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July 10, 2005

When insanity stares you squarely in the face, embrace it

My friends. Time has come.

I'm sorry. You know the post isn't going to be any good. It's okay to leave now.


The problem du jour is to figure out how many balls of yarn different Tivoli sizes would need... sizes that have never been knit. I have absolutely no idea how other designers figure this out. Absolutely none. But my geometry background is mighty good ;). I remember groaning about having to take Advanced Geometry when I was in college, since I wasn't studying mathematics, but so far it has proved to be really useful in everyday life!

I decided I would first figure out, what is the surface area (square inches or centimeters) one ball of yarn covers? There are two ways to figure this out - either use a predetermined length of yarn to find out how big or small a square it makes, or knit whatever project with that yarn, and take note of how long one entire ball lasts. The second method is what I chose to use while standardizing the Tivoli.

The hurdle I encountered is that the Tivoli is knit from the top down, and the yoke is not some perfect rectangle made for surface area calculations. So, the Calculus had to come down from the shelf to remind me how to calculate an area of a more complicated geometric shape - a trapezoid. And with the book's help, I got it:

Okey dokey, 1 ball of yarn lasts about 126 square inches.

Then I did some way more complicated math in Excel to figure out the surface areas of each of the Tivoli sizes:

Doesn't that look SCARY?

And you want to see the kicker?

The calculations say that the 44" size needs 7.035 balls of yarn, and the 48" size needs 8.043 balls of yarn! And I know I've been rounding up throughout because I don't want to be responsible for some poor knitter running out of the proper dye lot - it's happened to me, and is quite traumatic. But can I in good faith say that the 44" needs 7 balls, and the 48" needs 8?

Another nifty thing that came out of my adventures with the Calculus book is that I finally looked up that SOHCAHTOA thing from trigonometry and figured out the length of the Tivoli to shoulder.

I should rename my blog... Grumperina: knitting on another level.

Posted by Kathy on July 10, 2005 09:47 AM


Such dedication--you'll be guaranteed the right amount of yarn w/o the headache of worrying "is it enough, is it enough"! Start knitting pls!

We have THREE copies of Stewart in our apartment. Love it.

you're scaring the bejezzus out of me!

I love it! I can't speak for others, but that's exactly the way I'd approach it.

One thing you may want to add into the pattern (since you really have the info already) is how much extra yarn 1 inch of length would add to the sweater. I've seen this type of information in some lace scarf patterns and it's really helpful.

As for the number of balls of yarn, what do you think about just listing yardage? This way people can use whatever yarn they want and they can decide if they're close on number of balls and if that matters to them (e.g., if they end up shortening sweaters anyway they might be OK, but if they need to lengthen then they know they have to go up).

Oh my god, you are one sick puppy. Just like anybody who rubbernecks to see the car crash as they drive by... I found myself actually reading your post and looking at those photos. All the while my heart is pounding from the memories of taking and retaking Calculus in college. The horrible foreign teaching assistants who talked so fast I felt like crying. The professor with his thick Dutch accent - nope, couldn't understand him either. I finally just declared it my limit and gave up trying.

Now I had better stop to shower off the panic sweat.


You are insane. My head is swimming.

When I had to figure out yardages, I unravelled a bit of my swatch and figured out how many stitches were in a yard, then calculated how many stitches were in my garment, for all sizes. Probably way less accurate, but less work. And for some reason I'm way more daunted by knowing how many square feet of fabric I need to knit than how many stitches.

I'm all for just giving the estimated yardage. Then, the knitters can decide if they want to be daring (only buy 7 or 8 balls) or conservative (buy extra, just in case).

Incidentally, in a email exchange with Jenna from girlfromauntie, I learned how she found the estimated yardage for Rogue. She weighed her finished sweater, converted to yards, and tacked on 10% to cover her rear. So maybe you could come up with the estimated yardage and tack on 10% to cover YOUR rear.

Man oh man....all the math brought shivers of deja vu in college - CRAZY GIRL! It's like what Jody said - reading your calculus post is like rubber necking at a car wreck - I will never understand it all but I can't pry myself away from it :-) You are the math guru :-)

PS: I love Elizabeth Zimmerman, I've purchased EVERY video out there with her alone or with her Daughter Meg Swanson and Elizabeth together - not to mention all her books - including the OPinionated Knitter which I LOVE. If you dont' have her videos -pls check out "www.schoolhousepress.com" or "victorian-video.com" and get some - they are fantastic!

