# Engineering Calculations

Please Note: This article is written for users of the following Microsoft Excel versions: 97, 2000, 2002, and 2003. If you are using a later version (Excel 2007 or later), this tip may not work for you. For a version of this tip written specifically for later versions of Excel, click here: 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 the Cells option from the Format menu. Excel displays the Format Cells dialog box.
3. Make sure the Number tab is selected.
4. In the list of format categories, choose Custom. (See Figure 1.)
5. Figure 1. The Number tab of the Format Cells dialog box.

6. 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.)
7. 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
```

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (2928) applies to Microsoft Excel 97, 2000, 2002, and 2003. You can find a version of this tip for the ribbon interface of Excel (Excel 2007 and later) here: Engineering Calculations.

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Sergio Goncalves    13 Dec 2016, 12:28
Hi, good tips, thanks!

Is there any way to format the axis of a graph with that notation (k, M, G)?
John Mathew    21 Jan 2014, 21:27
Thank you, Allen. That is very useful.
It is an option that Microsoft should have built into the number formatting options.
Scott Renz    01 Jul 2013, 11:35
However, not all my numbers have the same units although they are all about height. Some have inches. Some have centimeters. Some have feet. I would like them all normalized to the same unit.

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