The Math Behind Patterns: What does “a multiple of 3 + 2” mean?

Because I design patterns, I embrace the multiples-math that is used to make patterns work. But even a novice knitter or crocheter can use a pattern’s repeats to customize a project’s size. All you need to do is pay attention to the basics of pattern construction.

What are Multiples?

Many patterns rely on a repeating stitch pattern that incorporates different types of stitches. These stitch patterns can be found in stitch dictionaries, which will tell a crocheter or knitter how to make a specific stitch. But do not incorporate those stitches into a finished object. Because the stitch is not a part of a finished object, the stitch patterns in a dictionary have no predetermined length or width. A stitcher (or designer) arrives at the appropriate length and width by repeating the patterns the necessary number of times.

My last blog about knitting lace contained an example of a stitch pattern that can be found in a stitch dictionary.

The blog example states:

Cast on any multiple of three plus two stitches.

Eyelet Stitch
1st Row: Knit
2nd Row: Purl
3rd Row: K2, *yo, k2tog, k1, repeat from * to end of row
4th Row: Purl

Continue working rows 1-4 as many times as you wish.

For this pattern you can cast on any number of stitches which are a multiple of 3 stitches, and then add two stitches. A multiple here is the same as in math class: a number that can be divided evenly into another number. So multiples of 3 are numbers that can be evenly divided by 3, such as 6, 9, 12, 30, or 60.

Some examples of numbers of stitches you can cast on for this stitch pattern are
3 + 2 = 5 sts
6 + 2 = 8 sts
9 + 2 = 11 sts
12 + 2 = 14 sts
15 + 2 = 17 sts
18 + 2 = 20 sts

Continue reading for a knit blanket, or skip down for the crochet blanket.

How Can I Make My Knit Blanket Bigger (or Smaller)?

Let’s take a close look at the Lace Chevrons Baby Blanket pattern.

Imagine that you want to make this baby blanket, but you want it to be about the size of a Twin sized bed comforter (approx. 54″ x 72″). To make the blanket longer, you just continue to knit until it is the desired length, but in order to make it wide enough, we’ll have to do a bit of math.

First off, the blanket pattern, as written is 36″ wide.  It asks you to cast on 156 stitches (giving us the gauge of 17 stitches per 4 inches). This gauge means we need to add approximately 18″ to the width of the blanket to make it as wide as a Twin comforter (54″ – 36″ = 18″). We will add about 78 stitches DEPENDING UPON the number of stitches in the repeated zigzag chevron pattern.  (156 stitches / 36 inches = 4.33 stitches per inch.  4.33 x 18″ = 78 additional stitches). Now we will refer to the pattern to see how many stitches are in the repeated pattern (and seed stitch border).

In the Stitch Pattern section, the pattern tells us that it uses an 11 stitch repeat, therefore we will need to add a multiple of 11 to the total of stitches that will be cast on. The closest multiple of 11 to 78 is 77, therefore you will cast on 233 stitches total (156 + 77 = 233).

Checking your work

You can check your work by taking the total number of stitches (233) divided by 54 (the number of inches we hope to achieve).  It should reach something close to 4.33 (in this case 4.314).

The pattern will be worked as written but instead of 13 repeats, you will have 20 repeats in your pattern work in each row. To make it longer, you’ll just keep knitting until it is the length you want.

Now let’s imagine we want to make it only 32 inches wide, such as for a stroller blanket. This means we need to remove as close to 4 inches from the width as possible. We know that 17 stitches = 4 inches (due to the gauge) so we will want to remove either 11 or 22 stitches from the original cast on and repeat the pattern either 12 or 11 times. If you cast on 145 (156 – 11 = 145) your blanket will be approx 33.5″ wide (with 12 repeats). If you cast on 134 (156 – 22 = 134) your blanket will be approx 31″ wide (with 11 repeats).

How Can I Make My Crochet Blanket Bigger (or Smaller)?

Let’s take a close look at the Rickrack Rainbow Baby Blanket pattern.

Like the knit blanket example, imagine that you want to make this ripple blanket, but you want it to be about the size of a Twin sized bed comforter (approx. 54″ x 72″). To make the blanket longer, you just continue to crochet until it is the desired length, but in order to make it wide enough, we’ll have to do some math.

As written, this blanket is 36″ wide. The pattern has you chain 157 to get 156 sts and it has a gauge of 18 sts = 4″ in the ripple pattern. We need to add approximately 18″ to the width of the blanket to make it as wide as a Twin comforter (54″ – 36″ = 18″). We need to calculate how many stitches to add, depending on the number of stitches in the ripple pattern. 156 stitches divided by 36 inches = 4.33 sts per inch. 4.33 sts x 18″ = 78 additional stitches, so we’ll add about 78 stitches. Let’s check that against the pattern.

Checking Against the Pattern

This pattern doesn’t tell us how many stitches are in the stitch repeat, so we need to figure it out by looking at the pattern. The stitches you repeat in Row 1 are “sc in next 4 ch, 3 sc in next ch, sc in next 4 ch, skip next 2 ch”. These are also the same stitches you repeat in Row 2, except working into single crochet stitches instead of into chain stitches. Adding up the stitches you repeat you end up with 11 sts, but this is not the entire row; you’re missing some on either end.

At the start of the row you did one sc into a stitch and also skipped a stitch, so you have 2 extra sts at the start of the row.

Let’s check this amount against the number of stitches. If we take 156 sts and subtract 2, we get 154 sts. 154 / 11 = 14, so we know 154 is a multiple of 11. This ripple pattern is a multiple of 11 + 2 for the pattern itself. For the foundation chain we will need to add an extra stitch to account for the turning chain.

The multiple of 11 that is closest to 78 is 77, so you will add 77 chains to the beginning chain for a total of 234 chains (157 original chains + 77 extra chains = 234 total chains) and 233 stitches. (One chain is the turning chain for the first row, so you are making one more chain than total number of stitches.)

Checking your work

You can check your work by taking the total number of stitches (233) divided by 54 (the number of inches we hope to achieve).  It should reach something close to 4.33 (in this case 4.314).

The pattern will be worked as written., but Instead of 14 repeats, you will have 21 repeats in your pattern work in each row. To make it longer, you’ll just keep crocheting until it is the length you want.

Now let’s imagine we want to make it only 32 inches wide, such as for a stroller blanket. This means we need to remove as close to 4 inches from the width as possible.  We know that 18 stitches = 4 inches (due to the gauge) so we will want to remove either 11 or 22 stitches from the original chain and repeat the pattern either 13 or 12 times. If you chain 146 (157 – 11 = 146) your blanket will be approx 33.5″ wide (with 13 repeats). If you chain 134 (157 – 22 = 135) your blanket will be approx 31″ wide (with 12 repeats).

Whew.  That’s enough math for me for today!!!