Factorial Calculator
Factorial Calculator
Enter a whole number to calculate its factorial. Factorials multiply every whole number from 1 up to n together, and grow extremely fast — this calculator uses exact arbitrary-precision math so even large factorials come out precise, not rounded.
Factorials are the building block behind almost every combinatorics formula — permutations, combinations, and probability distributions all reduce to ratios of factorials underneath. They also grow explosively: 10! is already 3,628,800, and 20! exceeds 2.4 quintillion, which is why ordinary calculators and spreadsheet formulas often lose precision or overflow on inputs most people wouldn't expect to be "large." Using exact arbitrary-precision arithmetic here means the result stays accurate no matter how big the input gets.
- Formula: n! = n × (n − 1) × (n − 2) × ... × 2 × 1, with 0! defined as 1.
- Grows explosively: 10! = 3,628,800 while 20! already exceeds 2.4 quintillion — factorials outgrow ordinary number types very quickly.
- Used throughout combinatorics: factorials are the building block behind permutations, combinations, and probability calculations.
What is 0! (zero factorial)?
By mathematical convention, 0! = 1 — this isn't a computed result but a definition that makes combinatorial formulas work correctly at the boundary case.
Why does the result show as text instead of a regular number for large n?
Factorials of even moderately large numbers (like 25! or higher) exceed the precision limits of standard number types, so the exact digit-by-digit result is computed and displayed as text to avoid rounding errors.
Factorial Calculator
Enter a whole number to calculate its factorial. Factorials multiply every whole number from 1 up to n together, and grow extremely fast — this calculator uses exact arbitrary-precision math so even large factorials come out precise, not rounded.
Factorials are the building block behind almost every combinatorics formula — permutations, combinations, and probability distributions all reduce to ratios of factorials underneath. They also grow explosively: 10! is already 3,628,800, and 20! exceeds 2.4 quintillion, which is why ordinary calculators and spreadsheet formulas often lose precision or overflow on inputs most people wouldn't expect to be "large." Using exact arbitrary-precision arithmetic here means the result stays accurate no matter how big the input gets.
- Formula: n! = n × (n − 1) × (n − 2) × ... × 2 × 1, with 0! defined as 1.
- Grows explosively: 10! = 3,628,800 while 20! already exceeds 2.4 quintillion — factorials outgrow ordinary number types very quickly.
- Used throughout combinatorics: factorials are the building block behind permutations, combinations, and probability calculations.
What is 0! (zero factorial)?
By mathematical convention, 0! = 1 — this isn't a computed result but a definition that makes combinatorial formulas work correctly at the boundary case.
Why does the result show as text instead of a regular number for large n?
Factorials of even moderately large numbers (like 25! or higher) exceed the precision limits of standard number types, so the exact digit-by-digit result is computed and displayed as text to avoid rounding errors.