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Knitting Math

These are user-friendly instructions to make your knitting math life easier.  Grab a calculator and a pencil and paper (so you can write your answers down). This page contains all previous knitting math articles, and will be kept current within a week of new math articles being published.  Look for BOLD TYPE to indicate the simple equations which are explained in the main text of each article.

Knitting Math 1 - Non-Fiction

I've been on both sides of the issue of Knitting Math: does it exist, or doesn't it? Math is math, right? Or is it like Business Math, and Cooking Math, where some functions are key to everything else working?

I am now firmly a believer in Knitting Math. Designing knitwear is one part sketching, 15 or 20 parts math, one part writing the pattern, and one big part knitting.

SIZE
If I want to design something simple like a baby blanket, I need to figure out how big I want it. Then I need to figure out what yarn I want to use. Then I knit test swatches to determine the gauge that gives me the look I want. Let's say it's 6 stitches x 7 rows.

Next, I need to multiply the width of the blanket by the stitches per inch. If I want the blanket to be 3 feet wide, that's 36 inches x 6 stitches per inch = 216 stitches. This becomes the cast on number.

Size I want (in inches) x stitches per inch  = cast on number.

If I want it to also be 36 inches long, for a square blanket, I need to multiply 36 inches x 7 rows = 252. Now I can create a graph, and start marking out stitches and color patterns.

Size I want (in inches) x rows per inch = total rows in pattern.

Stitch gauge and row gauge are the essential two pieces of information for almost all "knitting math." If you want your blanket larger, you multiply each inch by 6 stitches or 7 rows to know how much to add. Likewise if you choose to make a smaller blanket, you subtract 6 stitches or 7 rows for each inch you want to subtract.

YARDAGE
The gauge swatch gives you another critical piece of math to do - figure out how much yarn you're going to need. Make a swatch that is whole inches on both the top and the side (like 4x6). Multiply, and you get 24 square inches.

Length of swatch x width of swatch  =  total area.

Now cut the swatch off the ball, and weigh it on an accurate scale. What does it weigh? In this case, 1 gram. The ball comes in 100 yards per 50 grams. For now, disregard the yardage, and just focus on the weight. That means each gram will cover 24 square inches. Multiply that by 50 and you get 1200 square inches of knitting per ball.

Weight of swatch x area of swatch = total square inches per ball.

Multiply your original 36x36 blanket size out to square inches, and you get 1296 inches. This tells me that one ball of yarn won't quite do it, and you'll need to start a second ball.

DIFFERENCE IN GAUGE
But what if you don't knit to the gauge specified in the pattern? What if you knit to 5 stitches and 6 rows per inch instead? You're going to need a lot more yarn. Those same 216 stitches now represent 43 inches of knitting instead of the original 36. The 252 rows now make 42 inches instead of 36. (DO THE MATH!)  Now your blanket is 1806 square inches. Now you'll need 1 and 1/2 balls of yarn, because your piece is almost 30% larger than the designer planned for, and that's if your gauge is only off by one stitch! (Of course, the other option is to adjust the pattern using the math above!)

I know, it seems like a lot to digest. It's not really. Look up any pattern in any magazine, and do the math. You'll see that it works out every time. A little practice (and a calculator) makes it easy to remember what to do and how to do it.


Knitting Math 2 - Short Pattern Repeats

Pattern repeats add a variable to knitting math. The basic factors in knitting math are the stitch count per inch, and the row count per inch. But what about the pattern repeat? In this example, we'll work in the round, so the repeat has to line up exactly.



These mittens are my everyday winter mittens. They have a "pattern repeat" of 4 stitches (2/3 of an inch, or .6666). The stitches per inch is 6. What does that matter? Well, you'll need both numbers if you need to adjust the pattern to fit some other size. Pattern repeat = 4 stitches in 2/3 of an inch. Stitch count = 6 stitches per inch. So 1 and 1/2 repeats per inch.  Handy.

