Array Formulas

Learn Excel from MrExcel podcast, episode 2026 - My Favorite Formula in All of Excel!

Podcasting this entire book, click the “i” in the top-right hand corner to get to the playlist!

Alright, it was the 30th topic in the book, we were kind of at the end of the formula section, or in the midst of the formula section, and I said I have to include my favorite formula of all time. This is just an amazing formula, whether you have to count the number Friday the 13th or not, it opens a world into a whole secret area of Excel called Array Formulas! Put in a start date, put in an end date, and this formula calculates the number of Friday the 13ths that occurred between those two dates. It's actually doing five calculations on every single day between those two dates, 91895 calculations + SUM, 91896 calculations happening inside of this one little formula, alright. Now, by the end of this episode, you're going to be so intrigued by array formulas. I want to point out, my friend Mike Girvin has the best book on array formulas called “Ctrl+Shift”Enter”, this is a recent printing with the blue cover, used to be a yellow and green cover. Now, whichever one you get, is a great book, same content in both the yellow and the green one.

Alright so, let's start out on the inside of this, with a formula you may not have heard called INDIRECT. INDIRECT allows us to concatenate, or in some way build a bit of text that looks like a cell reference. Alright so, let's say we have a prize wheel here, and I just asked you to choose between A, B, and C. Alright, so you choose this and choose C, and then choose this and choose 3, alright, and your prize is a resort stay, because that's what's stored in C3. And the formula here is concatenated together whatever since C5 and whatever's in C6 using the & and then passing that to the INDIRECT. So =INDIRECT(C5&C6), in this case, is C3, that has to be a balanced out reference. INDIRECT says “Hey, we're going to go to C3 and return the answer from that, alright?” Back in Lotus 1-2-3 this was called the @@function, in Excel they renamed it to be INDIRECT. Alright, so you have in the INDIRECT, now here's the amazing thing that's happening inside of there.

We have two dates, how does Excel store dates, 2/17/1965, that's really just formatting. If we went and looked at the actual number behind that, it is 23790, which means that it is 23790 days since 1/1/1900, and 42167 days since 1/1/1980. On a Mac it'll be since 1/1/1904, so the dates will be about 3000 off. Alright, that's how Excel stores it, it's showing it to us though, thanks to this number format as a date, but if we would concatenate together B3 and a : and B4, it would actually give us the numbers stored behind the scenes. So = B3&”:”&B4, and if we would pass that to INDIRECT, it's actually going to point to all rows from 23790 down to 42167.

So there is the INDIRECT of B6, I asked for the ROW of that, that's going to give me a whole bunch of answers, and to figure out how many answers I used count, alright. And in order to make this work, if I just press Enter, it doesn't work, I have to hold down Ctrl and Shift and press Enter, and see, that adds the {} around the formula up here. It tells Excel to go into super formula mode, array formula mode, and do all of the math for everything popped out from that array, 18378, alright. So, that is an amazing trick, indirect of date1:date2, pass that to the ROW function, and here's a small example.

So we just want to figure out how many Fridays occurred in this July, here's a start date, here's an end date, and for each of those rows I'm going to ask for the WEEKDAY. WEEKDAY tells us what day of the week it is, and here in the ,2 argument Fridays will have a value of 5. So, I'm looking for the answer, and we're going to choose this formula, go to Formulas, and Evaluate Formula, and Evaluate Formula is a great way to watch a formula get calculated in slow motion. So there's the B3, the July 1st, and you see that changes to a number, and then we join the colon, right, there's the B4, that'll change to a number, and now we get the text, 42186:42216. At this point, we pass that to the ROW, and that simple little expression is going to turn into 31 values right here.

Now, in the example where I had everything from 1965 to 2015, it would pop out 86000 values, right, and you don't want to do that and evaluate formula, because would be kind of insane, alright? But you can see what's happening here with the 31, and now I'm passing those 31 days to the WEEKDAY function, and we get 3-4-5. So 3 means that it was a Wednesday, and then 4 means it was a Thursday, and then 5 means it was a Friday. Take all those 31 values and see if they're =5 which is a Friday, and we're going to get a bunch of FALSEs and TRUEs, so Wednesday, Thursday, Friday, and then 7 cells later would be the next TRUE, awesome!

Alright, so in this case we have 5 TRUEs and 26 FALSEs, In order to add those up, I need to convert the FALSE as to 0 and the TRUEs to 1, and a very common way to do that is to use the --. Alright, unfortunately it didn't show the answer there, where we saw a whole bunch of 1’s and 0’s, but that actually is what happens, and then SUMPRODUCT adds it up and gets us to the 5. Down here, if we want to figure out how many of 13th of the month there were this year, from this start date to this end date, very similar process. Although we're going to have 365, pass that to the DAY function, and check to see how many are 13, alright. For the 92000 row example, you know, we're getting the day, we're getting the weekday, checking to see if the, DAY=13, checking to see if the WEEKDAY=FALSE, multiplying this*this, and only in the cases where is a Friday the 13th does that end up as TRUE. The SUMPRODUCT then says “Add all those up”, and that's how we get the 86, literally 91895 calculations + SUM, 91896 happening inside of this one formula, it's crazy powerful! Go buy Mike's book, it's an amazing book, it will open an entire world of Excel formulas to you, and actually, you should just buy both books. Buy my book, buy Mike's book, and you will have an awesome collection that will get you through the rest of the year.

Alright, so recap: there's a secret class of formulas called array formulas, and array formula can do thousands of intermediate calculations. They usually require you to press Ctrl+Shift+Enter, but not always, and the best book on array formulas is Mike Girvin’s “Ctrl+Shift+Enter” book. Alright, so INDIRECT lets you use concatenation to build something that looks like a cell reference, and then INDIRECT goes to that cell reference. Concatenating two dates with a colon will point to a range of rows in Excel, and then asking for the ROW of the INDIRECT of date1:date2 will pop out an array of many consecutive numbers, maybe 31, maybe 365, or maybe 85000. Check each date to see if the WEEKDAY=Friday, check each day to see if the DAY=13, multiply those two arrays of TRUEs and FALSEs using the SUMPRODUCT. In many cases we'll use -- to convert the TRUE/FALSE to 1’s and 0’s to allow the SUMPRODUCT to work. It's an awesome formula, I didn't create it, I found it on the MrExcel message board, as I worked through it, I'm like “Wow, this is really cool!”

Alright, I want to thank you for stopping by, we'll see you next time for another netcast from MrExcel!