Syntax:

Dim I as Long
With Workbooks("Book1.xls")
   For I = 1 to .Worksheets.Count Step 1
       .Worksheets(I).Calculate
   Next I
End With

Remarks:

The above code calculates each sheet one by one starting from the first
sheet to the last sheet.  I also assumes that no worksheet is dependent on
some value of another worksheet later in the workbook, so if this isn't the
case, then the code would need to be modified to specify the order of the
worksheets to be calculated.

The other option to force a full calculation of everything would be the one
line code below:

   Application.CalculateFullRebuild

Instead of the question being does it need to be on the computer screen, the
real question should be, "Does it need to be open?"

The workbook does need to be open within Excel, but it does not need to be
visible on the screen itself.

For more information on how to open workbooks via code, look at the Open
Method on the Workbooks Collection.