Please Note: This article is written for users of the following Microsoft Excel versions: 2007, 2010, 2013, and 2016. 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: Counting Odds and Evens.

Counting Odds and Evens

by Allen Wyatt
(last updated July 2, 2018)

5

Pini has a range of whole numbers (let's say C2:J2) and some of the numbers can be odd and some even. He would like a formula to count the number of odd values in the range and another to count the number of even values in the range.

There are a couple of ways to derive the desired counts, without resorting to intermediate values or macros. One way is to use an array formula, such as the following, to determine a count of odd values:

=SUM((MOD(C2:J2,2)<>0)*1)

Enter the formula using Ctrl+Shift+Enter and you get the desired count. Only a small change is required for the array formula to return the count of even numbers:

=SUM((MOD(C2:J2,2)=0)*1)

If you prefer to not use an array formula, you could use SUMPRODUCT to return the same count, as a regular formula. For example, here is the formula to return a count of odd values:

=SUMPRODUCT(--(MOD(C2:J2,2)=1),--(C2:J2<>""))

This is the formula for even values:

=SUMPRODUCT(--(MOD(C2:J2,2)=0),--(C2:J2<>""))

Another advantage of using the SUMPRODUCT approach is that it compensates for possible blank cells in your range. The earlier array formulas will always count blank cells as if they contain an even value.

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (7987) applies to Microsoft Excel 2007, 2010, 2013, and 2016. You can find a version of this tip for the older menu interface of Excel here: Counting Odds and Evens.

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. ...

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What is five minus 4?

2017-08-09 13:02:53

Dave Bonin

Bryan,

I understand your dislike of the SUMPRODUCT() function; it has some quirks.

Unfortunately, the average, everyday user of Excel is not familiar with array formulae,
much less the Ctrl+Shift+Enter sequence used to complete an array formula.

This leads to issues when users "examine" a formula and then inadvertently re-enter
the formula without the Ctrl+Shift+Enter sequence. The newly-non-array formula
no longer produces the desired result and computational pandemonium ensues.

The SUMPRODUCT() function, acts like an array formula, but has no special entry
syntax. That makes them much safer for use around typical users.

In my humble opinion, Microsoft did a disservice to users when it introduced and
required the special array formula entry sequence, especially while doing nothing
much further to aid the user to identify an array formula. The brackets, while
helpful, are insufficient.

While working with array formulae, it's very easy to forget to Ctrl+Shift+Enter.
I've done it countless times and I suspect you have, too. If we're really good
with Excel and we mess up, imagine how much harder it is for more average
users.


2017-08-09 12:39:46

Neil

Another couple of non-array formula variations that work but ISEVEN counts blanks as even:
=SUMPRODUCT(ISODD(C2:J2*1)*1)
=SUMPRODUCT(ISEVEN(C2:J2*1)*1)
=SUMPRODUCT(--ISODD(--C2:J2))
=SUMPRODUCT(--ISEVEN(--C2:J2))
And some that don't count blanks as even:
=SUMPRODUCT(ISEVEN(A2:A22*1)*1, (A2:A22<>"")*1)
=SUMPRODUCT(--ISEVEN(--A2:A22), --(A2:A22<>""))


2013-08-06 11:28:24

Bryan

GJCase, it's another way of coercing the true/false into a number. The first negative multiplies by -1 then the second multiplies by -1 again. Yet another reason why I don't like this kind of formula.


2013-08-05 14:12:37

GJCase

Does anyone know why it is necessary to use the double negative on the SUMPRODUCT formulae? I have noticed in the past that these do not work without this, but I've never seen an explanation why this is so.


2013-08-05 07:49:26

Bryan

I always get a little confused with mods and coercions, so I prefer the following two array formulas:

=SUM(IF(ODD(C2:J2)=C2:J2,1,0))
=SUM(IF(EVEN(C2:J2)=C2:J2,1,0))

The odd form will count blanks correctly, but the even form will count them as even numbers (0).

These formulas are a little simpler to understand, but for some reason there's an extra coercion... ISODD/ISEVEN won't work like you expect them to in an array formula:

=SUM(ISODD(C2:J2*1)*1)
=SUM(ISEVEN(C2:J2*1)*1)

(For those who don't know, multiplying a true/false by 1 lets you add them together as if they were numbers. True*1=1, False*1 = 0. This is called coercion, as you are coercing the true/false to be numbers.)


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