My hand and the gauge and the original pattern all work out to the same size (I wear a mitten that's 8.25 inches around) so it works out nicely. But my husband's hand is larger than the original pattern, so for him I'll have to modify to make it fit. If I only mind the stitches per inch (6), my mitten will have a weird jog in it where the pattern doesn't line up, because the pattern repeats in 4s , not 6s. The mittens are stranded, which keeps them from being very stretchy, so I can't rely on stretch to save me if they're a little small. What to do?

Well, the pattern repeat of 4 stitches = 2/3 of an inch. If I measure my husband's hand, I discover that he needs a mitten that's 9.4 inches around. If I take a look at the original pattern, I see that the pattern repeats 12 times in 8.25 inches (or six times on the front and six on the back). Now I need to subtract 8.25 inches (pattern size) from 9.4 inches (the size I need for my husband). I get 1.15 inches that need to be added to make a mitten to fit the hubby. Size I have - size I need = amount of room I need to add (or subtract).

If I divide that 1.15" extra that I need by the pattern repeat of .6666 inches, I get 1.75, or one and three quarters of a repeat. 
Amount I need (in inches) x pattern repeat size (in stitches) = number of stitches needed.  (When this is not a full repeat, round up or down to make a full repeat)

That means I need 7 more stitches around to make the mitten exactly my husband's size. One more stitch (8 stitches) gives me a perfect pattern repeat of 2 (4 stitches in the repeat twice), or only one extra stitch over the entire circumference of the mitten. I can work with that! So, to make the mittens for my husband, I would need to add 8 stitches to the pattern, and just work those repeats in with the original pattern. I can work the decreases at the top by starting them at the tip of the hubby's little finger, and follow the decreases a few extra times until I run out of stitches.
Number of stitches needed / pattern repeat in stitches = number of repeats to add.
This will change thenumber of total repeats in the pattern.
Total stitches in inches / length of pattern repeat in inches = number of pattern repeats needed.

The thumb is a pattern repeat of 2 (which is 1/3 of an inch), so that math is really easy. I measure the original, subtract that measurement from the hubby's thumb measurement, and discover I need 3/4 of an inch extra. That's 4 and 1/2 stitches. I can afford to be a stitch short or a stitch over, so I choose over. (Tight thumbs stink!) I round the 4.5 stitches I need up to the next even number (6) to accommodate the pattern repeat, and I'm done.

Short pattern repeats give you more flexibility to modify size than long ones, but we'll work with long ones in the next article. Knitting math isn't hard if you know the formulas and you have a calculator. You can do it!

Knitting Math 3 - Centering Long Pattern Repeats

Now that we've given our calculators a workout with the short pattern repeat, the next question is: What do you do with a long pattern repeat that needs to be modified? Well, it depends on what it is you're trying to do. How long is a long pattern repeat? If it feels long to you, it's long, but usually it's anything that runs more than an inch and a half or more. Some repeats can run a foot or more!  Patterns that are within a gament are often called "motifs", and we will call them that here.

If you're making a flat-knit piece, it is a little easier than if you're making a project in the round, or even a garment with sleeves. Let's start there.

Above is the Flower Chart from the Soria Vest by Mari Muinonen, originally published in Knitty, Winter 2009. This is a beautiful, long pattern repeat (motif). If the gauge is 5 stitches per inch, this covers over 3.5 inches.

First, take a long look at the motif you want to use. Looking at the chart above, you can see that the column of stitched marked "1" is a connecting column. It isn't part of just one flower; it's how you would connect several together. If you only want one of the flowers, you need to ignore this column entirely, making your pattern now 17 stitches wide. (I tend to hide the unused column with sticky notes so I won't get confused.) Because 17 is an odd number, centering it pretty easy. You would center it on the column numbered "10" of the motif chart. How do you center it on the garment? Let's say the garment is 51 stitches wide.

Centering = total number of stitches - stitches in repeat = # of background stitches.
# of background stitches/2 = # of stitches to knit before inserting your repeat, and the number of background stitches to knit after your repeat.

or 51-17 =34. 34/2 = 17, so there would be 17 background stitches followed by the flower pattern, followed by 17 more background stitches per row.

That wasn't so hard. But what if you wanted three flowers across? This is when it helps to photcopy, cut and tape charts together, or grab some knitting graph paper and draw exactly what you want to do.

