If you've ever tried your hand at designing a sweater, you know that figuring out how to shape the sleeves is the trickiest part. Having tapered sleeves is also really important for winding up with a sweater that looks good. However, if you know how, shaping sleeves only takes a little math that isn't even hard to do. The instructions below are for a basic, drop-shoulder sleeve (that means there's no or very little shaping around the armhole on either the body of the sweater or on the sleeve itself). Figuring out shoulder shaping is a little more complicated, so I'm only discussing the absolute basics here.

A tapered sleeve is: a slope. If you aren't sure how to get the arm measurements you need, take measurements from a garment you already have that fits well. To start you need five pieces of information:

Based entirely on 5 measurements, I was able to figure out that I needed to decrease 2 every 6th row, 10 times, and then add a cuff to make the sleeves for my son's sweater. All I needed to know in order to get there was how to measure, multiply, and divide. And it worked.

A tapered sleeve is: a slope. If you aren't sure how to get the arm measurements you need, take measurements from a garment you already have that fits well. To start you need five pieces of information:

- armhole depth
- wrist circumference
- sleeve length measured from armpit to wrist (If you plan to have ribbing or some other kind of cuff at the wrist, subtract the planned length of the cuff from the sleeve length)
- stitches per inch in your garment's pattern stitch
- rows per inch in your pattern stitch

I like making sleeves by picking up stitches around the armhole, working in the round, and decreasing down to the cuff; because that means I don't have to sew the sleeves to the body and that the sleeves themselves are seamless. This process works whether you are knitting or crocheting; and the SAME math still works if you make sleeves flat or work them from the bottom up, it just involves increasing from the cuff to the armhole instead of decreasing down to the cuff. However, since making sleeves from the top down is the simplest way to go about it, these instructions are for that method.

- Double the armhole depth to get an upper arm circumference.
- Multiply the upper arm circumference by your number of stitches per inch. This is the number of stitches you want to have at the top of the sleeve. If you are using a pattern stitch, you will want to round this number to a multiple that will work with that stitch. If for instance, your pattern is a multiple of 4, you will want to round your number of upper arm stitches (preferably up) to the nearest multiple of 4.
- Multiply your wrist circumference by your stitches per inch, and round that number to work with your pattern stitch. This is the number of stitches you will have at your cuff.
- Subtract #3 from #2. This is the number you will have to decrease over the length of the sleeve.
- Multiply your sleeve length (minus the cuff length, if you plan to have a cuff) by your number of rows per inch. This is the number of rows in your sleeve, not including your cuff.
- Divide the number of rows that you found in #5 by the change in the number of stitches found in #4. This is where you figure out the "slope" of your sleeves. Round the result to the nearest whole number. This is how frequently you need to subtract (decrease) a stitch.
- Double the number you found in #6. Every time you do this number of rows, in the last row, you decrease at the beginning AND end of the row. This keeps your sleeve symmetrical, rather than tilting it to one side or the other. The exception to this step is when you are working in a large gauge. When you only have two or three stitches per inch, increasing or decreasing two stitches in the same row can give a lumpy appearance to the slope under the arm. When working in a big gauge, it can be better to increase or decrease once in a row, but twice as frequently, for a smoother appearance. Just make sure you alternate decreasing between the beginning and end of the row every time.

- Armhole depth = 6.5 inches. 6.5 x 2=13. Armhole circumference is 13 inches.
- Stitches per inch = 4. 4 x 13 = 52. I will have 52 stitches at the top of the sleeve. This is the number of stitches I pick up around the armhole.
- Wrist circumference before the cuff is 8 inches. 8 x 4 = 32. I will have 32 stitches at the wrist.
- 52 - 32 = 20. I like to work sleeves from the shoulder to the cuff, so I will decrease 20 stitches from the top to the bottom of the sleeve.
- My sleeve length is 12 inches, but the cuff is 2 inches. That means my decreases will be distributed over the 10 inches before the cuff. I have 6 rows per inch in my pattern stitch. 10 x 6 = 60. The sleeve will have a total of 60 rows before the cuff.
- 60/20=3. I need to decrease 1 every 3rd row, 20 times.
- BUT I want to decrease 2 stitches every decrease row in order to keep my decreases symmetrical. That means I will have 10 decrease rows, not 20. Therefore, I will decrease 2 every 6th row, 10 times.

This picture (left) is actually of a different son's sweater and used slightly different numbers for the sleeve decreases, but the process for finding those numbers was exactly the same as described above. The sweater I used for the written example was made in a dark variegated yarn, which makes the decreases hard to see in a photograph.

Based entirely on 5 measurements, I was able to figure out that I needed to decrease 2 every 6th row, 10 times, and then add a cuff to make the sleeves for my son's sweater. All I needed to know in order to get there was how to measure, multiply, and divide. And it worked.

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