Enter a number to calculate the Stirling’s approximation for the factorial of that number using this calculator.
Stirling’s Formula
The following formula is used to calculate Stirling’s approximation for a factorial:
n! ≈ √(2πn) * (n/e)^n
Variables:
- n is the number for which you want to find the factorial approximation
To calculate Stirling’s approximation for a factorial, multiply the square root of 2π times the number n by the number n raised to the power of n and then divided by Euler’s number e raised to the power of n.
What is Stirling’s Formula?
Stirling’s formula is an approximation for calculating factorials. It is particularly useful for large numbers where calculating the exact factorial would be impractical. The formula provides an estimate that becomes more accurate as the number n increases.
How to Calculate Using Stirling’s Formula?
The following steps outline how to calculate the factorial approximation using Stirling’s Formula.
- First, determine the number n for which you want to find the factorial approximation.
- Next, use the Stirling’s formula: n! ≈ √(2πn) * (n/e)^n.
- Finally, calculate the approximation and compare it with the actual factorial if needed.
- Use the calculator above to verify your results quickly.
Example Problem:
Use the following variable as an example problem to test your knowledge.
Number (n) = 10
