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: Finding the Sum of a Sequential Integer Range.

Finding the Sum of a Sequential Integer Range

by Allen Wyatt
(last updated November 21, 2015)

5

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 (9997) 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: Finding the Sum of a Sequential Integer Range.

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

Using Cross-References in Footnotes

Need to make a cross-reference from one footnote to another footnote? You can do it if you throw bookmarks into the mix, as ...

Discover More

Working with Roman Numerals

Understanding and using a function to replace an Arabic number with Roman numerals. And, as a bonus, how to change them back.

Discover More

Using a Custom Format to Add Dashes

Want some dashes automatically added in values you display in a cell? It may be trickier to develop a custom format than you ...

Discover More

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!

More ExcelTips (menu)

Deriving Monthly Median Values

When processing huge amounts of data, it can be a challenge to figure out how to derive the aggregate values you need. This ...

Discover More

Creating an Amortization Schedule

An amortization schedule is a report that shows how the outstanding balance on a loan changes with payments made over time. ...

Discover More

Non-adjusting References in Formulas

Sometimes making sure that a reference in a formula doesn't get changed is not as simple as putting dollar signs in front of ...

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. 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 9 + 4?

2016-10-17 06:46:19

Michael (Micky) Avidan

@Les McGarry,
Try:
=SUMPRODUCT((MOD(A1:A40,4)=1)*A1:A40)
--------------------------
Michael (Micky) Avidan
“Microsoft® Answers" - Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2017)
ISRAEL


2016-10-17 01:58:38

Les McGarry

If I have a column (or row) of numbers from A1 to A40 and want to sum the first and every 4th number (ie. A1, A5, A9, etc) is there a formula to do this?


2016-04-27 05:49:34

Michael (Micky) Avidan

@Brandon,
Try my suggested 'Array Formula' in the following picture:
(see Figure 1 below)
--------------------------
Michael (Micky) Avidan
“Microsoft® Answers" - Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2016)
ISRAEL

Figure 1. 


2016-04-26 18:17:13

Brandon

Is there a way to do this between two digits? For instance, the sum of every integer between-and-equal-to 8 and 26 is 323. Is there a way to dynamically refer to two cells with those two or any other integers?


2016-01-06 17:51:52

Rex

Thank you!


This Site

Got a version of Excel that uses the menu interface (Excel 97, Excel 2000, Excel 2002, or Excel 2003)? This site is for you! If you use a later version of Excel, visit our ExcelTips site focusing on the ribbon 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.