Calculate n factorial (n!) instantly
Factorial of n (written as n!) is the product of all positive integers from 1 to n. The formula is: n! = n × (n-1) × (n-2) × ... × 2 × 1. By definition, 0! = 1. The calculator uses an iterative approach, multiplying numbers sequentially. Factorials grow extremely fast - 20! exceeds 2 quintillion.
Factorials are fundamental in combinatorics, probability theory, and statistics. They count permutations (arrangements) and combinations (selections). Factorials appear in Taylor series expansions, calculus, and many mathematical formulas. They're essential for calculating probabilities, arranging items, and analyzing algorithms.
Permutations: 5! = 120 ways to arrange 5 distinct items. Combinations: n!/(r!(n-r)!) calculates ways to choose r items from n. Probability: Factorials determine outcomes in card games, lottery odds, and statistical distributions. Calculus: Used in series expansions of e^x, sin(x), and cos(x).
Memorize small factorials (0!=1, 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720) for quick mental math. Use Stirling's approximation (n! ≈ √(2πn) × (n/e)^n) for large n estimates. Remember that factorials are only defined for non-negative integers. For large calculations, consider using logarithms to handle the enormous numbers.
A factorial, written as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. Factorials grow extremely fast -- 10! is already 3,628,800 and 20! exceeds 2 quintillion.
Factorials are widely used in combinatorics to count permutations and combinations, in probability theory for calculating odds, and in calculus for Taylor and Maclaurin series expansions. They also appear in statistics, algorithm analysis, and physics equations involving quantum mechanics.
By mathematical convention, 0! equals 1. This is not arbitrary -- it ensures that formulas for permutations and combinations work correctly. For example, the number of ways to choose n items from n items is n!/(n!*0!), which must equal 1, and this only works if 0! = 1.