1.414: every quilter’s magic number

Numbers. I confess a love/hate relationship with them. They are so unyielding; so absolute. The mathematic principles that decree my checkbook should balance refuse to yield to my creative genius. I usually get three different totals when I add up my withdrawals and subtract them from the deposits. And do any of my numbers match the bank’s? They do not. Yet there are a couple numbers of which I am fond. My favorite number is 1.414.

That’s because 1.414 is the number they never told me about in that long-ago and best-forgotten geometry class. The only reason I got a “D” instead of an “F” is that the teacher was a young man and when I cried, he took pity on me. But I digress. I’ve since discovered that 1.414 is a quilter’s magic number. It is how you know the width of a block if you set it on point. It is how you know the size to cut setting triangles for on-point quilt patterns. It is how much longer the diagonal of a square is than the sides.

Say what? Okay, maybe I lost you on that last one.

How wide is a block set on point?

You are a quilter. You do it all the time. Take a square—let’s say a 2 1/2″ square—and cut it in half on the diagonal, from corner to corner. You now have two half-square triangles. The triangles each have two short sides and one long side. The two short sides are each 2 1/2″, but what is the measurement of the long side? Here is the magic. Multiply the length of the short side by 1.414, and that is very close to the length of the long side. 2.5″ x 1.414 = 3.535″. Yes. It is true. Measure the diagonal of a 2 1/2″ square and it will be just a little over 3 1/2″.

How to measure the diagonal of half-square triangles

I find the 1.414 magic number really empowering. Say I want to make a quilt on point, with 8″ square blocks set diagonally. Before I learned this trick, I’d draw an 8″ square on paper and then use my ruler to measure the diagonal. Honest! For a 10″ block I had to tape two pieces of paper together before cutting and measuring my square. I had a dim memory of some formula from my long-ago junior high geometry class. I even went so far as to look up a2 + b2 = c2, before I realized my calculator did not have a  √ sign, declared it hopeless, and went back to taping and cutting paper squares. But now I know I can simply multiply the measurement of the finished block by 1.414 and that will be the width set on the diagonal. So an 8″ block will be: 8″ x 1.414 = 11.312″. Round off to the nearest 1/8″. Technically, 11.312″ is between 11 1/4″ (11.25″) and 11 3/8″ (11.375″) but we’re talking about quilts and fabric and very human quilters. I’d probably round down and consider each block diagonal to be about 11 1/4″ just because I find 1/4″ easier to remember than 3/8″.

Magic Number i-3

Multiply the diagonal measurement of a block by the number of blocks set point to point to calculate the width and length of the quilt center. For example, 3 blocks x 11.312″ = 33.936″ and 4 blocks x 11.312″ = 45.248″, so the quilt below would end up about 34″ x 45 1/4″. I don’t think it matters if you round off your numbers before or after you multiply by the number of blocks unless you are trying to be hyper-accurate and fit an intricately pieced border to a large number of blocks. It is slightly more accurate to round off after you multiply the on-point width by the number of blocks, but very few quilters cut, sew, and press so precisely that the slight discrepancy will cause any problems. Having said that, I will confess I do all my calculations using numbers that I have not rounded off. Just to be safe.

Magic Number i-4

You can also use the magic of 1.414 to find out how to calculate setting triangles for your on-point blocks. (Yes, there is a setting-triangles formula!) Quilters usually make corner-setting triangles from half-square triangles, and side-setting triangles from quarter-square triangles. (This keeps the fabric’s straight of grain on the outside edges of the quilt and makes it less likely the edges will stretch and ripple.) As always, make all your calculations using the finished measurements and then go back and add the seam allowances. This is because the amount you add for seam allowances depends on the shape you are cutting. Add 1/2″ for squares and rectangles, 7/8″ for a square from which you cut two half-square triangles, and 1 1/4″ for a square from which you cut four quarter-square triangles.

Magic Number i-5

For this example, let’s pretend we have 12″ finished blocks. If you look at the diagram below, you can see the long side of a corner-setting triangle is the same measurement as the blocks. In this case you know the measurement of the long side of the triangle and you want to find out what the short sides are, so you’ll divide 12″ by 1.414 and find they measure 8.487″. Nice! That’s almost 8 1/2″. Add 7/8″ for seam allowances, and you’ll see you need to cut two squares, 9 3/8″ x 9 3/8″. Then cut each square in half on the diagonal to make the corner-setting triangles. Some quilters like to make setting triangles a little larger and then trim the excess, but that is entirely up to you.

