Somehow, this little magic formula found it's way into my brain. It works EVERY TIME for increasing or decreasing evenly along a certain number of rows.
The first thing you need to do is figure out your gauge! This won't work if you don't know your gauge.
The first thing we're going to shape is a sleeve.
With a stitch gauge of 5 sts/inch, figure out how many stitches you will have at the beginning of the shaping.
To do this, multiply 7¾" x 5 sts = 38.75 sts. Of course, we can't have a fraction of a stitch, so based on your stitch pattern, you'll need to round either up or down. I'm going to round down, I'll tell you why in a second. So, there are 38 sts at the cuff of the sleeve.
Now, lets figure out how many stitch there will be at the underarm: 12" x 5 sts = 60. That worked out perfectly, no fractions, and it's an even number. That's why I chose 38 over 39 sts for the cuff. You want to keep the numbers the same, either odd or even.
Now you want to figure out the difference between the two numbers.
60 - 38 = 22.
This tells us that we need to increase a total of 22 stitches to get to 12" from 7¾". Because we will be working our increases on each end of the rows, lets divide this in half so there will be 11 increase rows, with 1 st increased on each end on each row.
But how many rows do we have to increase in?
The whole length of the sleeve will be 17½" from the cast-on edge to the underarm. The first 2 inches will be worked without shaping, so we don't want to include those rows in our increasing. That leaves us to increase in 15½", which multiplied by the row gauge of 7 is 108.5 rows. Rounded to an even number is: 108 rows.
Now comes the fun part… how often do we work these increase rows?
108 ÷ 11 = 9.818181"
If you get a number that is between 1 and 2, see below **
Now we're going to figure out how many times for each of them.
Step 3: Multiply the larger of these two numbers (in this case, the 10) by the amount of times we need to increase: 10 x 11 = 110
Step 4: From this number, subtract the total amount of rows you will be increasing in 110 - 108 = 2
Step 5: Then divide that number in half 2 ÷ 2 = 1. Place that number beside the smaller of your two numbers (See diagram B).
Step 6: Now take the total number of increase rows and subtract the number you're left with in Step 5: 11 - 1 = 10 and place this number beside the larger of your two numbers in your diagram (See diagram C)
Step 7: To double check all this to make sure everything is right: multiply the number on the left by the number on the right for both the smaller number and the larger number: 8 x 1 = 8 then 10 x 10 = 100 (See diagram D). Then add the two numbers 8 + 100 = 108 rows! Yay, the rows are right!
Now check the amount of increase rows: Add the two right-side numbers 1 + 10 = 11 times (See diagram E) That's right too! Amazing!
**If you get a number between 1 and 2 from Step 1 above, continue as follows:
Of course if you get a number that is between 1 and 2, then choosing the even numbers above and below that number won't work. 0 just isn't a number that works in knitting. In this case you'll need to use 1 and 2 rather than 2 even numbers.
You may run into this if you are increasing a lot of stitches in fewer rows.
I'm going to pick random numbers here: we've got 20 rows to increase 13 times.
So, 20 divided by 13 = 1.53846... So we'll be using 1 and 2 for our numbers
Step 1: Set up your diagram in the same was as above, with the smaller number (1) on the top, and the larger number (2) on the bottom (See diagram F).
Step 2: Subtract the increase times (13) from the number of total rows (20) = 7. Insert that number beside the larger number (See diagram G).
Step 3: Subtract the number from Step 2 (7) from the total number of increase times (13) = 6. Insert that number beside the smaller number (See diagram H).
Step 4: Double check everything as in Step 7 above (See diagrams I and J).
The formula is the same for figuring out how to decrease. Simply decrease instead of increase when you work the decrease rows. I hope this is helpful for you all.