Google Sheets Arrayformula on both horizontal & vertical cells?

Question

In a sheet, I make calculations horizontally, however I can't build the arrayformula to expand calculation vertically on each row. See the following sheet:

https://docs.google.com/spreadsheets/d/1FbeoKhiJ3jqYXqfIgAK_tHXPZ_Z1Xrm33ulu9gomXuE/edit#gid=16063565

Select the tab "arrayformula", and point to the formula in column F

=COUNTA(B3:E3)

How can I apply arrayformula so it can expand to all the rows?

Answer 1

=ARRAYFORMULA(IF(LEN(A3:A), 
 MMULT(IFERROR(LEN(B3:E)/LEN(B3:E), 0), TRANSPOSE(COLUMN(B2:E2)^0)), ))

Answer 2

Digging the web I have found a Google Post that states:

Aggregating functions such as sum() will not produce multi-cell results in an arrayformula() wrapper. To calculate row-by-row totals of the numeric values in columns A to C from row 2 down, use simple addition instead of sum():

=arrayformula( A2:A + B2:B + C2:C )

When there are lots of columns, or if the array to be totaled row-by-row is not a range but another array expression, use mmult():

=arrayformula( 
                mmult( A2:C; transpose(sign(column(A2:C))) 
                      ))

See the illustrative sheet prepared by Top Contributor APL+ for more information on mmult() usage.

Some other aggregating functions that are not conducive for use in an array formula are listed below with examples of workarounds for producing row-by-row results.

and() -- use boolean arithmetic:

=arrayformula( if( (A2:A = "OK") * (B2:B > 10); "Ready"; "" ) )

or() -- use boolean arithmetic:

=arrayformula( if( (A2:A = "Yes") + (A2:A = "Maybe"); "Positive"; "" ) )

average() -- use addition and division:

   =arrayformula( (A2:A + B2:B + C2:C) / 3 )

count() -- use isnumber() and +:

  =arrayformula( isnumber(A2:A) + isnumber(B2:B) + isnumber(C2:C) )

counta() -- use not(isblank()) and +:

  =arrayformula( not(isblank(A2:A)) + not(isblank(B2:B)) + not(isblank(C2:C)) )

concatenate() -- use the & operator:

  =arrayformula( A2:A & B2:B & C2:C )

join() -- use the & operator: =arrayformula( A2:A & ", " & B2:B & ", " & C2:C )

max() -- use if():

    =arrayformula( if(A2:A > B2:B; A2:A; B2:B) )

min() -- use if():

    =arrayformula( if(A2:A < B2:B; A2:A; B2:B) )

product() -- use the * operator:

   =arrayformula( A2:A * B2:B * C2:C )