Magic Number i-6

You may have already figured out the side-setting triangles. They are the same size as a block that has been cut in half on the diagonal. So the short sides are about 12″, and the long side will measure the same as a block’s diagonal. Magic number time! 12″ x 1.414 = 16.968″. That is just shy of 17″. Add 1 1/4″ for seam allowances, and voilá , you know to cut squares 18 1/4″, then cut each square twice diagonally to make four side-setting triangles.

When I first learned about this magic number I didn’t believe it really worked. I cut and measured countless squares. I even bought a calculator with a square root key and painstakingly tested using the 1.414 multiplier against the time-honored a2 + b2 = c2 formula. It hurt my brain but I did it. It worked every time no matter how large or small the blocks or squares. It is not exactly, mathematically, perfectly accurate and you don’t want to perform brain surgery using it, but it is very, very, close. Close enough for the most exacting quilter. In fact, usually quilters simply use 1.4 instead of 1.414. I punch in the extra digits just because it is a teensy bit more accurate, and deep in my heart I still don’t believe it works.


Robin Strobel is the author of The Casual Quilter and Quilter’s Bounty.


39 Comments (leave a comment)

  • Thanks for the great info. I’m like you were cutting and measuring the paper. I’m saving this for future reference.

    —Mary on July 27, 2012
  • How cool is that!?! Thanks for sharing!

    Jean on July 27, 2012
  • This is amazing! I love it! Thank you so much for sharing this with us. 🙂

    Jacque on July 27, 2012
  • mahalo – what a great article !!!

    —Anne E. on July 27, 2012
  • What great information! I’ve included a link on my blog to this article; I know it will help many of my readers.

    Thanks!

    Lynda DeTray on July 27, 2012
  • Thank you, thank you, thank you!!!!!!!!!!

    —Michele on July 27, 2012
  • Now that’s really useful! Dang, you make it sound – easy even! Thank you!

    Sally on July 27, 2012
  • Woo-hoo! I’m empowered. Best thing that has happened all day. This is printed off and going in the 3-ring I keep in my studio. Thank You!

    —Claudia on July 27, 2012
  • PS: I love blocks set on point.

    —Claudia on July 27, 2012
  • Thank you for explaining this to me where I could clearly understand it. it made it far more fun to do. THANK YOU Hugs Jeanne

    —Jeanne Marie Wallace on July 27, 2012
  • Ah-ha! Now I can actually do the math because I have the magic number. Thank you!!

    Linny on July 27, 2012
  • Years ago I was told that the magic number was 1.416, either way, it still works and that’s all I care about.

    —JoQuilter on July 27, 2012
  • Merci de toutes ces explications claires et précises!
    et de ces croquis et modèles!
    j’aime la géométrie, mais ce nombre! je vais m’en servir et ne penser qu’à toi maintenant!
    bye

    patchcath on July 27, 2012
  • Hi patchcath, we’ve translated your comment to read: "Thank you for all these explanations, clear and precise! and the sketches and models! I like the geometry, but this number! I’m going to use it only now! bye." Thanks for your comment!

    —Jenny on July 28, 2012
  • As soon as I saw that number I knew why it works! It’s the square root of 2! But math was my favorite subject in school and I use it a lot in my work. I never thought of 1.414 as a multiplier. I just used the other formula. But your way is simpler!

    I work in a fabric store. Often, at the cut table, people come with their projects and want help determining how much fabric to get. (Sometimes, I think they are waiting for me to volunteer or even offer myself for hire to get their projects done, but we are not allowed to do that…) I get out an empty bolt and ask them to draw their projects. If they aren’t able, then I draw it to be sure we are seeing the same thing. Then we write in the measurements and do the math. I have noticed that the ladies in their 60’s – 80’s are the sharpest at doing the math in their heads.

    —Sheri on July 27, 2012
  • very helpful thanks

    Sue on July 29, 2012
  • Dude, will you marry me?! LOL! Oh … wait … that won’t work. ‘Cause I can’t balance a check book either. 😉 Awesome info. Thanks a bazillion.