In order to get the pattern centered, we've already determined that we need the flower (without connectors) to have 17 stitches on either side of it. The garment is 51 stitches wide.  The flower will need a connector on each side to join it to the next flower, making 19 stitches wide. This leaves 16 stitches before and 16 stitches after the centered flower. To make this work, you need to leave off the first two columns of the pattern in the first flower, then follow the whole chart once (connector plus flower), then follow the first 17 stitches of the pattern again for the third flower (connector plus 16 stitches of the flower).  A smidge of the flower will be left off at each edge of the garment, and the total pattern will be centered.

When you draw this, start with a graph 51 stitches wide, and start on the center stitch (number 26). You're going to draw this so that if you fold the paper in half lengthwise, the stitches to the right of stitch 26 will mirror the stitches to the left of it. Center just the first flower. Next, add a connector column to each side. Then, add the left 16 stitches to the right side, and the right 16 stitches to the left side. See how nicely that worked? Now you have a chart representing exactly the stitches you plan to knit - there's nothing left to keep in your head. Just follow your hand-drawn chart.

The centering equation will always work, unless you end up with an odd number of background stitches. When this happens, you can usually add one stitch to the total number of background stitches so that it will balance from side to side. If you can't even out the number of background stitches, you'll have to decide whether you can live with it being off by one stitch, or whether you need to choose a new motif.


Knitting Math 4 - Vertical Pattern Repeats

We all know by now that we need to keep an eye on our stitch gauge. The number of stitches per inch is how we know whether a piece will be the size we were aiming for: too few and it's too big, and too many and it's too small. But what about row gauge?

This is not the time to get faint of heart. Row gauge is important for many types of patterns, and nearly always for vertical patterns. Colorwork only works in exact numbers of rows (not "knit 4 inches"), and if your row gauge is off, your piece will be too long or too short. Shapes that were intended to be circles become ovals, squares become rectangles, and the pattern becomes a funhouse mirror version of the original. Knowing your row gauge makes several things easier.
The socks at left were knit and posted on Ravelry by Stacey14, from a pattern by Priscilla Gibson-Roberts in her book, Ethnic Socks and Stockings. There are several patterns here, some running vertically and some horizontally. If you need to shorten or lengthen a vertical repeat, what do you do? Maybe you want a shorter version of this sock. Now what?
Well, you need to do your math. (This is why the Lord created calculators and scrap paper!) If the total pattern repeat is designed to be 1 3/4 inches tall, and you want a shorter sock, no problem. First, knit a swatch including two pattern repeats. Measure your row gauge. Does it match the pattern? If yes, cool. You'll want to decrease in whole repeats to maintain the look, so you'll decrease the finished size by increments of 1 3/4 inches. If the total sock has a 12 inch leg, with each full pattern repeat you take out, you subtract 1 3/4 inches. Originally there were 6 repeats + cuff = 7 units of height. Don't take off the cuff - it anchors the look. Remove one or more of the leg motif repeats.

Total length in inches - (# of repeats x 1.75 inches) = new total length.

But what if your row gauge doesn't match the pattern? Well, there are two ways to go - try to get the row gauge, or live with your unique gauge. I tend to go with the one that matches the pattern, because it retains the original shapes in the design. If your stitches are right on, and rows are off, you have the right needle size, but not the right material. Too few rows mean you need stickier needles (bamboo like Clover, or non-slippery plastic, like Denise) and too many rows mean you need slippery needles (Addi's or Boye.) If this works, you're all set to move on.

If you're already using the recommended needle material, it's probably you. Maybe you knit a little tightly, or a little loosely by nature. No worries. Stick with your unique gauge. Then to get the dimensions in the pattern, you may need to knit more or fewer total rows. If you're knitting at 1 1/2 inches per pattern repeat, you'll need to do 7 repeats + cuff = 8 total to make it the length specified in the pattern. The design will look like a shorter, fatter version of the original, and if you like it, go with it. (If not, pick a new pattern!)

