Engineering Calculations

In an engineering environment, it is not unusual to need to "normalize" numbers in some manner. For instance, you may need to show numeric values normalized to multiples of 10^3, such that 7340 is expressed as 7.34 and 73400 is expressed as 73.4.

It is possible in Excel to use a custom number format to express information in scientific notation that will normalize the display of a number to a multiple of 10^3. To do this, you would follow these steps:

1. Select the cells you want formatted.
2. Choose Cells from the Format menu. Excel displays the Format Cells dialog box.
3. Make sure the Number tab is selected. (Click here to see a related figure.)
4. In the list of format categories, choose Custom.
5. In the Type box, enter ##0.0E+0 as your format. (This provides only one number to the right of the decimal place. If you want more, increase the number of zeros after the decimal place.)
6. Click on OK.

Now, when you enter a number such as 7340 into the cell, Excel displays it as 7.3E+3. Because of the way the cell format was entered, the portion after the E will always be a multiple of 3.

This is fine and good, but what if you want just the 7.3 in the cell, and then a metric prefix with a unit in an adjoining cell, such as kilograms? This is a bit more complex, but it can be done using formulas. For instance, let's assume you have your original number in cell A2, you wanted the normalized number in cell B2, and the metic prefix and unit name in cell C2. All you would need to do is enter the following formula in cell B2:

=IF(OR(A2>=1,A2<=-1),SIGN(A2)*(ABS(A2)/(10^(3*INT(LOG(ABS(A2))/3)))),
IF(A2=0,0,SIGN(A2)*(ABS(A2)*10^(-3*INT(LOG(ABS(A2))/3)))))

Assuming the units you are working with are an imaginary unit called a foo, in cell C2 you would use a different formula, as follows:

=IF(OR(A2>=1, A2<=-1),CHOOSE(INT(LOG(ABS(A2))/3)+1, "Foos", "Kilofoos",
"Megafoos", "Gigafoos", "Terafoos", "Petafoos", "Exafoos"),
IF(A2=0,"",CHOOSE(INT(-LOG(ABS(A2))/3)+1, "Millifoos", "Microfoos",
"Nanofoos", "Picofoos", "Femtofoos", "Attofoos")))

These formulas may seem a bit long, and they are. However, they will work for any number between approximately -9.99999E-18 to 9.99999E+20. For instance, if you put the number .000125 in cell A2, then cell B2 will contain 125 and cell C2 would contain Millifoos.

If you prefer to not use longer formulas such as these in your workbooks, you can develop a couple of VBA functions to do the trick. The following function, MySciNum, returns a normalized number. Thus, you would use =MySciNum(A2) in cell B2 to get the same results as noted above:

Function MySciNum(BaseNum As Double) As Double
    Select Case BaseNum
        Case Is >= 1
            While Abs(BaseNum) > 1000
                BaseNum = BaseNum / 1000
            Wend
        Case 0
            'Do nothing
        Case Else
            While Abs(BaseNum) < 1
                BaseNum = BaseNum * 1000
            Wend
    End Select
    MySciNum = BaseNum
End Function

This function only returns a number. To return the units with the appropriate metric prefix, you would use the following function. All you need to do is pass it the cell reference and the name of a single unit. For instance, you could use =MySciPre(A2, "foo"). The macro is as follows:

Function MySciPre(BaseNum As Double, Unit As String) As String
    Dim OrigNum As Double
    Dim Pref As Integer
    Dim Temp As String

    Pref = 0
    OrigNum = BaseNum
    Select Case BaseNum
        Case Is >= 1
            While Abs(BaseNum) > 1000
                BaseNum = BaseNum / 1000
                Pref = Pref + 1
            Wend
        Case 0
            Pref = 99
        Case Else
            While Abs(BaseNum) < 1
                BaseNum = BaseNum * 1000
                Pref = Pref - 1
            Wend
    End Select

    Select Case Pref
        Case -6
            Temp = "atto" & Unit
        Case -5
            Temp = "femto" & Unit
        Case -4
            Temp = "pico" & Unit
        Case -3
            Temp = "nano" & Unit
        Case -2
            Temp = "micro" & Unit
        Case -1
            Temp = "milli" & Unit
        Case 0
            Temp = Unit
        Case 1
            Temp = "kilo" & Unit
        Case 2
            Temp = "mega" & Unit
        Case 3
            Temp = "giga" & Unit
        Case 4
            Temp = "tera" & Unit
        Case 5
            Temp = "peta" & Unit
        Case 6
            Temp = "exa" & Unit
        Case Else
            Temp = ""
    End Select

    If Len(Temp) > 0 Then
        Temp = LCase(Temp)
        Temp = UCase(Left(Temp, 1)) & Mid(Temp, 2)
        If Abs(OrigNum) <> 1 Then Temp = Temp & "s"
    End If

    MySciPre = Temp
End Function