I recently updated my open-source KnitFitter project to do the calculations for round-yoke and raglan sweaters as well as for poncho sweaters.
I'd worked up a Broad Spiral Rib pattern in a lovely Peace Fleece yarn that I wanted to make into a zippered sweater. I put the gauge and my dimensions into the KnitFitter and tinkered with the raglan figuring until the program gave me a sensible answer.
This took a lot longer than I expected.
Raglans were the first sweaters I designed. I knit them exclusively for years. They're fairly straightforward to knit. They fit a wide variety of bodies nicely and work with a wide range of designs.
As I tinkered with my program, I discovered that getting the numbers right for raglan yokes is more complicated than I had realized. The logic for round-yoke sweaters is 15 lines long. The logic for raglans and poncho sweaters is 80 lines long, and it only covers the basics.
The good news is that figuring raglans is easier for humans than it is for computers. You just juggle things until they're right. You have a lot of options, a lot of factors you can fudge to get the numbers to come out right. Computers can't do that; they need to do things the same way every time.
A raglan has four or five distinct sections: the front (or left front and right front, if the sweater is a cardigan), the back, the left sleeve, and the right sleeve. Each section is separated by a raglan marker and one or more raglan line stitches. The increases for each section are done before and after the raglan markers.
In the Broad Spiral Rib Jacket, the five sections of the sweater are separated by a single Knotted Rib that emphasizes the raglan line.
Each section of the sweater grows from its initial width at the neck to the desired width at the underarm. Sleeve increases and body increases can be independent of one another; front and back increases can also be independent of one another.
The standard raglan instructions say to increase before and after each raglan marker until the sweater is wide enough and then to knit straight until the desired underarm depth is reached. For a lot of sweaters, this leads to a wide-enough sweater with appropriately-sized sleeves and an underarm somewhere in the neighborhood of the wearer's underarm. I find that this basic formula works well for children's sweaters worked in stockinette. For other stitch patterns or other sizes, it doesn't work well at all.
Okay, so a few numbers that we'll need to figure the raglan yoke:
Raglan rows: multiply the underarm depth of the wearer by the row gauge of the stitch pattern. This number tells us how many rows we have to make the raglan increases.
Sleeve stitches: multiply the desired sleeve width at the bicep by the stitch gauge.
Body stitches: multiply the chest measurement by the stitch gauge.
Neck stitches: the number of stitches cast on for the neck. In a basic crew-necked raglan, this is ((2 * back-neck) + 2) * stitch-gauge.
Underarm cast-on: A small number of stitches cast on at the underarm to form a gusset between the sleeves and the body and allow freedom of movement. In standard raglan sizes, this is usually an inch or two. I usually allow 1" for children's sizes and 1.5" for adult sizes. Multiply that number by the stitch gauge to get the underarm cast-on.
You have some variables to play with. You have a fair amount of wiggle room in dividing the neck stitches between the sleeves and body. You can adjust the underarm cast-on by a few stitches. You can undershoot the raglan rows by an inch or overshoot it by two inches.
Look at the numbers for neck stitches, body stitches, and sleeve stitches. About an inch of the neck is usually apportioned to each sleeve. So start by assigning an inch of stitches to each arm and divide the rest between the front and the back. Find the number of increases for each section by subtracting the neck stitches for that section and the underarm cast-on from the total number of stitches needed for that section.
Are the body and sleeve increases close to the same? If so, you might be able to juggle the neck stitches so that you can do the same number of increases on the sleeves as you do on the body. If not, the sleeves and the body will have to grow at a different rate.
Once you've juggled the neck stitches, figure the rate of increase for each section. Divide the number of increases you need to do by 2 to get the number of increase rows you need. Next, divide the raglan rows by the increase rows to get the increase rate. The increase rate tells you how often you'll need to do raglan increases for that section. If the increase rate is close to a whole number, your increase instructions for that section are simply Increase at beginning and end of section every [increase rate] rows until section is wide enough.
Now, if the increase rate is not close to a whole number, you'll have to do more fancy figuring to get those increases in. There are also stitch patterns where you don't want to increase on wrong side rows, so you might want to do more fancy figuring in those cases as well.
The simplest kind of fancy figuring is to round down to the nearest whole number, stop increasing when you have enough increases, and then work straight to the underarm depth. This conforms pretty well to the shape of the human body. The shoulders widen quickly, then the torso continues straight until the underarm. At the underarm, the sleeves and body of the sweater need to expand to form tubes around the arms and body. Ideal shaping for a sweater looks something like this:
Another option is to build a complex-angle raglan which conforms to the shape of the ideal sweater. This will fit better than a simple raglan. To build a complex angle raglan, you decide that you need to work so many increases, say, every row, and so many other increases, say, every other row. You put the more frequent increases towards the neck, saving an inch or two for just before the underarm and do the less frequent increases on the chest section where the body isn't changing.
Arms, luckily enough, follow a similar pattern. The sleeve cap can use a little extra ease, and the sleeve also needs extra width at the underarm.
Once you've figured out the rate of increases for each body section, you can write your pattern to the underarm.