Square needles and gauge: the math-lete approach

I recently (well, no so recently anymore, but it fits my narrative better) purchased a Louet Kollage Square Interchangeable Needle Set (review coming soon!). Square needles are apparently better for people with wrist or carpal tunnel problems (probably because the sides allows for an easier grip). They’re also known for changing your gauge, and some people recommend going up a size when knitting with them. I wanted to see for myself, and armed with a caliper and a little bit of math, I dug through.

Properly measuring the needle size

I started by measuring a round needle and then comparing with the size of a square needle. For both needles, I was able to get the exact same measurement by taking the diagonal of the square.

Figure 1: Diameter (and diagonal) of a round and square needle

Looking at the figure 1, we can see the relationship between a square and a round needle. This is the reason why a square needle will look tinier than its cylindrical counterpart. The real questions then are

  • How much is the difference where the yarn is wrapped around the needle?
  • Will that affect my gauge?

Geometry class to the rescue!

For a circle of diameter d, we can compute the circumference by using the following formula

Since we also know that the diagonal of the square is also d, we can also use the Pythagorean theorem to deduce the side of the sides (hereon called c)

Since it’s a square, each side measures c. A little bit of algebra takes care of the rest. Taking d = 4mm, we would then have c = 4 / 1.4142 = 3.5355mm.


Now, if we make the assumption that the yarn wraps the whole needle each stitch, we just have to compute the circumference/perimeter of the two figures and compare the result.

We already know the full formula for the circumference of a circle. To compute the perimeter of the square, we simply multiply c by four.

So, the round needle of size d mm will use 3.1416d mm of yarn each stitch, while the square needle will use 2.8284d mm. It means that the square needle will use (2.8284/3.1416) = 0.9003 or approximately 90% of the yarn a identically sized cylindrical needle would.

So, looking at the American needle system, would our get down a needle size when using square ones work

US sizes, Metric Equivalent (mm), Round circumference and Square perimeter (mm)

I think the people who came with that rule are knitters who mostly stay in the worsted-weight range, where a US7 is 90% of the diameter of a US8. It works great there, but this is far from being applicable to every needle size. Furthermore, the US system increases in 0.25mm increments, then 0.5mm, then 1mm.

Finally, it’s important to remember that every knitter has a different tension and will have more or less yarn around the needle for each stitch. Switching to square needles will certainly affect your grip and your tension by the same occasion.

Conclusion

Square needles have a smaller diameter than cylindrical needles of the same size. If we suppose that a knitters applies the exact same tension to each stitch (i.e. wraps the needle fully each stitch), then square needles will use approximately 90% of the yarn cylindrical needles would. This does not take into account the change in grip, the material or coating of the needles, or any other factor that might affect gauge. The oft-repeated rule of go down a needle size cannot reliably be used for every needle size, but might be a good starting point.

In some way, one advantage of square needles is that they force us not to be complacent about a project/ball band stated gauge. You will have to swatch to be 100% sure, and that might just give you the motivation to do so.

If square is too much of a change for you, perhaps hexagonal needles would be more up your alley? I will measure them and come with an approximate gauge adjustment the moment I can get my hands on them.

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