The Magic Quilting Number 1.41

All month, one of my online groups has been discussing the number 1.41. It turns out that this little number is really quite magical.  And it is incredibly magical, as well as useful, for quilters.

Simply put, it is the square root of any square. And to find the need requirements for turning blocks or quilt blocks on point, one simply multiplies or divides by 1.41.

Let's say you have a five inch block. You want to put it on point, but you don't know what size to make the little triangle piece that will fill the on point shape you have just created and turn it into a square.

Even the most seasoned of quilters don't always know this technique. When I made the quilt shown above, without a pattern, without a plan ..just winged it...about 7 years ago...none of my books told me exactly what to do or how to do it.

I literally used my imagination to cut a shape that fit. Oh, my goodness! Was I nuts or what?  And while it is hardly a perfect little quilt. It was made as quickly as I could make it and given to a young couple getting married on a magical little island in my homestate of Alaska.  The same magical little island with its magical little shrine that I got married in, decades ago!

I had to make them something special. And of course, after surviving the quilts creation, without a pattern or directions...

As they say:

"When you know better, you do better."

Here is how the magic of 1.41 works.

Quilts with blocks set on point have triangular openings around their outer edges where each diagonal row of blocks ends.

You can assemble triangular half-blocks to fill in the spaces, but quilters often use large fabric triangles instead.

Two types and sizes of triangles are used to fill in the blanks. One size fits into the gaps along the top, bottom and sides of the quilt. Four smaller triangles are used to create the quilt's corners.

The triangles all appear to be cut in exactly the same way, but their structure is very different:

Corner triangles are half-square triangles, created by cutting a square in half once diagonally to produce two triangles with the straight grain on their short edges. The stretchy bias along with the longest edge, the edge that is sewn to corner blocks.

Setting triangles are quarter-square triangles, created by cutting a square in half twice diagonally to produce four triangles with the straight grain on their long edges. The stretchy bias runs along short edges and each short edge is sewn to the side of a block in the finished quilt..

In order to minimize stretch, it's best to assemble quilt units with the fabric's straight of grain along edges that will be on the outer perimeter of a block or entire quilt, so that there's less chance of stretch as you work.

If setting triangles were cut like corner triangles, their long edges would be cut on the stretchy bias, making the outer edges of a quilt stretchy -- those edges sometimes tend to stretch out of shape a bit anyway as you finish the project.

Cutting triangles to fit a space:

o cut two corner triangles, you divide a parent square once diagonally.

Start by calculating the finished length of a block's diagonal.

Now, here is where you use the magic number of 1.41

Finished block size x 1.41 = finished diagonal

Divide the answer, the finished diagonal, by 2. Add 0.875" and round up to the nearest 1/8" to find your parent block size.

Cut two parent blocks that size and divide each in half once diagonally to make a total of four corner squares.

Corner Squares Example - for 10" finished size quilt blocks

10" block size x 1.41 = , 14.10" finished diagonal

Parent square size = 14.10" / 2 = 7.05" + .875" = 7.925, round up to 8"

Corner Triangle Parent Squares for Common Quilt Block Sizes:

4" blocks: use 3-3/4" parent squares

6" blocks: use 5-1/8" parent squares

9" blocks: use 7-1/4" parent squares

10" blocks: use 8" parent squares

12" blocks: use 9-3/8" parent squares

14" blocks: use 10-3/4" parent squares

15" blocks: use 11-1/2" parent squares

To Cut Setting Triangles:

We'll cut a parent square twice diagonally to produce four setting triangles with the fabric's straight grain on their long edges. Use this formula for setting triangles:

Finished block size x 1.41 = finished length required on the triangle's longest edge.
(Round up to nearest 1/8")

Cut a square with sides that are 1-1/4" longer than the number in Step 1.

Cut the square in half twice diagonally.

Setting Triangle Parent Squares for Common Quilt Block Sizes 

4" blocks: use 7" parent squares

6" blocks: use 9-3/4" parent squares

9" blocks: use 14" parent squares

10" blocks: use 15-3/8" parent squares

12" blocks: use 18-1/4" parent squares

15" blocks: use 22-1/2" parent squares

Setting Blocks Squares of fabric placed between blocks are called setting blocks. Cut them to match the unfinished size of your quilt blocks.

Decimal to Fraction Chart - 1/8" 

0.125 = 1/8"
0.250 = 2/8" or 1/4"
0.375 = 3/8"
0.500 = 4/8" or 2/4" or 1/2"
0.625 = 5/8"
0.75 = 6/8" or 3/4"
0.875 = 7/8"

Math done for you...

1.5" 2" 3-3/8"
2" 2-3/8" 4-1/8"
2.5" 2-3/4" 4-7/8"
5"4-1/2" 8-3/8"
5-1/2" 4-7/8" 9-1/8"
6" 5-1/8" 9-3/4"
6-1/2" 5-1/2" 10-1/2"
7" 5-7/8" 11-1/4"
8" 6-5/8" 12-5/8"
9" 7-1/4" 14"
10" 8" 15-1/2"
11" 8-3/4" 16-7/8"
12" 9-3/8" 18-1/4"
13" 10-1/8" 19-3/4"
14" 10-7/8" 21-1/8"
15" 11-1/2" 22-1/2"
16" 12-1/4" 23-7/8"
17" 13" 25-3/8"
18" 13-5/8" 25-3/8"
19" 14-3/8" 28-1/2"
20" 15-1/2" 29-5/8"

Michele Bilyeu blogs With Heart and Hands as she shares a quilting journey through her life in Salem, Oregon and Douglas, Alaska and all of her AAQI Quilting. Sharing thousands of links to Free Quilt and Quilt Block Patterns and encouraging others to join in the Liberated Quilting Challenge and make or donate small art quilts to the Alzheimer's Art Quilt Initiative (AAQI) Help us change the world, one little quilt at a time!