**ETA:** Check out the worksheet I’ve put together as a quick-and-easy alternative to this text.

I love set-in sleeves in a ridiculous way. I think they’re stylish and flattering. They’re also, as we’ve all been told, the hardest sleeve to design and the hardest sleeve to attach to the sweater body. Here, I’ll be talking about how to design a set-in sleeve in a way that’s reasonably easy and involves very little trigonometry.

I had a terrible time with the sleeves on the SSS. I ended up knitting the sleeve caps three times, and seaming them onto the sweater three times. Ugh! I think the problem is that everyone is always telling me how complicated set-in sleeves are. I questioned my judgment, and as a result, had an awful time getting things right. What I’d like to do here is explain the mistakes I made and how I fixed them, and in the process explain the simplest way to design a good-fitting set-in sleeve cap.

My personal set-in sleeve guide is Jenna Wilson’s Knitty article. It is fantastic, and I recommend it unreservedly. In case you’re feeling a bit lost in it, however, here’s my simplified breakdown of what you need to know to design a sleeve cap:

FYI: Armscye == the armhole you shape in the body of your knitted garment, and to which you attach the sleeve.

- The inches of your initial armpit bindoff in the sweater body,
**A**.
- Half the perimeter of your armscye, in inches,
**B**
- The final bindoff of the sleeve cap, which is typically 2.25″,
**C**
- Half the width of your sleeve at its widest point,
**D**.
- Your gauge.

A, C and D:

A, C and D are relatively easy to get. It’s #B that seems to be the killer. Jenna recommends heavy doses of trigonometry, and it’s definitely a method that works, if you do the math right and don’t forget any numbers. But you can also do it a simpler, if less precise, way.

1. You’ll need a piece of string, and your blocked sweater with the armhole.

2. Lay the sweater down flat on the ground. Without stretching the string, lay it down *on the knitting* so that it follows the curve of the armhole from side seam to shoulder seam, as shown in this picture:

B:

3. Pick up the string, careful to keep track of the length you’ve just determined. Maybe you could just cut the string at that point?

The length of that string is approximately half the perimeter of your armscye. It is important to lay the string down on the knitting and not on the ground beside the knitting on the inside of the armscye, since laying it along the inside of the armhole curve will cause you to underestimate the armscye perimeter.

So now you have A,B, C and D, plus your gauge. Here’s how you figure out your sleeve cap math:

Your goal is to get a sleeve cap whose perimeter is equal to the perimeter of your armscye, or **B * 2**. Since you’ll be doing the same shaping on each side of the sleeve cap, we’ll just figure out the math for one half of the sleeve cap, and you can do the exact same thing on the other side.

First, we have to take care of the lengths of the perimeter already accounted for by your initial and final bind offs. We’ll call that leftover perimeter **F**.

**F = B (total perimeter) – (A (stitches you bound off right away) + 1/2 * C (remember, we’re only doing half the sleeve) + 1/2 * C)**

So far, you know you’ve bound off **A** inches to start, which takes care of a certain number of inches of your perimeter. And you know that at the END of the sleeve, you’re going to bind off **1/2 * C** stitches and in the row before that, another **1/2 * C** stitches. Together, these form the flattish top of the sleeve cap. That takes care of some of your perimeter, but you still have all the space between the beginning and the end of the sleeve cap to deal with.

Now the trigonometry comes in. The Pythagorean Theorem states that, if the two shorter sides of a triangle are called *x* and *y*, then the third side, *z*, can be attained through this formula:

*x*^{2} + *y*^{2} = *z*^{2}

Why do we care? Well, the perimeter you have left, **F**, represents *z*, the long side of the triangle. The base of the triangle *y* is **G**, calculated as **D – A**, or half your sleeve width minus the armpit stitches you already bound off. The height of the triangle, *x*, will be the height of your sleeve cap, and it’s what we need to know.

So to get it, you plug in the numbers:

*x*^{2} + **G**^{2} = **F**^{2}

Which, if you rearrange it to put all the things you know on one side and the things you don’t know on the other side, is the same as:

*x*^{2} = **F**^{2} – **G**^{2}

Solve for *x* by taking the square root of **F**^{2} – **G**^{2}. *x* is the height of your sleeve!

So now you know that you have a sleeve cap that is *x* inches high, not counting the rows you used to cast off in the beginning (A) and at the end (C). And you are left with **H** = **D** (half sleeve width) – **A** (inches bound off at start) – **C** (inches bound off at end) , the number of inches of width you need to decrease on each side of the sleeve as you get to that height.

Now it’s time to bring stitches back into the equation. If you convert **H** from inches to stitches using your *stitch* gauge, you know how many stitches you need to decrease away. If you convert *x* from inches to stitches using your *row* gauge, you know how many rows you have to do those decreases in.

You can choose to do your decreases regularly, or to do more decreases at the beginning and end of the sleeve cap and fewer in the middle, which will get you closer to the classic bell shape. For what it’s worth, I did the SSS sleeve cap with regularly-spaced decreases.

If you have so many stitches to decrease that you would need to decrease more than one stitch per side per row, you can add a few rows more to the sleeve cap to keep things smooth. Better a sleeve cap that’s a bit big (up to one additional inch in the perimeter) than too small.