(Total length) 12 / 1.5 (height of repeat) = 8

Wouldn't it be cool if it all worked out that way? Well, it usually does. But sometimes you want your garment to be longer or shorter in an increment different from the repeat. If you have a 2 3/4 inch repeat and you only need 4 more inches, you won't be able to work in full pattern repeats and still get the measurements you want. That means you either pick a different pattern, or you live with a partial repeat somewhere. Put the partial repeat in the less visible part of the garment, usually the bottom. You'll do your regular math of

Row gauge x total desired length (in inches) = total # of rows - then -

Total # of rows / # of rows in one repeat = # of repeats, with the remainder being the number of extra rows

If you need to do a partial repeat at the bottom, you'll want to work the top part of the pattern in the extra rows. If you need to do a partial repeat at the top, do the bottom part of the pattern.

You can do this. Get some coffee or tea, and your scrap paper and calculator, and do the math first. Sketch it on some graph paper to make sure it makes sense. Write out your new directions as thoroughly as possible so you don't have to do the work again. Then, get knitting!


Knitting Math 5 - Increases and Decreases

Ok. We've covered gauge, long and short horizontal repeats, and vertical repeats. Yes, there is still more, and we'll take the next step in little bites. How do you place increases and decreases in an even way?
There's one equation in this math that is absolutely critical: Stitches you have - stitches you want for decreases, and stitches you want - stitches you have for increases. The answer will be stitches difference, or the number to decrease or increase respectively.

Grab your calculator and a pencil, and let's do it.

You know I love mittens, so I'm going to use them as the example here for increases. In my cuff I have 40 stitches. I need 48 for the body of the mitten, and the instructions say "distribute increases evenly" for the increase row - no specifics. Yikes!  48-40=8, so I need 8 more stitches. How to do it evenly? Divide.

Divide stitches you have BY stitch difference= number of stitches between increases/decreases. In this case, 40/8 = 5, so there are going to be 5 stitches between increases.

The way to implement is to knit a couple of stitches in the beginning of your row or round. Increase one. Then knit 5, increase one across or around. The increases will be even, and they will be a couple of stitches in from your edges, making any seaming necessary easier.

The example here for decreases is a skirt on a child's garment. The original skirt has 56 stitches. The decreased row has 40.

56 (stitches I have) - 40 (stitches I want)=16, so I need to decrease 16 stitches. 56/16=3.5. Three and a half stitches between decreases - - ? I have no idea how to make a half a stitch, but I can trade off between 3 stitches + one increase, and then 4 stitches + one increase. That would work. OR I can take that .5 (a remainder) and realize that it represents 8 stitches (3 x 16 = 48 48 +8 = 56). I can put half of them at the beginning of my row or round, and half at the end. I'll knit 4, then K3, M1 until I get to the last 4 stitches.

Unless it's stated otherwise, do not increase or decrease on the first two stitches of a row or round. It makes seaming much easier. If your pattern tells you to, then do as it says.



Knitting Math 6 - Change Sheets

Even if you never pick up a calculator, there are a couple of steps in the land of Knitting Math that we all seem to forget. Mostly they involve writing down the stuff we did and changed, as it's different from what the pattern said. Two years later, when you decide to make this project again, you'll really want to know what the heck you did!

Let's say you did some knitting math to place your decreases evenly, which your pattern asked you to do. Well, if the pattern doesn't specify how often to decrease and you did the math on your calculator, you know what to do for your decrease row. But if you take a little post-it note and stick it to the pattern, all the better.

Modify the sleeve length? Another post-it. Modify the gauge or change the yarn? Yep, more post-its.

Why all the post-its? Because if you knit past your changes and turn out not to like them, you'll rip back, and change it again. Then you can peel the first note and replace it with what change you liked better. This way you're not writing directly on the pattern. When you finish the garment, then you can take all the post-its and write out one final "change sheet". Make a little highlighter dot on your pattern every time you need to look at the change sheet for the next time you make the project. And of course, place a photo of the finished piece on the change sheet, or at least keep one with the pattern.

