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.
by Allen Wyatt
(last updated November 21, 2015)
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:
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:
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.
Excel Smarts for Beginners! Featuring the friendly and trusted For Dummies style, this popular guide shows beginners how to get up and running with Excel while also helping more experienced users get comfortable with the newest features. Check out Excel 2013 For Dummies today!
One branch of mathematics allows you to work with what are called "simultaneous equations." Working with this type of ...Discover More
Sometimes it is helpful to see the actual formulas in a cell, rather than the results of those formulas. Here's how to ...Discover More
Excel allows you to easily combine text together. The key is to understand and use the ampersand operator.Discover More
FREE SERVICE: Get tips like this every week in ExcelTips, a free productivity newsletter. Enter your address and click "Subscribe."
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.