Please Note: This article is written for users of the following Microsoft Excel versions: 2007, 2010, 2013, 2016, 2019, and Excel in Office 365. 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.

# Finding the Sum of a Sequential Integer Range

by Allen Wyatt
(last updated June 29, 2019)

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, 2013, 2016, 2019, and Excel in Office 365. You can find a version of this tip for the older menu interface of Excel 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

Understanding Footnotes and Endnotes

Footnotes and endnotes are often used in scholarly and formal writing as a way to provide additional information about a ...

Discover More

Turning Off Automatic Numbered Lists

Type what Word thinks is a numbered list, and it will helpfully format the text to match what it thinks your numbered ...

Discover More

Creating Scenarios

Excel allows you to create different scenarios for the data in your worksheet. These can be saved and managed using the ...

Discover More

Solve Real Business Problems Master business modeling and analysis techniques with Excel and transform data into bottom-line results. This hands-on, scenario-focused guide shows you how to use the latest Excel tools to integrate data from multiple tables. Check out Microsoft Excel 2013 Data Analysis and Business Modeling today!

##### More ExcelTips (ribbon)

Counting Employees in Classes

Excel is very good at counting things, even when those things need to meet specific criteria. This tip shows how you can ...

Discover More

Retrieving the Last Value in a Column

Need to get at the last value in a column, regardless of how many cells are used within that column? You can apply the ...

Discover More

Evaluating Formulas

Need a bit of help in figuring out how Excel is evaluating a particular formula? It's easy to figure out if you use the ...

Discover More
##### Subscribe

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

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. Youâ€™ll be prompted to upload your image when you submit the comment. Maximum image size is 6Mpixels. 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 five more than 5?

2019-06-29 19:20:43

Bill Multack

To find the sum of numbers from one integer to another, one can use this formula: [assumes Y>X] =(Y*(Y-1) - X*(X-1))/2.
If A1 and A2 contain the intergers (A2 larger) then the entry to find the sum from A1 to A2 could look like this: =(Y^2 + Y -X^2 + X)/2.

##### 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.