The Knitting Fiend

Design the armhole.

Chest Width
Next we need to know how may stitches we have across the full body width. I want Jim's sweater to measure 38" around the chest. (Jim's chest measures less than that; I've already added ease.) That means I need to front and back to measure 19" each. Depending on the stitch pattern used, I may need to round to the nearest stitch, an even number, or an odd number. The correct choice depends on what is required to center a decorative pattern and make it look nice.

To begin calculations, I'll enter the chest measurement, and select how I want to round:

To obtain the number of stitches, I multiply the chest width by the stitch gauge and round. The chest width requires stitches.

Now, I want to decide how may stitches I need across the shoulders. Jim needs 16.5" to fit well across his shoulders.

Calculating just as for the chest, the shoulder width requires stitches.

I subtract the number of shoulder stitches from the chest stitches, and find I will need to decrease a total of stitches to narrow the sweater from the chest width to the shoulder width; that means I'll reduce a total of stitches on each side.

Recall this simplified design requires me to reduce some number of stitches all at once and then reduce at a rate of 1 stitch every two rows. So, how many should I reduce in each pass? Well, my rule is this: 

• The first reduction will equal the smaller of two possible values:

• one half of the total to be reduced, rounding up. That is reduce stitches on each side side.
• 16% or the body stitches for the front or back of the sweater. That is stitches if we count both sides or stitches on one side.

The remaining stitches will be reduced at a rate of 1 stitch every two rows. So for this case the directions will read:

1. Armhole Reductions

1. Hang a row marker to indicate the beginning of the bind off.
2. Bind off stitches; work in stitch pattern to end of row.
3. Turn, bind off stitches work to the end of the row.
4. Repeat the following times:
• Knit 1 stitch, ssk, work in stitch pattern until 3 stitches remain, k2tog, knit last stitch.
• Turn, work back in stitch pattern.
5. Hang a marker.

The armhole reduction directions are complete.

Ordinarily, knitting directions would not mention how deep the armhole when you finish the armhole reductions and they would not suggest you hang a second marker. I have you mark it because we need to know this depth to design the sleeve cap. Notice I've knit rows since the first bind off. So, the depth to this point is obtained by dividing the number or rows by the row gauge. This results in inches between the first and second marker. The final instruction for the armhole is to knit without shaping until the armhole depth is achieved. Jim's sweater needs 9.5" deep armholes. I just type that in the box below.

• Work even until the armhole measures from first marker.
• The length measured from the second marker is UD = inches. This is an important length. It's labeled as "Unshaped Depth" in the illustration above; I will use the symbol UD for this value when I later do some math.

The sleeve cap.

It just so happens that the particular simplified cap design permits a range of sleeve widths between a minimum and a maximum width. I'll defer explaining why there is the minimum sleeve width, and simply state the minimum and maximum widths are inches and inches. Luckily for Jim, his preferred sleeve width falls in this range. (If you are designing your own sweater and are changing or plan to change values in the boxes, don't suggest sleeve widths outside this range.)

Now, I'll calculate the sleeve cap.

• Begin Shaping Sleeve cap.
• Begin right side facing. There should should be stitches on the needle.
• Follow the directions 1a - 1e for shaping the armhole up to and including hanging the second marker.
• For the purposes of understanding this discussion, hang the second row marker near the edge and then put a slippable ring marker between the two center stitches on the needle (or round the center stitch if the number of stitches are odd).
• Note the number of stitches on the needle is , and width of the knitting should now measure inches. The width from the edge to the center ring marker is half that, that is W= inches. I've labeled 'W' on the figure below and to the right.

Next, you will need to continue binding off at a rate of 1 stitch on both edges every other row as in direction 1-d. We'll figure out how many more times you need to do this.

The left hand side of the remaining portion of the cap is illustrated in the figure to the right; this is the part we have not yet calculated. If you had knit as far as the current directions suggest, the needle and work would be at the bottom of this figure.

Note the red 'X' on the lower left hand corner; this indicates the location of the row marker I suggested you place at the edge. As you knit and shape, the top of the cap will lengthen; the red "X" at the top right indicates the slippable ring marker I suggested using to indicate the center of the row. When shaping the very top of the cap, the goal is to keep decreasing stitches until you find the length measured from the left edge row marker to the center ring marker equals UD = inches. Note: This is the "Unshaped Depth" defined when I discussed knitting the armhole.

If the length of this final portion of the cap equals UD, then the length of the whole cap will match the length of the armhole. That's the idea, and it's simple enough. Unfortunately, to figure out the number of times to shape, we need to collect 4 equations and solve for 4 unknowns. The four equations dictating the lengths of the illustrated quantities are:

• T + H = UD. (That is, sum of the length along the slanted region and the top of the cap equals the unshaped armhole depth.)
• L+T = W. (That's clear from the figure.)
• 2 * (L/ stitch_gauge) = ( h/ row_gauge) I divide "L" by the stitch gauge to find the number of stitches in the length "L". I divide "h" by the row gauge to get the number of rows. Since I'm decreasing 1 stitch every two rows, there will be two rows for each stitch.
• H² = h² + L². This is Pythagorean theorem to describe the triangle shown on the left side of the cap illustration.

I could rearrange in a variety of ways and show you the formula, but likely as not, anyone who wants to see the formula will enjoy doing the algebra! So, instead, I'll just tell you that I arranged to solve for the width of half the cap top. I get:

The width indicated as L = inches.

This corresponds to stitches. (Note: I round up! Remember some designers suggest the cap should be a little longer? Well, I at least make sure it's not shorter.)

So, the remaining directions become:

• Repeat the following more times:
1. Knit 1 stitch, ssk, work in stitch pattern until 3 stitches remain, k2tog, knit last stitch.
2. Turn, work back in stitch pattern.
• Bind off the remaining stitches.