Factorial calculator — n!
The factorial of n (written n!) is the product of all positive integers from 1 to n. This calculator shows the exact value for small inputs and scientific notation for large ones.
n! =
—
Saved to favorites
Your favorites are on the home page under “Your favorites.” They are saved only in this browser on this device, so they will not appear on another device or browser. No account, no server.
Formula
n! = n × (n−1) × (n−2) × … × 2 × 1
0! = 1 (by definition)
Common values
| n | n! |
|---|---|
| 0 | 1 |
| 5 | 120 |
| 10 | 3,628,800 |
| 20 | 2.433 × 10^18 |
| 50 | 3.041 × 10^64 |
| 100 | 9.333 × 10^157 |
References
- Factorial (n! and the 0! = 1 convention)Wikipedia · en.wikipedia.org
Frequently asked
What is a factorial?
n! = n × (n−1) × (n−2) × … × 2 × 1. By definition, 0! = 1. Factorials grow extremely fast: 10! = 3,628,800 and 100! has 158 digits.
Why does the calculator switch to scientific notation above 170?
JavaScript's floating-point numbers (IEEE 754 doubles) overflow at about 1.8 × 10^308. Since 171! ≈ 1.24 × 10^309, exact computation exceeds the representable range. The calculator uses a logarithm-based approach to show the scientific notation accurately.
What is 0! and why is it 1?
By convention, 0! = 1. This preserves the identity n! = n × (n−1)! when n = 1 (giving 1 = 1 × 0! = 1 × 1) and makes combinatorial formulas like C(n,0) = 1 work correctly.
How many digits does 100! have?
100! has 158 digits. The digit count equals floor(log10(n!)) + 1.
How do I share my calculation?
Click "Share with my numbers" to copy a URL that saves your input.
Embed this calculator
Add this free calculator to your own site. Copy the snippet — it works anywhere you can paste HTML, and stays in sync with this page.