So how does your method of estimating work for the already established sizes? That would be a good way to check how accurate the estimates are.

Stewart and I, while well acquainted, are not friends.

I'm a little worried about Almost Felted Lauren having THREE copies. One was all I needed!

Dude- Next time- Just weigh the already knit items, and then weigh the intended yarns, and Voila- you could totally calculate this way.

you could, ahem, find test knitters!

I had that EXACT same book. How funny. But I'm a nut like you and would have done the exact same thing. My boyfriend thinks I'm crazy for liking math.

good on you for doing the math! thanks!

Wow - it is entirely too early on a Sunday morning to be reading about calculus! But you rock for doing the maths and figuring it all out so precisely.

I hope all that stuff actually works... It's almost like.. voodoo or something. lol.

I'm pleased to know that you're so thorough. : )

Hey wait.. is this just an example of what you did for the 44" and 48" sizes.. or.. does this mean the 28" is out? : (

Tsk, tsk, tsk.

You're hopeless, Miss!


I'm only kidding of course. Myself, I'd just measure out a yard and place a marker before knitting my swatch and then measure it after washing it. I'd then take the stitch count and factor that into the spi count.

However, I do know that that method is what a lot of Designers use (the other being weighing the garment and converting), but they also end up knitting one of each version they give measurements for (or they hire test knitters).

I'd be interested to see how accurate (I'm sure it's VERY accurate) your method is. Maybe you could have someone develop a simple program, based on your formula? The knitting world would LOVE that! Seriously!

I have to confess I didn't read the whole post - the mathematics made me dizzy! But I didn't leave before writing a comment either! LOL!
About Tivoli with sleeves, short row did come to my mind ... but last night after reading your email, I suddenly overcome the hurdle of how to knit short row for the sleeves and knit the body of the tee together! I don't have to do that at the same time! So now, either I frog the one I am making back to the armhole bind off and experiment what I have in mind, or I have to make a third one ... this time with sleeves!

The weighing method that others have mentioned is what we do for our patterns, too, and then we calculate how much bigger the next sizes are in terms of percentage, and use that for yarn requirements. Another good thing to do is use Sweater Wizard, as it gives you a rough estimate of required yardage -- we use it to produce different finished sizes with the right gauge, then add a percentage to it's estimated yardage (the estimated yardage never includes finishing/necklines).

My own Trivoli is almost to the armhole bind offs, I'm making the 37" size and am into the second ball of Cathay.

I'm impressed. My lowest grade ever in my life was in Calculus. Had this subject been explained to me in terms of yarn, however, and results may have been different.

i think i just passed out from sheer shock and woke up in some weird time warp from a science fiction film!

all credit to you...my brain wouldn't even think of looking for the book and my calculator.

MY EYES!!!!!!!!!!!!

I am in awe of you. I think I need a lie-down.

Gah! Attack of the maths!

Dude, you kick knitting ass!

I'd round up. You'll also need yarn for swatching purposes.

Ok, I think it would be faster for me to knit it than me trying to figure all that out...seriously!

I'm new here, but I would really recommend the PDA program, KnitAble. It has the best yardage calculator I've found yet. That's what I use when I design and need to refigure for sizes.

Btw, had the same fear of the Calculus book. My dad made me take through Calc II or he wouldn't pay for college (engineer, don't you know)--and I was an English major! Gack! Now, if they'd taught it as knitting, I'd probably done better . . .


(previous comment cut off before I could finish) Nice work. I would have gone straight to the geometry book, myself, rather than integrating to find that formula.

Whoa! I got math anxiety just reading this!!! I am also impressed! I personally got "Christmas C's" in math. (That's when the teacher writes down a "C" and looks at you and says "MERRY CHRISTMAS" because they are giving you a gift!)


You are totally craaazy.. I think other designers just add/subtract a couple skeins from the model, but there is a whole other level of precision going on here!

