HSTs & QSTs: It’s Not You, It’s the Math

HSTs & QSTs: It's Not You, It's the Math

Have you ever wondered why points are so difficult to match up when you’re making a block with half-square or quarter-square triangles? It’s not so bad if the entire block is HST’s or QST’s by themselves (except that the block will most likely not finish to exactly the expected size), but pair either one with squares or rectangles and expect the corners and points to match up and everything to be sized right in the end, and you’re likely to be disappointed, no matter how carefully you’ve sewn or how accurate your 1/4″ seam allowance is.

Half Square Triangles

Well, I’ve got a news flash for you: it’s not you or your sewing skills, it’s the math. And I don’t mean that you or the pattern designer have miscalculated the cutting sizes either. What I mean is that mathematically, when you calculate the size of square to cut for a certain finished size of half-square or quarter-square triangle, you won’t get a size that’s rotary cutter friendly. It’s some algebraic formula like Asquared+Bsquared=Csquaredyaddayadda, and I did actually do the math a couple of years back though I don’t remember the formula at the moment.

This whole issue can be proven with graph paper as well. Try this: draw HST#1 with 2″ straight sides on graph paper, and then add 1/4″ seam allowances all the way around. Then draw HST#2 at the universally accepted cut size, with 2 7/8″ straight sides (the formula to determine the cut size for a HST is finished size + 7/8″). Measure the straight sides on the HST#1, which should be 2 7/8″, but they’re not. Sure, it’s not THAT far off, but when a block contains 8 or 16 HST’s, or when those HST’s are supposed to fit together with a 2 1/2″ square patch, this can cause issues down the road.

The bias edge across the middle of the HST adds its own measure of instability and inaccuracy, and it all equals wonkyness that’s not likely to be the right size in the end. What to do? I’ve gotten to the point where I cut large and trim down after the HST’s or QST’s are sewn, so that I know I’m getting the right size and everything is really square. I use the formula, then add 1/2″ or 3/4″ to the squares when I cut them. I dislike doing this for two reasons: one, it’s an extra step, and in multiples no less, since how many quilts need just one or two HST’s or QST’s, and two, it’s a fabric waster which is really not okay. There is a silver lining though (see, I can find one in this morass!): when you trim the HST’s or QST’s down to size, you’re trimming away the “dog ears” at the same time, so that’s a bonus.

Some patterns these days may just tell you to do that from the beginning, cut large and trim to the right size after piecing, but I’m basing all this on my personal experience with patterns and books, which is probably old since I don’t generally buy patterns or make quilts out of books anymore, preferring to tumble over the cliff of my own creativity into the scrappy mess of UFO’s and failed fabric experiments at the bottom. When I was buying books and patterns a few years ago, patterns were written based on cutting the “exact” size you need, and expecting the HST’s and QST’s to be the right size in the end and they never were, and the edges were curvy and wonky in the bargain.

So what’s your solution to the HST and QST finished size/cutting size quandary? Do you have these issues with patterns these days? Do you cut bigger and trim, or just deal with the fallout on the fly when piecing blocks?

Edit: Crazy Accuracy Freak Girl wrote this while I was having breakfast. 😉 I try to keep her penned up and away from the blog, but sometimes she sneaks out and adds her two cents…or two dollars, as the case may be. Thanks for putting up with her.—Nadine

20 thoughts on “HSTs & QSTs: It’s Not You, It’s the Math

  1. I’m like you Nadine, I cut larger and trim down. I hate the extra work, but it’s the only way I can make *my* HST’s behave. Thanks for your post. I thought it was just me. 🙂
    Robin in Short Pump


  2. Hi Nadine!

    This will probably sound like a shameless plug for my Easy Star and Geese Ruler, but honestly, it WORKS and solves the problem with all half-square and quarter-square triangles. Side A of the ruler makes perfect quarter-square triangles and Side B makes perfect half-square triangles from strips of fabric cut just 1/2″ larger than the FINISHED size you need. No trimming, no wasted fabric. Yes, your strips need to be cut accurately, and you do need to use a scant 1/4″ seam allowance. But you won’t need to trim your unfinished HST and QST units to the perfect size, and there will only be one dog ear to trim off.

    Thanks for allowing me to share my full-proof method!


  3. This is Pat, refugee from Ms. Einmatic’s blog. The ruler works. You just have to cut accurately & without scootching your ruler even the teensiest bit. I find that one of those turn-table cutting mats helps, along with a nice fresh blade on the cutter. The other solution is to cut big and trim back. I HATE doing that because it takes so much extra time. Of course it also takes so much extra time when you have to unsew your wonky squares or you have to put ice on the fingers that you’ve burned while trying to steam those suckers flat…..


  4. If I need to be really accurate, I cut big and trim. But usually I just try to stay away from designs that require crazy accuracy! Avoidance is bliss.


  5. Hi Joyce! Glad to know I’m not alone. 🙂

    Hi Robin, and Welcome! Nope, it’s not just you, as all the responses here prove. Thanks for your comments!

    Kimberly, I did think about doing these with the ruler, but not until I’d already cut them the “normal” way. But I’ve had this whole mathematical issue running around in my head for way longer than I’ve had the ruler as well, and I know there are lots of folks out there who probably think it’s just weird why their HSTs and QSTs never come out quite right. I always wondered why, until I did the math a couple of years ago and then it all made sense!