    Kristyne on August 5, 2012
  • It’s wonderful
    I like it very much
    great

    —Sybille CUVELIER on September 10, 2012
  • WOW! Awesome. I have bookmarked this tutorial to read and reread. Thanks a Whole bunch!!! I have so often thought there was an easy way to figure it (the on point measure) but I just didn’t know how.

    —Sue on May 21, 2013
  • Soy nueva en esa www y estoy alucinando de las cosas que estoy aprendiendo muchas gracias.

    —francesca on May 23, 2013
  • And you girls thought you’d never use Pythagoras’s Theorem after high school…

    —Aaron on May 24, 2013
  • THANK you!!!!! Saved my butt (and a whole lot of wasted fabric.

    —Jill on July 6, 2013
  • A heartfelt thanks from the UK – yours was the third explanation of how to calculate setting triangles that I looked at and the first that didn’t make my brain hurt!

    —Sue S on August 25, 2013
  • 1.414= 1/cos45 (It is alternative to Pythagorean theorem. Trigonometry.))

    Roolen on October 10, 2013
  • WOW!!!!!!!!! I had never heard of 1.414. Thank you Thank you Thank you.
    I have tried many times to figure out the on point measurements including cutting paper up.
    This is my favorite number forever.

    —Irene Foss on November 15, 2013
  • Very enlightening ! Thanks much .

    —Surabhi on May 9, 2014
  • I have to tell you, this information has completely BLOWN MY MIND!!! Do you know how often I struggle with this? And I can even remember 1414 to use it when I need it!

    —Trish on June 5, 2014
  • Thanks you so much – this has made my sewing and patch working life soooo much easier.

    —Leanne on July 17, 2014
  • oH mY! This is so beautifully explained: every time I felt a bit fuzzy you added a picture or broke down the steps really clearly. THANK YOU so much: this will save me so much time, confusion, and money (will know EXACTLY how much fabric to buy)

    Sally

    —Sally on September 4, 2014
  • Great information! Thank you. Can you please tell me where I might find the lantern pattern. I love it

    Hi Sandi, I’m afraid there isn’t a pattern for the exact lantern featured in this post, but there is a similar lantern block featured in a quilt from the book Quilting with Precuts and Shortcuts. Click through the gallery to photo #12 and you’ll see it. Thanks for your question! –Jenny

    Sandi Benfield on March 7, 2015
  • I am in awe and I love to calculate regular quilts but not on point ones. I work in a fabric store and have never heard of this. It is 4:17 am here, and I can’t sleep, so trying to figure out a quilt size for my little granddaughter. Your site just blew my mind! Can’t wait to share it at the shop. Thank you so much! May actually get started now, rather than give up.

    —Brenda on March 12, 2015
  • I meant to ask what pattern that is you used?

    —Brenda on March 12, 2015
  • Wish I had this 2 wks ago, it would have greatly simplified determining corner triangles for a quilt I designed and made. I will never forget the quilter’s magic number. Thanks so much.

    —Darlyn on July 23, 2015
  • Just found this website and absolutely love this ’roundup 52′ post. So much good, helpful, creative information. Thanks, Martingale!!

    —Ella on September 28, 2015
  • Wondering how the numbers were arrived at for the seam allowances: 1/2, 7/8 and 1 1/4. They are a factor of 3/8 difference. Is that another magic number? 🙂

    —D Mueller on January 14, 2016
  • Math has always been my bug a boo. I can add and subtract, but your solution makes my brain hurt. I mean I "get" it but I can’t "do" it. Thankfully my husband can do this calculation in his head without having to write it down. I will now make quilts without having to use patterns that give setting triangle measurements. I avoid using on point blocks even though I love the look. Yea! Now I can on point. My husband loves helping and math loves him.

    —Alice on September 6, 2016
  • Thank you. This was really useful. I needed the calculation to work out the right size to cut fabric as I was making the pattern rows up on the go.

    —bronny blackburn on September 3, 2017
  • Wonderful ! have you ever tried to look up that teacher again and thank him for giving you a D and letting him know, it actually was worth not failing you, because now look what you do with it.. .and it was all because you remembered in the back of your mind what he taught you ! I was a very poor student on paper, but I do remember a lot more of what the teachers taught me than they will ever know, or what was ever proven by a test ! Cheers !

    —Suzi on September 30, 2017
  • 1.414 is the square root of 2. There is so much more math behind this than you could possibly imagine.

    —Russell on October 29, 2017

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