Please Note: This article is written for users of the following Microsoft Excel versions: 2007, 2010, and 2013. If you are using an earlier version (Excel 2003 or earlier), this tip may not work for you. For a version of this tip written specifically for earlier versions of Excel, click here: Avoiding Rounding Errors in Formula Results.

Avoiding Rounding Errors in Formula Results

by Allen Wyatt
(last updated October 27, 2014)

2

Nick notes that the formula "=0.28*100-INT(0.28*100)=0" returns False even though it is obviously true. He believes the issue has to do with rounding and how the computer uses binary arithmetic, etc. Nick is using the formula as a part of a larger IF statement, and he assumes there are other rounding errors in Excel that can reach out and bite him. He wonders if there is a simple way to avoid formula pitfalls such as this.

Before looking at simple ways to avoid this type of problem, it is important to understand why the problem exists. As Nick notes, it really has to do with binary arithmetic and the fact that Excel rounds information. Behind the scenes, Excel always rounds information to 15 digits. Consider the calculation that Nick is working with:

=0.28*100-INT(0.28*100)=0

When Excel first calculates this, the precedence followed by Excel calculates it in this manner:

=(0.28*100-INT(0.28*100))=0

Note the extra set of parentheses. The result of everything to the left of that final equal sign is 3.55E-15, which means that you end up with this (longhand) formula:

=0.00000000000000355=0

This is obviously not true, which is why you get the value False returned. There are several ways to "fix" this situation. In this case, perhaps the easiest is to simply change your formula to remove the need to compare to zero:

=0.28*100=INT(0.28*100)

This formula returns True, as you would expect. This may not work for all your needs, however. So, a better rule of thumb to avoid problems is to never rely on Excel's rounding. You do this by implementing your own explicit rounding, as shown with these formulas:

=INT(0.28*100)-INT(0.28*100)=0
=ROUND(0.28*100,0)-INT(0.28*100)=0
=ROUND(0.28*100,5)-ROUND(0.28*100,5)=0

Note that you are, in these instances, not allowing Excel to perform calculations to its full precision since that can cause some unexpected results when you are comparing to a specific value, such as zero. Instead, you are forcing Excel to round the values—all the values you are working with—to whatever level of precision you need for your comparison.

Another approach is to not do the comparison to an exact value, like zero. Instead, allow for some "fudge factor" in the comparison, which allows for rounding issues. For instance, you may determine that you only care if the comparison is accurate to one one-hundredth of whatever units you are assuming. In that case, the original formula could be modified in this manner:

=0.28*100-INT(0.28*100)<0.01

This returns True, as one would expect.

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (8145) applies to Microsoft Excel 2007, 2010, and 2013. You can find a version of this tip for the older menu interface of Excel here: Avoiding Rounding Errors in Formula Results.

Author Bio

Allen Wyatt

With more than 50 non-fiction books and numerous magazine articles to his credit, Allen Wyatt is an internationally recognized author. He  is president of Sharon Parq Associates, a computer and publishing services company. ...

MORE FROM ALLEN

Disabling Track Changes Completely

Have you ever had problems with a document because you accidentally pressed a keyboard shortcut? The good news is that you ...

Discover More

Getting Rid of the Paste Options Box

Paste something in a Word document, and you may notice a dynamic little set of options appear right next to what you pasted. ...

Discover More

Replacing All Building Blocks

Word's Building Blocks can be a great tool to improve your productivity when writing. Depending on the type of writing you ...

Discover More

Professional Development Guidance! Four world-class developers offer start-to-finish guidance for building powerful, robust, and secure applications with Excel. The authors show how to consistently make the right design decisions and make the most of Excel's powerful features. Check out Professional Excel Development today!

More ExcelTips (ribbon)

Errors When Subtracting

When you subtract two numbers from each other, you have a certain expectation of what Excel should deliver. What if you get ...

Discover More
Subscribe

FREE SERVICE: Get tips like this every week in ExcelTips, a free productivity newsletter. Enter your address and click "Subscribe."

View most recent newsletter.

Comments

If you would like to add an image to your comment (not an avatar, but an image to help in making the point of your comment), include the characters [{fig}] in your comment text. You’ll be prompted to upload your image when you submit the comment. Maximum image size is 8Mpixels. Images larger than 600px wide or 1000px tall will be reduced. Up to three images may be included in a comment. All images are subject to review. Commenting privileges may be curtailed if inappropriate images are posted.

What is 7 - 0?

2015-07-29 10:01:09

ong\'aro Moses

Thanks guys, I find this group very helpful.


2013-10-07 08:51:27

Bryan

This is the second time I've found an article that I know I've commented on, where comments have been deleted. As recently as 9/24/13, the following comments were on this article:

-----------------

Bryan 30 Jun 2013, 09:13
Very true, but since we are talking about Excel if I had meant factorial it would have been =0.28*FACT(100) ;-)

-----------------

Greg 28 Jun 2013, 09:43
Bryan be careful with your exclamation marks: .28*100! means .28*Factorial 100 and as factorial 100 is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 thus you could expect to see a rounding error :-)

-----------------

Bryan 28 Jun 2013, 07:47
This is definitely unexpected behavior. Even with extra precision, you wouldn't expect to ever see a rounding error with .28*100!

Another way to avoid this error (especially if you can't use the INT or ROUND functions for data integrity reasons) is to separate the calculations into two separate cells. So, if A1 = 0.28*100-INT(0.28*100), then in cell B1 the formula =A1=0 returns TRUE.

I can't explain why, but it works.

-----------------
Source:
http://cc.bingj.com/cache.aspx?q=Avoiding+Rounding+Errors+in+Formula+Results&d=4530422873524231&mkt=en-US&setlang=en-US&w=_oZRDCzaNpsMMsvnPbGNYx4zGfxcvK00


This Site

Got a version of Excel that uses the ribbon interface (Excel 2007 or later)? This site is for you! If you use an earlier version of Excel, visit our ExcelTips site focusing on the menu interface.

Newest Tips
Subscribe

FREE SERVICE: Get tips like this every week in ExcelTips, a free productivity newsletter. Enter your address and click "Subscribe."

(Your e-mail address is not shared with anyone, ever.)

View the most recent newsletter.