Wednesday, January 27, 2010

My Favorite Formula --CORRECTED!

I initially posted this blog Wednesday night but I made an error in the short-cut formula. Thank you to everyone who pointed out my error! (This is why I love tech editors.)


A few weeks ago, I taught a short workshop on the mathematics of knitting for the Front Range Knitting Guild. Before I go on, I’d like to thank the members for being so exceptionally nice to me as I faltered at the white board. (I'd also like to ask your patience with my bad images--I'm just learning to use a digital camera.)

At the end of the meeting, I was asked how to adapt a pattern written for one gauge to another gauge. For example, let’s say that a pattern calls for worsted-weight yarn at a gague of 5 stitches to the inch and you want to adapt it for sportweight yarn at a gauge of 6.5 stitches to the inch. Let's say that the pattern calls for casting on 98 stitches. How many stitches would you cast on to produce a piece the same width at your tighter gauge of 6.5 stitches to the inch?

1. The answer lies in a simple relationship of ratios:


2. If we plug in the numbers, we have:


3. To solve for the unknown (Number of sts at your gauge), simply cross multiply between the two ratios:


4. Then divide both sides by the Your gauge (in this case, 5):



5. Solve for the unknown number of stitches:



Because you can’t cast on partial stitches, you’d need to round up to 128 stitches (if you wanted to work with an even number of stitches) or round down to 127 stitches (if you wanted to work with an odd number of stitches).

For a short cut, simply plug in the following equation every time the pattern lists a number of stitches to determine the number of stitches to work at your gauge:




For example, if the pattern said to bind off 30 stitches at the center neck, you’d bind off 39 stitches instead.



                                     

If you chose to work with an even number of stitches initially (128 stitches), you’d want to adjust this number to be an even number as well so that there would be the same number of stitches on each side of the neck. Keep in mind that it’s your choice whether to adjust up to 40 stitches or down to 38 stitches--the difference of a stitch won't make a visible difference.

Now, I don't need to tell you to power of this little formula. It's what I used to figure out all of the additional gauges for the patterns in The Knitter's Handy Book of Patterns and The Knitter's Handy Book of Sweater Patterns.

For each project, I figured out the pattern for a gauge of 6 stitches/inch, then used this formula to determine the stitch count for all the other gauges. If there is no specific pattern repeat row-wise, you can simply knit to the specified length to the underarm, shoulder, etc. But be aware that it doesn't work as well if you're altering the gauge in a set-in sleeve cap or if your working with a stitch or color pattern that's designed to end at a particular point at the armholes, neckline, or shoulders. In these cases, the original row gauge is an important factor in the design. (But these adjustments can made as well, using the same formula along with a little practical sense.)

16 comments:

yahaira said...

does the short cut equation only work for subsequent numbers (not the cast on)? for some reason I can't get the same cast on number from the first example. 98*5 = 490 div by 6.5 = 75.4 not 127 or 128.

also, is it "wrong" to figure out the cast on for your gauge by dividing the co number by the pattern gauge and then multiplying by your gauge? it's basically the same thing, but I guess I wasn't thinking about ratios but more about the finished width

Karen Frisa said...

I think the short-cut formula should be: (number of sts at your gauge) = [(number of sts in pattern) * (your gauge)] / (pattern gauge)

:)

Kael Hunt said...

Good to know I don't have to feel too terribly nerdy about using algebra with knitting ;-) (I use variables in my calculations)

Virginia said...

Kael:

What kind of variables? Like

(number of sts at your gauge)*(number of times you're interrupted attempting to do the math)*(number of children under the age of 3 in the hosue)*(number of times your husband asks you to find something because he's desperately late and then discovers it's been in his pocket the entire time)/(the amount of time it takes you to calm down after the insanity has stopped) = [crap, my gauge has gotten so tight I can't even move the stitches off the needles]

yahaira said...

aha! thanks for the correction!
late night + math = not good

Ali P said...

Any chance of getting this in a handy dandy easy to print and read PDF? This is valuable knowledge!

pat said...

AGREED a pdf would be so helpful

thank you for val. info

Kael Hunt said...

Virginia:
In my case, it’s more like x=(number of stitches needed), so x=[(gauge)*(width in inches)]+[(number of stitches ripped per severe error)*(number of people in the house + number of mammalian pets in the house)*(number of interruptions) - (number of times older children threatened with sharp DPN’s)]

Kael Hunt said...

PS Virginia: Oldest boy was threatened with DPN's many times during the making of his own gloves: http://yarnvana.blogspot.com/2010/01/gloves.html

I begin to think he enjoys it, as he usually laughs while quickly dodging out of spearing range: those size 00's don't go very far.

Virginia said...

Kael: I like it! An excellent calculation for all.

pattiannes said...

Thanks Ann for showing that we need not fear the math in our knitting. I was just recently asked my a non-knitting friend "Why knitting, what drew you into loving it so much?" And strangley enough after only a momements hestitation my answer was "The Math". Which then lead to discussion that only other knitters or nerdy accountants like me would realy enjoy. Good luck with your new blog and keep the math coming :)

kewpiedoll99 said...
This comment has been removed by the author.
kewpiedoll99 said...

I converted text from this post into a PDF, in case you would like to post it here, Ann. I would be happy to send it to you. I couldn't find any email address for you, but you can find me at kewpiedoll99 (at) yahoo (dot) com.

Barclay
http://babablacksheepyarns.blogspot.com

Knitcrazy said...

It sounds soooooooooooooooo Easy when YOU say it BUT... ???

TinaTinaTina said...

Bless you for showing me that I need not fear the math. I'm putting it into use this very evening. Wow! My knitting addiction is crossing so many boundaries. Thank you and keep on blogging.

katkin said...

That is awsesome to have this info.Where do we get the PDF of this information?.I have a knitting group that would love to have this.
Kathy