    I do the same thing actually, Emma, when I forget to add some extra to the cut squares, or I’m in a rush. I always regret it.

    Hiya Pat! Refugees from elsewhere are always welcome here! I have these extra appendages that keep my fingers from getting burned most of the time, but I hear you! Way easier to cut big and trim back. (P.S. “extra appendages” being long, long fingernails! 😉 )

    Kristin, funny you should mention “avoidance!” That’s what I’m doing now: avoiding writing instructions for one of the projects in The Book! It’s one of those “make it up and size it as you go along” things, and I’m having a difficult time translating that into clear, step-by-step instructions without just saying “you make it up and size it as you go along” which I don’t think is going to fly with the editor. 😀


  6. I need to correct something.

    I think I may have left the wrong impression & perhaps chosen my words incorrectly. I am not really a “refugee” from Kimberly Einmo’s blog (as in I have fled from her blog). I am a friend of Kimberly’s who wandered over to your blog because she has a link on her blog to yours, AND I know how much she thinks of you. I can see why. Your blog is delightful, as well as informative. In my pea-sized brain, I have also been thinking of Ms. Einmo as “Ms. Einmatic” because she is like this automagic creature who can do a gajillion things at once (all of them well), smiles with a smile that lights up a room, and never utters a grouchy word to anyone. That little internal name for her

    By the way, her Easy Stars & Geese ruler is pretty spiffy as well, but not nearly as spiffy as she is.

    There. I’m not a refugee. I’m a visitor? a trans-internetian wanderer?


  7. Oh thank goodness its not just me, there are lots of us:-) I didn’t get into the math part just knew the method that worked for everyone else didn’t work for me. So I too have been cutting big and trimming for a couple of years now, like everyone else I hate the extra time it takes and the fabric waste, but prefer that to unpicking or trying to steam the suckers into submission along with burning my fingers too…. Must grow my nails again!


  8. Hi again Pat! Truly, I don’t think there was a need for you to correct anything at all. None of your comments raised a big red flag with me whatsoever. I might not have made the connection between you and Kimberly’s blog if you hadn’t clued me in, and it’s always fun to know where new friends come from! I appreciate your lovely comments about my blog, and you can wander here to your heart’s content anytime!


  9. Hi Julie, and Welcome! Nope, not just you, and I was sure there were folks out there who thought like you did (and I did, before I did the math), that it was just their sewing or some other nebulous “thing” that kept those HSTs and QSTs from turning out right. I agree, unsewing and burned fingers is not my cuppa tea, so cutting large and trimming down seems to be the consensus.

    Thanks for stopping by!


  10. Has anyone noticed any difference in accuracy if you do the technique where you put 2 squares on top of each other, sew on the diagonal, then cut? Or use those pre-printed guides for piecing? I was thinking that those pre-printed guides might be helpful if you had to piece a lot of the same HST sets? I’ve seen ones where you put the pre-printed strip on top of your 2 strips, sew, then cut. I’ve always been curious about them.


  11. Hey Pat, I would think that the pre-printed piecing guides would have the math issues all worked out so they would be perfectly accurate, or what would be the point? Especially since it’s just harder anyway, in my opinion, because you have to remove all the paper after you sew! (I’m a confirmed paper-piecing hater you see, so I’ve never tired those!)

    Anyone else have any experience with those?


  12. I think I will give them a shot on a future project, just to see how they work. It’s probably a trade-off on what tedious thing you dislike least: cutting down/squaring off, or picking off thangle residue. Maybe with some luck I could teach my cat to do the latter; I won’t let him near my rotary cutter ever since he threatened the dog with it.


  13. I used to use the cut larger, trim off. Then I took the Kaye England class and my eyes were opened. The trimming method is a waste of fabric and time.

    I now use Kaye England’s triangles and rulers (Cut for the Cure), although I am sure there are many other ruler lines that would work. For a 2″ HST, you would cut a 2″ strip, lay the triangle on top and slice. It’s perfect. (I typically cut two 2″ strips – one of each triangle side of fabric, put them face together, and then slice my triangle. It saves TONS of time.)


  14. Or you could use Perfect Patchwork templates to cut half-square triangles and cut the dog ears off at the same time. 🙂 The templates are mathematically correct for the finished sizes so half-square triangles and other shapes match up perfectly. And no fabric is wasted because you cut the triangles from strips that are as wide as one dimension of the template.

    I have worked for Marti Michell for 15 years and thousands of quilters around the world love our templates because they are so accurate and easy to use. Sewing triangles to squares is super easy because the corners match. We would be happy to send you a corner trimmer if you will send us your address. I’m reluctant to publish my email address here because I don’t want it to be picked up by a spambot, but you can contact us through frommarti.com. If you send us your mailing address and mention Inchies, we’ll send you a corner trimmer and a catalog of all of our other products. 🙂

    Happy Thanksgiving!


  15. Hi Patti! Thanks for sharing the information about the Perfect Patchwork templates. For things like HST’s I’m still a ruler girl as opposed to a template girl (despite the fabric waste and other issues); for me, it’s still just easier to cut big and trim down rather than cutting around a template! Yeah, I think I might have a tiny aversion to templates…I know that there are many other styles of Perfect Patchwork templates though, so perhaps I’ll need them for something else at some point.

    Thanks for stopping by!


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