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You can creat a function or paste the following in a stand alone module.

Function CountVisibleFilterRows(MyRange As Range) As Long
On Error Resume Next
CountVisibleFilterRows = MyRange.SpecialCells(xlCellTypeVisible).Count
End Function

Then you can access the function with this, for example;

CountVisibleFilterRows(Range("A1:A20")) in Excel formula or

in VBA use;

Application.WorksheetFunction.CountVisibleFilterRows(Range("A1:A20"))

Sorry, the function I mentioned before should be re-written as follows;

Substitute your information where necessary

Function CountVisibleFilterRows(ByVal Sh As Worksheet)
Dim Target As Range
Dim c As Range
Dim i As Long
'If the Filter is not used
If Sh.FilterMode = False Then
CountVisibleFilterRows = 0
Exit Function
End If
Set Target = Sh.AutoFilter.Range
For Each c In Target.SpecialCells(xlCellTypeVisible).Areas
i = i + c.Rows.Count
Next
CountVisibleFilterRows = i - 1 '-1 stands for remove header row
End Function

Here is an example how to use in VBA

Application.WorksheetFunction.FilteredRowsCount(ActiveSheet) ; where "ActiveSheet" is the Worksheet your filter is on