Home › Math › Factorial Calculator

Factorial Calculator

Computes n! = 1 × 2 × … × n for integers from 0 to 170, together with the number of decimal digits, the number of trailing zeros and a scientific-notation form.

When to use

You need the factorial of an integer, e.g. for counting arrangements or as a building block of permutations and combinations.

Do not use when: n exceeds 170 (the result overflows double precision; use Stirling's approximation or log-gamma) or you need C(n, k) / P(n, k) directly (use combinations-permutations).

Formula

n! = n × (n − 1) × … × 2 × 1, with 0! = 1; digits = ⌊Σ log10(i)⌋ + 1; trailing_zeros = Σ ⌊n / 5^k⌋

Inputs

Parameter	Type	Unit	Required	Description
`n`	integer		yes	Non-negative integer up to 170. Range: ≥ 0, ≤ 170

Outputs

Output	Type	Description
`factorial`	number	The factorial. Exact up to 22!; above that correct to about 16 significant digits.
`digits`	integer	Decimal digits of n!: ⌊log10(n!)⌋ + 1.
`trailing_zeros`	integer	Zeros at the end of n! (Legendre's formula: ⌊n/5⌋ + ⌊n/25⌋ + …).
`scientific_notation`	string	n! with 5 significant digits, e.g. '2.4329 × 10^18'.

Example

5!: {"n":5} → {"factorial":120,"digits":3,"trailing_zeros":1,"scientific_notation":"1.2 × 10^2"}

20!: {"n":20} → {"factorial":2432902008176640000,"digits":19,"trailing_zeros":4,"scientific_notation":"2.4329 × 10^18"}

GET https://tttkmbb.com/api/v1/calculate/factorial?n=5

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/factorial (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/factorial · Markdown: https://tttkmbb.com/math/factorial.md · JSON definition: https://tttkmbb.com/math/factorial.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="factorial"
OpenAPI operationId: calculate_factorial
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Factorial (reference)
NIST Digital Library of Mathematical Functions §5.2 – Gamma function: definitions (n! = Γ(n + 1)) (standard)
Wolfram MathWorld – Factorial (reference)

FAQ

Why is 0! equal to 1?

By definition (the empty product), which keeps the recurrence n! = n × (n − 1)! and the counting formulas consistent.

Is the result exact?

Up to 22! every digit is exact. From 23! on the value has more than 53 significant bits, so only the first ~16 significant digits are reliable; the digit and trailing-zero counts stay exact.

Related calculators

Combinations and Permutations Calculator — Counts of selections and arrangements built from factorials.
Exponent Calculator — Powers, the other fast-growing product.