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.

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″.

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 a^{2} + b^{2} = c^{2}, 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″.

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.

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.

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.

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 a^{2} + b^{2} = c^{2} 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*.

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, 2012How cool is that!?! Thanks for sharing!

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

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

—Anne E. on July 27, 2012What 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, 2012Thank you, thank you, thank you!!!!!!!!!!

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

—Sally on July 27, 2012Woo-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, 2012PS: I love blocks set on point.

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

—Linny on July 27, 2012Years 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, 2012Merci de toutes ces explications claires et précises!

—patchcath on July 27, 2012et 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

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, 2012Hi 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, 2012very helpful thanks

—Sue on July 29, 2012Dude, 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, 2012It’s wonderful

—Sybille CUVELIER on September 10, 2012I like it very much

great

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, 2013Soy nueva en esa www y estoy alucinando de las cosas que estoy aprendiendo muchas gracias.

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

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

—Jill on July 6, 2013A 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, 20131.414= 1/cos45 (It is alternative to Pythagorean theorem. Trigonometry.))

—Roolen on October 10, 2013WOW!!!!!!!!! I had never heard of 1.414. Thank you Thank you Thank you.

—Irene Foss on November 15, 2013I have tried many times to figure out the on point measurements including cutting paper up.

This is my favorite number forever.