It might look like this: Change Sheet for Emma Jumper

Yarn: Used Cascade Rustic instead, total of 4 hanks

Needle: Used US 8

Cast - on: liked cable cast-on better, stayed with it

Length: found the original length too long for Jane (5 yrs old), and shortened it to 12" before the decrease

Decreases: k3, k2tog

Finishing: Finished by single-crocheting the V-neck bind-offs and the armhole for a smoother look.

Remember, the Change Sheet only represents what you did differently. It doesn't have to include anything you did the way the pattern suggests, just the changes. Paper clip this to the original pattern, and some day, (just long enough for you to not remember what you did differently), it will be there to remind you. Or it can remind your dear friend, who wants to borrow the pattern once they see the beautiful work you did.

This will feel silly until you go back to a pattern you never thought you'd use again. But you will use it again, because as knitters, our comfort zones move around. Let's say you didn't like all the cable work in a pattern. By the end of next year, you may suddenly want the challenge. What if you got through a colorwork pattern by the skin of your teeth, and are sure that's the end of colorwork for you? Well, in five years, you may LOVE colorwork. (Stranger things have happened.) Trust me on this. Making up a change sheet can't hurt you, it can only help you. There are so many patterns I've changed and didn't make a change sheet, and now I kick myself when I go back to them! Learn from my mistakes.
 
 
 

Knitting Math 7 - cables, ribs, dropped stitches, lace and bobbles

When you're doing your knitting math, there's always the possibility that you're working with a pattern with measurements that don't work out to the gauge math. The listed stitch gauge multiplied by the listed inches does not even out at all. What if you want to modify the original design? Change its size or overall looseness? Grrrr!
Ribs and Cables - very contracted!
Brioche Rib, a big contractor


Don't panic. Does your pattern contain cables, ribs, dropped stitches, lace or bobbles? If none of these are represented in the suggested gauge swatch, you've probably found your problem. (If this isn't it, it may be "ease", covered in the next article.)

Shrinkers - ribs and cables both contract your knitting horizontally when they're verticle, and cables will also contract it a little vertically. Twisted stitches are also in this category. When you're ribbing horizontally (like garter stitch, or any combo of right-side knit rows alternated with right-side purl rows) it will contract your knitting vertically.

Growers - dropped stitches, lace and bobbles all cause the knitting to grow. Dropped stitches create wide, elegant ladders of open work, and are the stitch that expands your knitting the most horizontally. Lace will expand it horizontally, and usually expand it even more vertically. Bobbles, because they disrupt the tension of the rest of the row, will usually expand the row horizontally just a little.

How do you know how much these decorative elements have affected the stitch count? Ah, I think we all know the answer, we just want to avoid it. Yep. You have to swatch it.

After you achieve correct gauge on your basic swatch you need to make a separate swatch with the design element. Use the needles that gave you gauge. For your first row:

Make an 8 stitch moss stitch border, then an inch of stockinette, then a full repeat of the design element. Then repeat the inch of stockinette and 8 stitch moss stitch border. One row completed.

Keep following the pattern for the design element until you've finished one repeat of it vertically, or for four verticall inches of knitting, whichever is longer. Now, measure your swatch at its narrowest and widest points, excluding the first and last two rows. Just like you would any other swatch, launder it the way you will launder the garment, and block it. Measure again.** Now you have a pretty good idea of what affect the design element will have on the measurements.

Our demo numbers: Gauge is 6 stitches per inch, design element is 10 stitches per inch. The design element is one inch wide. Our total stitches inches in the row are 106, and total inches are 17.

If your design element occurs once, the math is this: Total inches - design element (in inches) = inches in regular gauge. If you need to make adjustment, make it in the regular gauge stitches, and make it match left to right unless you want something off
center.

17 - 1 = 16 I have 16 inches where I can make an adjustment without messing with my design element.

If your design element occurs more than once: Total inches - (design element number of repeats x design element in inches) = inches in regular gauge.

If my design element occurs 6 times, 17 - 6 = 11. I have 11 inches where I can make my adjustment.

**Why do you need to measure twice? Because how your garment will lay and measure after laundering and blocking is often very different from how it knits up. If you don't measure it twice, you won't know how much it will grow or shrink, and you may end up making the wrong size by mistake.