Factorial Calculator
Calculate n! exactly for any integer up to 5,000. Uses BigInt arithmetic for exact results — no floating point approximation.
n! = n × (n−1) × ... × 2 × 1. 0! = 1 (by definition). Key values: 5! = 120 · 10! = 3,628,800 · 20! ≈ 2.43×10¹⁸ · 100! ≈ 9.33×10¹⁵⁷ (158 digits).
Common values
Factorials in Math Curricula by Country
| Country / Exam | Grade level | Context |
|---|---|---|
| 🇺🇸 USA (AP Stats) | Grade 11–12 | Permutations, combinations, probability |
| 🇬🇧 UK (A-Level) | Year 12–13 | Statistics: nPr, nCr, binomial |
| 🇩🇪 Germany (Abitur) | Klasse 11–12 | Kombinatorik, Wahrscheinlichkeit |
| 🇫🇷 France (Terminale) | Terminale | Dénombrement, arrangements, combinaisons |
| 🇯🇵 Japan (数学A) | High school | 順列・組合せ (Permutation/Combination) |
| 🇮🇳 India (CBSE) | Class 11 | Chapter: Permutations and Combinations |
| 🌍 IB Mathematics | IB Year 1–2 | Combinatorics, Pascal's triangle |
Frequently Asked Questions
Why does 0! equal 1?
0! = 1 by definition. The mathematical justification: there is exactly one way to arrange 0 objects (the empty arrangement). Also, the formula nCr = n! / (r!(n−r)!) requires 0! = 1 to work when r = 0 or r = n.
How many digits does 100! have?
100! = 9.332621544... × 10¹⁵⁷. It has 158 digits. The number of digits in n! can be estimated as ⌊log₁₀(n!)⌋ + 1, or via Stirling: approximately n·log₁₀(n/e) + ½·log₁₀(2πn).
What is the double factorial n!!?
n!! is the product of every other integer down to 1 or 2. For even n: n!! = n × (n−2) × ... × 4 × 2. For odd n: n!! = n × (n−2) × ... × 3 × 1. Example: 8!! = 8×6×4×2 = 384. Used in probability and physics.
How are permutations and combinations related to factorials?
Permutations (order matters): nPr = n!/(n−r)!. Combinations (order doesn't matter): nCr = n!/(r!(n−r)!). Example: Choosing 2 from 5: 5P2 = 5!/3! = 20 arrangements; 5C2 = 5!/(2!3!) = 10 subsets.