Factorial Calculator
Compute N! exactly for any N from 0 to 1000 using BigInt arithmetic — no floating-point rounding. Our factorial calculator shows the result in scientific notation, the exact digit count, trailing zeros via Legendre's formula, Stirling's approximation, and the full exact value. No signup required, all calculations run locally in your browser.
Enter a non-negative integer N (0–1000) to compute N! exactly using BigInt arithmetic. Results include the exact value, scientific notation, digit count, and trailing zero count. All calculations run locally in your browser.
Supports N = 0 to 1000 (exact BigInt arithmetic)
Why Use Our Factorial Calculator?
Exact BigInt Arithmetic up to 1000!
Our factorial calculator computes N! exactly for any N from 0 to 1000 using JavaScript BigInt — no floating-point rounding. 1000! has 2,568 digits and is computed precisely in milliseconds.
Scientific Notation & Digit Count
Our factorial calculator displays results in scientific notation, shows the exact digit count, counts trailing zeros using Legendre's formula, and provides Stirling's approximation for comparison.
Secure Factorial Calculator Online
All factorial calculations happen locally in your browser — your numbers never leave your device. Use our factorial calculator online with complete privacy and no data collection of any kind.
Factorial Table for Small N
For N ≤ 20, our factorial calculator displays a complete factorial table from 0! to N! with exact values. For larger N, the full exact value is shown with a scrollable display and a "show all digits" option.
Common Use Cases for Factorial Calculator
Combinatorics & Probability
Compute factorials for permutation and combination formulas — P(n,r) = n!/(n-r)! and C(n,r) = n!/(r!(n-r)!). Our factorial calculator provides the exact BigInt values needed for combinatorics problems in probability and statistics.
Mathematics Education
Verify factorial calculations for homework, exams, and coursework in discrete mathematics, combinatorics, and calculus. Students use our factorial calculator to check answers and explore how rapidly factorials grow.
Algorithm Analysis
Calculate exact factorial values for analyzing O(n!) time complexity algorithms such as brute-force permutation generation and the traveling salesman problem. Our factorial calculator handles the large integers needed for complexity analysis.
Taylor Series & Calculus
Compute factorial denominators for Taylor and Maclaurin series expansions — e^x = Σ x^n/n!, sin(x) = Σ (-1)^n x^(2n+1)/(2n+1)!. Our factorial calculator provides exact values for series convergence analysis.
Cryptography & Number Theory
Use factorial values in Wilson's theorem (p is prime iff (p-1)! ≡ -1 mod p) and other number-theoretic applications. Our factorial calculator supports the large integers required for cryptographic research.
Physics & Chemistry
Calculate multinomial coefficients and partition functions in statistical mechanics and quantum chemistry. Our factorial calculator handles the large N values needed for Boltzmann entropy calculations and molecular combinatorics.
Understanding the Factorial Calculator
What is a Factorial?
The factorial of a non-negative integer N, written as N!, is the product of all positive integers from 1 to N. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1 (the empty product). Factorials grow extremely rapidly — 10! = 3,628,800, 20! ≈ 2.43 × 10¹⁸, and 100! ≈ 9.33 × 10¹⁵⁷. Our factorial calculator computes N! exactly for any N from 0 to 1000 using JavaScript BigInt arithmetic, which handles integers of arbitrary size without floating-point rounding errors. 1000! has 2,568 digits.
How Our Factorial Calculator Works
- 1. Enter N:Type any non-negative integer from 0 to 1000 in the input field. Press Enter or click "Calculate N!". All processing happens locally in your browser — your data never leaves your device.
- 2. BigInt Computation: Our factorial calculatoruses JavaScript's native BigInt type to multiply integers from 2 to N iteratively. BigInt supports integers of arbitrary precision, so 1000! is computed exactly — all 2,568 digits — with no rounding.
- 3. Results Displayed: The factorial calculatorshows the result in scientific notation, the exact digit count (via Stirling's log approximation), the trailing zero count (via Legendre's formula), and the full exact value with a scrollable display for large results.
Trailing Zeros in N!
- Why trailing zeros? Trailing zeros in N! come from factors of 10 = 2 × 5. Since factors of 2 are always more abundant than factors of 5 in N!, the number of trailing zeros equals the number of times 5 divides into N!.
- Legendre's Formula: The number of trailing zeros in N! = ⌊N/5⌋ + ⌊N/25⌋ + ⌊N/125⌋ + ⌊N/625⌋ + … (sum until the term is 0). For example, 100! has ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24 trailing zeros. Our factorial calculator applies this formula instantly.
- Example — 1000!: Trailing zeros = ⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249. So 1000! ends in exactly 249 zeros.
Stirling's Approximation
For large N, Stirling's approximation provides a close estimate: N! ≈ √(2πN) × (N/e)^N. In logarithmic form: log₁₀(N!) ≈ ½ log₁₀(2πN) + N log₁₀(N/e). This gives the number of digits as ⌊log₁₀(N!)⌋ + 1. Our factorial calculatorshows both the exact BigInt result and Stirling's approximation side by side, so you can see how accurate the approximation is. For N = 100, Stirling gives ≈ 9.325 × 10¹⁵⁷ vs the exact 9.332... × 10¹⁵⁷ — an error of less than 0.1%.
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Frequently Asked Questions About Factorial Calculator
A factorial calculator computes N! — the product of all positive integers from 1 to N. Our factorial calculator supports N = 0 to 1000 using exact BigInt arithmetic, showing the result in scientific notation, the digit count, trailing zeros, and the full exact value — all processed instantly in your browser.
0! = 1 by definition. This is the empty product — the product of no numbers, which equals the multiplicative identity 1. This definition is essential for combinatorics formulas like C(n, 0) = 1 and the Taylor series for e^x.
100! ≈ 9.3326 × 10¹⁵⁷. It has 158 digits and 24 trailing zeros. Enter 100 in our factorial calculator to see the exact 158-digit value and all associated statistics.
1000! has exactly 2,568 digits and 249 trailing zeros. In scientific notation, 1000! ≈ 4.0238 × 10²⁵⁶⁷. Our factorial calculator computes this exactly using BigInt arithmetic — all 2,568 digits are available to view.
Our factorial calculator uses JavaScript's native BigInt type, which supports integers of arbitrary precision. Unlike regular floating-point numbers (which lose precision beyond ~15 significant digits), BigInt computes 1000! exactly — all 2,568 digits — with no rounding errors.
Trailing zeros in N! come from factors of 10 = 2 × 5. Since factors of 2 are always more abundant, the count equals the number of times 5 divides N!. Using Legendre's formula: trailing zeros = ⌊N/5⌋ + ⌊N/25⌋ + ⌊N/125⌋ + … For 100!, this gives 20 + 4 = 24 trailing zeros.
Stirling's approximation estimates N! as √(2πN) × (N/e)^N. It's useful for estimating the magnitude of large factorials without computing the exact value. Our factorial calculator shows both the exact result and Stirling's approximation so you can compare their accuracy.
Absolutely. All factorial calculations happen locally in your browser using JavaScript. Your numbers are never sent to any server, ensuring complete privacy every time you use our factorial calculator online.
Yes! Our factorial calculator is 100% free with no signup, no usage limits, and no premium features. Calculate factorials as many times as you need — completely free, forever.