Written by Allen Wyatt (last updated August 22, 2020)**This tip applies to** Excel 97, 2000, 2002, and 2003

Cesarettin noted that the MOD worksheet function cannot produce a result when the number is being evaluated is 268,435,456 or larger and the divisor is 2. If the number is less than this, there is no problem. For example, if the function is MOD(268435455, 2) there is no problem. He wonders if there is a way to use the MOD function with larger numbers and a divisor of 2?

The problem is actually bigger than what Cesarettin proposes. Microsoft knows about this problem; it seems to stem from issues with the internal formulas used by MOD. You can find more information about the error here:

http://support.microsoft.com/kb/119083

Basically, the MOD function returns an error if the divisor (the second argument in the MOD function), multiplied by 134,217,728, is less than or equal to the number being evaluated (the first argument in the MOD function).

Thus, the problem occurs when the number being evaluated is 268,435,456 and the divisor is 2, the number being evaluated is 402,653,184 and the divisor is 3, the number being evaluated is 536,870,912 and the divisor is 4, etc.

The solution suggested by Microsoft is to simply not use the MOD function and instead rely upon the following formula:

=number-(INT(number/divisor)*divisor)

This is not the only solution, however. There are other formulaic approaches you can use, as well. For instance:

=MOD(MOD(number,134217728*divisor),divisor)

This will solve for larger numbers much larger than the limit for MOD, but theoretically will hit the same problem when the number being evaluated reaches 134,217,728*134,217,728*divisor. For most uses, this is limit is large enough that it will never be reached.

If you only need to find the modulus of a number divided by 2, then you can insert a check into your formula in the following manner:

=MOD(IF(A1>=268435456,A1-268435456,A1),2)

This checks if the number being evaluated (in this case, in cell A1) is larger than the limit, and if it is it subtracts the limit from the number before calculating the modulus. You could also effectively remove the MOD limit by using this formula:

=MOD(MOD(number,2^16),2))

This takes the large number modulo 2 to the 16th power, then takes the resulting value modulo 2. If the numbers are viewed as binary, it's easy to see what is happening. MOD(largenum,2^16) just drops all bits to the left of the 16th binary digit. For modulo 2, only the right-most digit is required to determine the result anyway, so the dropped bits never affect the result, regardless of value.

Of course, you could simply create your own MOD function in VBA and use it in your formulas instead of the built-in MOD function.

Function DblMod(Dividend, Divisor) ' Declare two double precision variables Dim D1 As Double Dim D2 As Double ' Copy function arguments to local variables D1 = Dividend D2 = Divisor DblMod = D1 Mod D2 End Function

The function simply lets you pass two arguments to the VBA function. It then relies upon the VBA Mod function, which doesn't have the same limitation as the MOD worksheet function.

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This tip (3302) applies to Microsoft Excel 97, 2000, 2002, and 2003.

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2021-12-06 22:21:55

Eric

Here is a frustrating example =MOD(2357.74,0.77) returns 0.77, what!? My name is Batman if this should not have returned 0 !!!

Eric

2020-09-12 17:49:21

Joe User

2020-09-12 15:34:15

Joe User

I do believe MOD(n,d) returned #NUM for n >= d*2^27 (134217728) in Excel 2003 and earlier.

But at least as of Excel 2010 (and perhaps Excel 2007), the threshold is larger.

Now, MOD(n,d) returns #NUM for n >= d*1125900000000.

YMMV for versions after Excel 2010, which I cannot test. But MOD(1125900000000,1) does return #NUM in Excel Online (onedrive.live.com) -- today.

Anyway, the following do __not__ return errors in Excel 2010 and Excel Online: MOD(134217728,1), MOD(268435456,2), MOD(402653184,3), MOD(536870912,4).

FYI, 1125900000000 is an unusual number. It is not a simple power of 2. It is 13 digits, which is less than 15. It does fit into a 32-bit binary floating-point (type Single); but so do a lot of other values, larger and smaller.

In any case, with modern computers, there is no good reason (IMHO) not to calculate MOD straight-forwardly using 64-bit binary floating-point (type Double).

2020-09-12 05:17:31

Joe User

results in an overflow error when D1 exceeds 2^31-1 because VBA Mod converts its operands to type Long.

A more-reliable alternative is

DblMod = D1 - D2 * Int(D1 / D2)

which is, after all, the alternative "suggested by Microsoft"

2020-09-12 05:02:15

Joe User

Is there an alternative URL that still works?

2020-08-22 10:38:39

Rick Rothstein

' The arguments to the BigMod function can be up to 29 digits as long as

' either number is less than 79,228,162,514,264,337,593,543,950,335

' (a limitation of the Decimal data type used in the calculations).

' And, of course, if you are going to feed the BigMod function super

' large numbers, they must be passed in as quoted text strings.

Function BigMod(Number As Variant, Modulus As Variant) As Variant

Number = CDec(Number)

Modulus = CDec(Modulus)

BigMod = Number - Modulus * Int(Number / Modulus)

End Function

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