**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: Finding the Sum of a Sequential Integer Range.

Excel includes the FACT worksheet function which returns the factorial of a value. (The factorial of the number X is the result of multiplying 1 * 2 * 3 ... * X.) Sabeesh wonders if there is a similar function that will return the sum of the values (1 + 2 + 3 ... + X) instead of the result of the values.

There is no such function built into Excel, but a quick mathematical formula will do the trick. The proper terminology to refer to this type of sum is a "triangular number." This derives from the fact that if the sum was represented with objects, they could always be arranged in the form of a triangle. For example, if you had 5 objects on the bottom row, 4 on the next, 3 three on the third, 2 on the fourth, and 1 on the top row, you have a triangle. Summing the number of objects (5 + 4 + 3 + 2 + 1) is what Sabeesh wants to do.

The answer to this problem can be expressed as a mathematical formula, reportedly discovered by Carl Friedrich Gauss. (Which is the source for another name of this type of number: a Gaussian Summation.) Note that the sum of opposite rows in the above example are always the same: 5 + 1 is the same as 4 + 2. This is true regardless of the number of rows; if there were 100 rows, then 100 +1 is the same result as 99 + 2, 98 + 3, 97 + 4, etc. What you end up with is 50 "pairs" of numbers equal to 1 more than the upper limit of your range.

The upshot of all this—without going through a lot of explanation—is that you can find the triangular number for any positive value (where you start at 1 and end with X) in the following manner:

=X*(X+1)/2

Thus, if you had a number in cell A1 and you wanted to know the sum of the range of 1 through that number, you could use this formula:

=A1*(A1+1)/2

This formula provides a simple way to determine the sum required, without the necessity of resorting to using a macro.

*ExcelTips* is your source for cost-effective Microsoft Excel training.
This tip (9998) applies to Microsoft Excel 2007, 2010, and 2013. You can find a version of this tip for the older menu interface of Excel here: **Finding the Sum of a Sequential Integer Range**.

**Create Custom Apps with VBA!** Discover how to extend the capabilities of Office 2013 (Word, Excel, PowerPoint, Outlook, and Access) with VBA programming, using it for writing macros, automating Office applications, and creating custom applications. Check out *Mastering VBA for Office 2013* today!

Adding row numbers to a column of your worksheet is easy; you just need to use a formula to do it. Here's a quick look at ...

Discover MoreIf you have a range of values that can be either positive or negative, you might wonder how to determine the largest ...

Discover MoreWhen working with large amounts of data, it is a good idea to make sure that the data all consistently follows a pattern. ...

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

2017-02-22 05:16:05

naseemkanwal

how to -2,-2,-2=-6 & +2,+2,+2=6

2016-04-27 08:55:39

Michael (Micky) Avidan

Your second formula can be "sinplified" to:

=(A1*(A1+1)-(B1-1)*(B1))/2

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

Michael (Micky) Avidan

“Microsoft® Answers" - Wiki author & Forums Moderator

“Microsoft®” MVP – Excel (2009-2016)

ISRAEL

2016-04-26 18:28:44

Brandon

=(A1*(A1+1)/2)-((B1-1)*((B1-1)+1)/2)

Which should be simplified to:

=(A1*(A1+1)/2)-((B1-1)*(B1)/2)

Thank you Allen, helpful article! Sorry for double comment, didn't realize the first comment was on the page for the older versions of Excel, though I guess they're the same formulae for both.

2016-04-26 18:19:51

Brandon

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.

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

Copyright © 2019 Sharon Parq Associates, Inc.

## Comments