Factorial Calculator
Compute n! exactly using BigInt for any 0 ≤ n ≤ 5000, with digit count.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this factorial calculator
- Enter a non-negative integer n between 0 and 5000.
- Press Calculate to compute n! exactly.
- Read the digit count and the scientific-notation approximation.
- Use Copy to put the exact value on your clipboard, or Reset to clear the input.
About this factorial calculator
The factorial calculator computes n! — the product of every positive integer from 1 up to n. It uses JavaScript BigInt arithmetic, so the result is exact even when n! has hundreds of digits and would overflow ordinary floating-point numbers.
The formula is n! = n × (n − 1) × (n − 2) × … × 1, with the convention 0! = 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely quickly: 10! is already 3,628,800; 20! exceeds 2 × 10^18 (beyond the safe integer range of a regular number); and 100! has 158 digits. The tool caps the input at n = 5000 to keep the browser responsive — 5000! has 16,326 digits and computing it on demand stays under a second on modern hardware.
Factorials underpin permutations, combinations, probability, series expansions (such as e^x), and many counting problems in maths and statistics.
FAQ
- What does the factorial calculator do?
- It computes n! — the product of every positive integer from 1 up to n — exactly using BigInt arithmetic. Inputs from 0 to 5000 are supported.
- What is the formula for n!?
- n! = n × (n − 1) × (n − 2) × … × 1, with the special case 0! = 1 by definition. Each step multiplies the previous result by the next integer down.
- Why is the upper limit 5000?
- 5000! has over 16,000 digits and is computed by an iterative BigInt multiplication. Beyond that the page would start to feel sluggish on slower devices, so the input is capped.
- Why does 0! equal 1?
- It is the conventional definition that keeps combinatorial formulas consistent — for example, the number of ways to arrange 0 objects is 1 (the empty arrangement), and binomial coefficients require 0! = 1 to behave correctly.
- Does this tool store my numbers?
- No. The calculation runs entirely in your browser; nothing is sent to a server or saved between visits.
- Is the factorial calculator free?
- Yes. It is free to use with no signup, no account, and no usage limit.