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.


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