Stirling's Approximation for big factorials


Staff member
4 Jun 2021
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Stirling's Approximation is a gloriously imprecise way to calculate really large factorials that gets more accurate as the factorials get bigger, even though the difference between the actual number and the approximation keeps getting bigger too. Yeah, a bit hard to get one's head around and the formula doesn't exactly look convenient either with e, pi and square roots in it, but it really helps at those large sizes above 69 where most calculators can't go. Check out the video.

And here's a really short bonus video on the largest factorial that most calculators can work out, 69.

Here's an easy to read and understand Wikipedia article on this, without any complicated maths. Let us know if you need any help understanding it.

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