Calculate the factorial of any non-negative integer (n!). See step-by-step multiplication and related values. Free online factorial calculator.
The Factorial Calculator computes n! (n factorial) for any non-negative integer. The factorial of n is the product of all positive integers from 1 to n: n! = n × (n−1) × ... × 2 × 1.
Factorials grow extremely fast. While 10! = 3,628,800, by 20! the result exceeds 2.4 quintillion. Despite this explosive growth, factorials are fundamental — they appear in permutations, combinations, probability distributions, Taylor series, and countless mathematical formulas.
This calculator handles values up to 170! (the limit of JavaScript's floating-point precision) and shows the number of trailing zeros, which is determined by the number of times 5 divides into n!.
Integrating this calculation into regular planning habits ensures that work priorities reflect actual data about where time and energy produce the greatest results each week. Precise measurement of this value supports better personal and professional planning, helping you make informed decisions about how to prioritize tasks and manage competing demands.
Factorials grow astronomically fast and are tedious to compute by hand. This calculator instantly provides exact results (up to floating-point limits) and shows step-by-step multiplication. Data-driven tracking enables proactive schedule management, helping professionals protect focused work time and reduce the cognitive overhead of constant task-switching throughout the day. This quantitative approach replaces vague time estimates with concrete data, enabling professionals to plan realistic schedules and avoid the pattern of chronic overcommitment.
n! = n × (n−1) × (n−2) × ... × 2 × 1 0! = 1 (by definition) Trailing zeros = Σ floor(n/5^k) for k = 1, 2, ...
Result: 3,628,800
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800. It has 7 digits and 2 trailing zeros.
The number of permutations of n objects is n!. Combinations use factorials: C(n,r) = n!/(r!(n−r)!). Many probability distributions (binomial, Poisson) involve factorials.
For large n, n! ≈ √(2πn)(n/e)^n. This approximation is remarkably accurate even for moderate n and is essential in statistical mechanics and information theory.
For exact results beyond 170!, arbitrary-precision arithmetic (BigInt) is needed. Many programming languages provide big-integer libraries specifically for factorial-related computations.
Mastering this concept provides a strong foundation for advanced coursework in mathematics, statistics, and related quantitative disciplines. Understanding when and how to apply factorials is essential for solving real-world problems in probability and combinatorics.
n! (read "n factorial") is the product of all positive integers up to n. For example, 5! = 120. It counts the number of ways to arrange n distinct items in order.
By convention and the empty product rule. There is exactly one way to arrange zero items. It also makes formulas like C(n,0)=1 work correctly.
Extremely fast. 10! = 3.6 million, 20! = 2.4 quintillion, and 100! has 158 digits. Factorials grow faster than exponential functions.
Trailing zeros come from factors of 10 = 2×5. Since there are always more factors of 2 than 5, count the factors of 5: floor(n/5) + floor(n/25) + floor(n/125) + ...
The gamma function Γ(z) extends factorials to all complex numbers except negative integers. For positive integers, Γ(n) = (n−1)!. Γ(0.5) = √π.
n!! is the product of all integers from 1 to n with the same parity. 7!! = 7×5×3×1 = 105. It appears in combinatorics and certain integrals.