Factorials of larger(er) numbers in Excel

You can use Stirling's Approximation to calculate the log of the factorial of large numbers:

	A	B	C
1	n	170	B1: Input
2	n!	7.26E+306	B2: =FACT(B1)
3	log(n!)	306.86078	B3: =LOG(B2)
4	≈log(n!)	306.86057	B4: =LOG(2*PI()*B1) / 2 + B1*LOG(B1/EXP(1))
5
6	n	1,000	B6: Input
7	n!	#NUM!	B7: =FACT(B6)
8	log(n!)	#NUM!	B8: =LOG(B7)
9	≈log(n!)	2567.6046	B9: =LOG(2*PI()*B6) / 2 + B6*LOG(B6/EXP(1))
10
11	n	10,000,000	B11: Input
12	n!	#NUM!	B12: =FACT(B11)
13	log(n!)	#NUM!	B13: =LOG(B12)
14	≈log(n!)	65657059	B14: =LOG(2*PI()*B11) / 2 + B11*LOG(B11/EXP(1))

1E308 is not just Excel's limit, but that is the standard limit for double precision float variables across programming languages (at least those that use standard IEEE like definitions for double precision floating point). And, since double precision stores only 15 digits of precision, any result above ~1E16 will exhibit rounding error.

The real problem is that Excel (and all other spreadsheets as far as I know) only knows how to store numbers as double precision. My first recommendation is to seek out a different programming language, if you really need to work with these kinds of numbers. My limited search found:
R appears to also be limited to double precision, but I found a few references to some external libraries that can extend to higher precision (maybe even arbitrary precision).
Java has the BigInteger and BigDecimal data types that appear to be arbitrary precision.
I have seen procedures for VBA that implement some arbitrary precision operations (add, substract, and multiply, but I have not seen a factorial function).
I expect that other languages like Python or Mathcad/Mathematica will also have arbitrary precision algorithms available.

Choices will depend on exactly how large of a number you need to compute and how many digits of precision you need.

Wikipedia's article on arbitrary precision uses factorials as an example https://en.wikipedia.org/wiki/Arbitr...hmetic#Example where they talk about doing these calculations in log() space, or using what it calls Stirling's approximation (link in Wikipedia article also see shg's example in previous post). Pseudocode for an "arbitrary" precision algorithm is also given.

How do you want to proceed?

I'd also add my 5 cents

Well, I'd say if you need exact result you are in problem already with 21!

Note that true value is:
51 090 942 171 709 440 000
while, with numbers beeing represented in Excel as IEEE double precision floating point (ca 15 digits accuracy) FACT calculates it as
51 090 942 171 709 400 000

Now a bit better news if you shall stick to Excel:
If you:
1) can live with the accuracy limit, and
2) need to calculate logarithms (quite often for large factorials)
then you can use gamma distribution:
=GAMMALN(n+1)
which is equal to
=ln(FACT(n))

Of course you cannot calculate the latter for n>170 in excel because FACT(n) will return #NUM! error, but with GAMMALN you can go waaaaay further

And if you need log(n!) not ln(n!) nothing easier than: =GAMMALN(n+1)/LN(10)

GammaLn, of course! Forgot about that.