The new blog name would be completely appropriate :-)

Umm....now that you've figured this out for Tivoli. Can I ask you to make calculations for me for other patterns?? ;-)

Neat! I was looking at your rounding closely, but I think it's OK - very conservative, and one other place for slop is in how much yarn people use for joins (I know I use kind of a lot). One of my favorite sayings is 2 + 2 = 5 for sufficiently large values of 2. The box around your "final" answer delighted me (in the pen & paper page), and how often can you use SOHCAHTOA in everyday talk. :^)

Wow, you definitely take knitting to a new level! :)

Oh my head! The MATH! Make it stop!

Oh my goodness. I grumbled all through my 8 a.m. calculus class in college about how I'd never ever use it in real life. And here you go, proving that it's useful. Impressive!

When I opened your post and saw a picture of Stewart, I knew you were a girl after my own heart! :) I could have used a copy of him this weekend as I studied for my oral comps -- the damn quotient rule evaded me! thanks for being such a wacky blogger.

i am not even sure how one figures out how to figure out the figures. when i make up a pattern, i just make a rough guestimate and get way more yarn than it could possibly use. i can take it back. i won't, but i could. when i had to take chem, to try to get into an art restoration mfa program, i considered putting a cheat sheet into my calculator. i sucked so much at it, i wasn't even sure how to cheat. and that, my friend, is really really bad. i am not a cheater, but i couldn't have even if i wanted to.

I understand what you're doing in theory (I had to take calculus in high school and college), but understanding doesn't really make it less scary.

I love it! I recently pulled out the Trig book to help figure out armhole / sleeve cap shaping, which are really sine curves. Using the surface area approach seems to be best, but instead of listing how many balls it takes why not list the total yardage for a specific gauge. This way other knitters can easily substitue yarn. Fun post -- the Tivoli pattern just gets better and better!

Ha ha, Laura's comment about covering your rear. I have no idea how to determine yarn weights; usually what I do is count the number of joins I've made from old ball to new ball, and round up. So unscientific! But that's why I'm a designer and you, Mz. Grumpy, are the fabulous neuroscientist! I love the maths!

Did you do those calculations in red pen? As if the calculus and advanced geometry weren't impressive enough, you did it in pen??

You are describing the method I use to write the yardage estimator for my sweaters. But, then I code the formulas so the come up with an estimate for each sweater. Go here, click the button and get your own pattern:Husband Sweater

Does this hopefully mean that you are going to offer the sweater pattern for a 48” or 50" size???? (hopeful look of desire) I adore the pattern but I can never really figure out how to upsize a pattern written in the round. Something never clicks in the calculations for me.

I really adore your pattern. Thanks :)

Good gravy. That's really all I can say!

Hmm,..perhaps you should be tagged Grumperina, the knitterly statistician.

I'm impressed.

On the other hand, I tend to use the seat-of-the-pants technique, allowing a bit for Kentucky windage. In other works, I'm knitting this tee for a 46" bust with a 34" waist...using Cascade's Sierra yarn with a size 7 needle. I bought 4 balls...764 yards total.

I've added 16 extra stitches to the front and back since I don't need them in the sleevage. I haven't decided how much extra I'll need to decrease for the waist, but I'll wing it when I get there. Really professional, eh?

I'm keeping records and I'll let you know how it turns out...


I'm impressed.

On the other hand, I tend to use the seat-of-the-pants technique, allowing a bit for Kentucky windage. In other works, I'm knitting this tee for a 46" bust with a 34" waist...using Cascade's Sierra yarn with a size 7 needle. I bought 4 balls...764 yards total.

I've added 16 extra stitches to the front and back since I don't need them in the sleevage. I haven't decided how much extra I'll need to decrease for the waist, but I'll wing it when I get there. Really professional, eh?

I'm keeping records and I'll let you know how it turns out...


I got a headache looking at your math. I was just tickled that your tivoli sweater was figured out in my size, saving me the trouble of having to figure out my own!! I'm having better luck with the yarn you dislike, so far 4 balls and only 1 splice (I've had much worse luck with more expensive yarn...and I'm knocking on wood hoping that there's not a million splices between now and when I finish the sweater!!

I'm in awe of your math skills as I don't know that I would have a clue. I'm just curious is you are working the pattern for a few larger sizes or not. I'd thought of making the pattern, but a 37" is a little snug to me, 40" is usually a better bet. Tivoli is such a cute pattern, I hope to make it soon.

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