custom Excel function (also known as a User-Defined Function or UDF) to perform error propagation for multiplication or division.

PropagateError_ExcelFunction

'1. Press `ALT` + `F11` to open the Visual Basic for Applications (VBA) editor in Excel.

'2. In the VBA editor, click `Insert` > `Module` to insert a new module.

'3. Copy and paste the following VBA code into the module:

Function PropagateError(operation As String, value1 As Double, sigma1 As Double, value2 As Double, sigma2 As Double) As Double
    Dim result As Double

    Select Case operation
        Case "multiply"
            result = value1 * value2
            PropagateError = result * Sqr((sigma1 / value1) ^ 2 + (sigma2 / value2) ^ 2)
        Case "divide"
            result = value1 / value2
            PropagateError = result * Sqr((sigma1 / value1) ^ 2 + (sigma2 / value2) ^ 2)
        Case Else
            PropagateError = CVErr(xlErrValue) ' Return an error if the operation is not recognized
    End Select
End Function

'4. Close the VBA editor and return to your Excel worksheet.

'You can use this custom function in your worksheet to calculate the propagated standard deviation for multiplication or division.

'For example, if you want to multiply two values `A1` and `A2` with standard deviations `B1` and `B2`, you can use the function as follows:

- 'To calculate the result of the multiplication:
    =PropagateError("multiply", A1, B1, A2, B2)
  
- 'To calculate the result of the division:

  =PropagateError("divide", A1, B1, A2, B2)
  
`Replace`A1`,`A2`,`B1`, and`B2`with the appropriate cell references in your Excel worksheet. The function`will return the propagated standard deviation for the specified operation.