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Stirling’s Factorial Approximation

Stirling’s Factorial Approximation calculator estimates the factorial of a large number using an efficient logarithmic formula. It’s especially useful in statistics, probability theory, and combinatorics when exact factorial values become too large to compute. This tool provides a fast and accurate approximation using Stirling’s formula.

Stirling's Approximation Calculator

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Stirling’s Approximation Formula

Formula
$$n! \approx \sqrt{2\pi n} \left(\frac{n}{e}\right)^n$$

Explanation:
This approximation becomes more accurate as n increases. It simplifies calculations by replacing factorial expressions with exponential and root operations, reducing computational complexity. Often used in asymptotic analysis.

Stirling’s approximation is commonly applied in problems involving large factorials, such as entropy in information theory, binomial coefficients in combinatorics, or probabilities in normal distribution approximations. For instance, calculating 100! directly is computationally intensive, but Stirling’s formula gives a close estimate in seconds. The formula assumes large n, so it becomes less accurate for small integers.

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