How to Use the Factorial Calculator
This calculator instantly computes n! and, when r is provided, also calculates permutations nPr and combinations nCr. It covers all the basics needed for combinatorics and probability problems.
Factorial Basics
The factorial n! is the product of all positive integers from 1 to n. Example: 5! = 120. By definition, 0! = 1. Factorials grow extremely fast — 20! has 19 digits and 170! is about 7×10³⁰⁶.
Permutations and Combinations
Permutation nPr = n!/(n−r)!: the number of ordered arrangements of r items from n. Combination nCr = n!/(r!(n−r)!): the number of unordered selections. nCr = nPr ÷ r!.
Calculation Range
Exact integer results are guaranteed for n ≤ 20. For n = 21 to 170, values are shown in scientific notation as floating-point approximations. n > 170 overflows 64-bit floating point and is not supported.
Frequently Asked Questions
Use permutation when order matters (e.g., PIN codes, race rankings). Use combination when order doesn't matter (e.g., team selection, lottery numbers).
It's a convention that makes formulas consistent. For instance, nC0 = 1 (one way to choose nothing), which requires 0! = 1. Without it, many combinatorics formulas would break.
No. You can't choose more items than exist. The constraint r ≤ n is required. When r = n, nPn = n! and nCn = 1.