on a shelf: 5! = 120.

Mathematical Series and Approximations

Factorials appear in Taylor series, binomial expansions, and other mathematical formulas. Use this calculator to quickly compute factorial terms for such expressions.

Example: Compute 10! for a term in a series expansion.

Frequently Asked Questions

What is a factorial?: A factorial of a non-negative integer n, denoted n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.
Why does the calculator only accept non-negative integers?: Factorials are defined only for non-negative integers. Negative numbers and fractions do not have standard factorial values. This calculator is designed to compute n! exactly for any non-negative integer within its supported range.
What is the largest n this calculator can handle?: The calculator can compute factorials exactly for n up to 170. Beyond that, the result becomes extremely large and exceeds the limits of standard numeric representation, so the calculator restricts input to ensure accurate results.

Tips & Common Mistakes

Tips

Remember that 0! is defined as 1, not 0. This is a common convention in mathematics.
For large n, the factorial grows extremely fast. For example, 20! is already over 2.4 quintillion.
Use the factorial result to compute combinations: C(n, k) = n! / (k! * (n-k)!).
If you need a factorial for a non-integer, consider using the gamma function, but this calculator only handles non-negative integers.

Common Mistakes to Avoid

Entering a negative number: Factorials are not defined for negative integers. The calculator only accepts non-negative integers.
Entering a decimal or fraction: Factorials are only defined for whole numbers. This calculator requires an integer input.
Assuming 0! is 0: The correct value is 1, which is a standard mathematical convention.

Last updated: August 13, 2026

Use Cases

Combinatorics and Probability

Calculate the number of ways to arrange or choose items, which often involves factorials. Useful for permutations, combinations, and probability problems.

Example: Number of ways to arrange 5 books on a shelf: 5! = 120.

Mathematical Series and Approximations

Factorials appear in Taylor series, binomial expansions, and other mathematical formulas. Use this calculator to quickly compute factorial terms for such expressions.

Example: Compute 10! for a term in a series expansion.

Frequently Asked Questions

What is a factorial?

A factorial of a non-negative integer n, denoted n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.

Why does the calculator only accept non-negative integers?

Factorials are defined only for non-negative integers. Negative numbers and fractions do not have standard factorial values. This calculator is designed to compute n! exactly for any non-negative integer within its supported range.

What is the largest n this calculator can handle?

The calculator can compute factorials exactly for n up to 170. Beyond that, the result becomes extremely large and exceeds the limits of standard numeric representation, so the calculator restricts input to ensure accurate results.

Tips & Common Mistakes

Tips

Remember that 0! is defined as 1, not 0. This is a common convention in mathematics.
For large n, the factorial grows extremely fast. For example, 20! is already over 2.4 quintillion.
Use the factorial result to compute combinations: C(n, k) = n! / (k! * (n-k)!).
If you need a factorial for a non-integer, consider using the gamma function, but this calculator only handles non-negative integers.

Common Mistakes to Avoid

Entering a negative number: Factorials are not defined for negative integers. The calculator only accepts non-negative integers.
Entering a decimal or fraction: Factorials are only defined for whole numbers. This calculator requires an integer input.
Assuming 0! is 0: The correct value is 1, which is a standard mathematical convention.

Use Cases

Combinatorics and Probability

Calculate the number of ways to arrange or choose items, which often involves factorials. Useful for permutations, combinations, and probability problems.

Example: Number of ways to arrange 5 books on a shelf: 5! = 120.

Mathematical Series and Approximations

Factorials appear in Taylor series, binomial expansions, and other mathematical formulas. Use this calculator to quickly compute factorial terms for such expressions.

Example: Compute 10! for a term in a series expansion.

Frequently Asked Questions

What is a factorial?

A factorial of a non-negative integer n, denoted n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.

Why does the calculator only accept non-negative integers?

What is the largest n this calculator can handle?

Tips & Common Mistakes

Tips

Remember that 0! is defined as 1, not 0. This is a common convention in mathematics.
For large n, the factorial grows extremely fast. For example, 20! is already over 2.4 quintillion.
Use the factorial result to compute combinations: C(n, k) = n! / (k! * (n-k)!).
If you need a factorial for a non-integer, consider using the gamma function, but this calculator only handles non-negative integers.

Common Mistakes to Avoid

Entering a negative number: Factorials are not defined for negative integers. The calculator only accepts non-negative integers.
Entering a decimal or fraction: Factorials are only defined for whole numbers. This calculator requires an integer input.
Assuming 0! is 0: The correct value is 1, which is a standard mathematical convention.