The Magic Number is used for several calculations in quilting. A case in point is Nancy's question where she inquires...
My 8" blocks will be set on point. My quilt needs to measure 100" x 110". How many blocks will I need?
I know I need triangles to fill in the spaces on the sides. Thanks in advance for all your help!
This is a TERRIFIC question because it has several applications in quilting. On this page, we'll learn what the magic number is and how to calculate it and share an example using it to determine a quilt's size.
Allergic to math? Don't worry. There's a free chart to download at the bottom of this page with the calculations done for you!
It's calculated using the Pythagorean Theorem. Mathematicians use the theorem to describe the relationship between the hypotenuse and the two shorter sides of a right or 90° triangle.
Huh, what??! Hy-pot-a-who???
Everyday, quilter's use it to quickly find the diagonal width of blocks and determine what size to cut setting- and corner-square triangles for on-point quilts. Knowing this one number can save you a lot of time and headache.
It's not really magic. Just math.
Now if you trust me, you can skip this next section with the light blue background—it just shows the calculations used to arrive at this number—and skip down to using it to find the diagonal length of a block.
All you really need to know for quilting is that it works!
To find the diagonal measurement of Nancy's 8" finished blocks, multiply the side measurement, 8", by the Magic Number, 1.414.
8" x 1.414 = 11.312"
The width of an on-point 8" block is 11.312".
For a patchwork design measuring 100" wide by 110" long, simply divide the finished width and length by 11.312".
100" ÷ 11.312" = 8.840 blocks wide
110" ÷ 11.312" = 9.724 blocks long
Since we don't make partial blocks, you can either round up or down to the nearest whole one, depending on your design needs.
Choose the measurement that works best for you. I've worked out the possible finished sizes in the chart below.
|Rounding the # of Blocks|
|Dimension||Down to...||Up to...|
|Width||8 x 11.312" = 90.496"||9 x 11.312" = 101.808"|
|Length||9 x 11.312" = 101.808"||10 x 11.312" = 113.12"|
At this point, to come closer to your desired finished size, you may want to audition different sashing or border alternatives.
In our example, the diagonal of an 8" block is 11.312".
Since I don't do these calculations in my head, but rather on a calculator, I prefer to round only when I get to the final answer. The number is close enough for my needs.
You, however, could choose to round 11.312" either up or down to the nearest rotary cutter 'friendly' number.
For this example, that would be either 11-1/4" or 11-3/8" because it's right in the middle between 11.25 and 11.325.
This magic number is also used it figure the cutting dimensions for setting- and corner-triangles for quilts set on-point as in this example.
Click here to learn more about the calculations for those units You can skip the math if you'd like, it's done for you at the bottom of that page!
No magic needed!
Just click on the image to the right to download your free PDF cheat sheet "Diagonal Measurements of Finished Blocks".
It includes finished block sizes up through 20" square along with their diagonal measurements to three decimal places and that number rounded up to the nearest 1/8" for a rotary cutter friendly dimension.
Print and keep a copy (or two) by your sewing machine for quick access!