On nth-child, mathematics, and that moment in school when your teacher said you'd use Algebra in real life

CSS's nth-child and nth-of-type are powerful, but recently I've seen them used improperly by mistakenly using the multiplier as the offset.

Recently, I’ve seen a recurring error with how :nth-child() and :nth-of-type() selectors are being used, so I wanted to host an anonymous algebra moment on these, my favorite CSS Level 3 selectors.

Frequently, I see :nth-child() selectors used for making columns:

Six Columns

From here, I see a lot of selectors like this:

  • :nth-child(1n)
  • :nth-child(2n)
  • :nth-child(3n)

Here’s why that is incorrect: the browser starts counting at 1 (the first item) and checks item each to see if that element matches the pattern (an+b) where “a” is the number you gave it, “n” is a set of all integers, and “b” is the offset that I’ve seen omitted (which defaults to zero). This is what happens:

Six columns with all N values

As you can see:

  • :nth-child(1n) matches every single column. And why wouldn’t it? The set described as (1n+0) where n is a set of all integers results in […0, 1, 2, 3, 4, 5, 6, 7, …]. In other words, this selector doesn’t actually do anything, you could stick with the element or class selector.
  • Similarly, :nth-child(2n) matches every other column because the set described as (2n+0) is […0, 2, 4, 6, 8, …]
  • 4n and 5n look safe, but what if there’s a second row?

TL;DR: The important take-away here is that the repetition is the a in an+b. So a is the total number of columns in your layout, not the “column number” you’re trying to address. The column number is the “+b”, The Offset!

What you want is this:

With correct N values

  • :nth-child(6n+1) matches the first column (the first, seventh, thirteenth, nineteenth, … elements)
  • :nth-child(6n+6), which can be written simply as :nth-child(6n), matches the last column (the sixth, twelfth, eighteenth, … elements)
    • Why can the “+6” column number (the offset) be omitted? The set of (6n+6) is […-6, 0 6, 12, 18, 24, 30…] and the set of (6n) is […-12, -6, -, 6, 12, 18, 24…]; they are the same.
    • If dropping the offset might be confusing when re-reading code, then leave it! It does no harm, and might even be a good idea to retain.

And this stacks vertically as expected:

Three columns, multiple rows

But the way I had it (usually) worked! What’s wrong with that? Two reasons: it doesn’t always work, and pride. ;-)

Look at it this way:

Three columns, bad N values

  • By selecting :nth-child(1n), the middle column is selected, too!
    • The reason this may go unnoticed is that the :nth-child(2n) is likely written after the 1n rule, with the same selector specificity, so it overrides the first.
  • Two problems arise when selecting :nth-child(2n):
    • The first column of the second row is also selected. Why? It’s the fourth element, which is in the set defined as (2n).
    • That second column on the fourth row is not selected. Why? It’s the eleventh element, which is not in the set defined as (2n).
    • Worse, with an odd number of columns, even/odd flips on each row! Count it out:
    • Three columns, counted out
    • You’d run into the same changing “rhythm” with other numbers of columns or a different incorrect interval. (This might be your intention, if you were making a pattern, and it’s cool that CSS lets us do that so easily, but ya gotta know the rule before you break it.)

Why am I pestering you with this?

  • Even if the site renders correctly now, imprecise code is difficult to maintain.
  • If someone is inspecting your code, I want them to see excellent examples of your work.
  • :nth-child() is one of my favorite selectors because of its power, which I encourage to be used for carefully constructed good.
  • Because if you don’t, I’ll make you use dastardly class names like .three-column-layout--column-first which seem to be all the rage right now.
    • Some folks out there think that this is the right way to go. The only convincing argument I see in favor of this approach is that it allows developers to avoid learning.
    • Using intelligent selectors is far more graceful.

Does it matter if only one row is used in the layout?

Yes. That :nth-child(1n) selects every column and the :nth-child(2n) selects every even column, overriding the first rule. That’s inefficient and makes debugging and careful overrides that much harder.

And what about :nth-child() vs. :nth-of-type()?

  • element:nth-of-type() uses the same math as element:nth-child(), but anything that isn’t element will be skipped in the counting in addition to not being selected. In other words, when counting the addresses of elements to select div:nth-of-type(), a span would not be counted as an element in the set.
  • I frequently see nth-of-type() when nth-child() would have been sufficient. As such, nth-child() is probably the safer option (unless you need type specificity in counting) because it will make erroneous or disorganized HTML output more obvious.
  • Bottom line: specificity and consistency. Using the simplest selector possible for the task at hand is a CSS best practice. Straying from consistency is my biggest pet peeve.

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