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Magic Formula | Any Size Circle

Magic Formula | Any Size Circle

Magic Formula to make any size flat circle.

In our knitting and crochet craft club on Facebook I’ve had the pleasure to meet many people of all walks of life virtually.  Meet Joann Fernstrom. Many years ago she became friends with a lady named Alles Hutchinson.  Alles published a wonderful educational magazine (booklet) called NEWS & VIEWS put out by ALLES KNITTING PUBLICATIONS from Pittsburgh, PA. She wrote and taught about machine knitting especially. She had a Magic Formula for knitting any size circle to make hats, shawls, afghans and the like.  You can apply it to many things.  Before she passed Alles gave her friend Joann the formula to help others.  In an effort to get this out there, for her dear friend, Joann has asked me to share it with you today.  Alles wrote many patterns and charts for machine knitting and can be used on looms.  I urge to to check out those older publications as well!  Here is a word from Joann. – Kristen Mangus

“I have seen some of you [the group] asking how to figure out how to make a circle. I have a formula for doing this any size you would like. It is called the magic formula and you can figure out what ever size you want you circle to be as long as you have a long enough loom. When you make a flat circle blanket you must determine the size of a circle to make then how many panels you want then after a few figures. The Magic Formula was figured out by a very dear friend [Alles] who passed away about 30 years ago and she gave it to me to share as I pleased.”- Joann Fernstrom


Circle Magic Formula (corrected)

by Alles Hutchinson

 Magic Formula for Circles by Alles Hutchinson (Click to Download Magic Formula)


This is Magic Formula offered to you so that you can learn the way to figure out short rowing. Once you learn this formula you will be able to do hats shawls or Afghans.

According to Alles Hutchinson:

There is probably more advanced math in this than in anything else you have done.
The entire piece is done by short rows (partial knitting). You will need only one measurement— how wide do you want the finish piece to be.

For example we will use 2.25 stitches and 4 rows = 1 inch. The diameter will be 40 inches. With 10 panels. You will substitute your own stitches and rows, and how many panels you want, but follow the same principle.

  1. Find the circumference of the circle.
    FORMULA: to find the circumference of a circle, multiply the circumference of a circle,40 inch circle.
    40 x 3.14 (pie) = 125.6 (six is larger then 5 so the answer is 126)
  2. Change inches to rows.
    126 x 4 rows per inch = 504 rows around the edge.
  3. Decide how many panels you want:
    10 panels …..504 rows divided by 10 panels = 50.4 (4 is less then 5 so the answer is 50).
  4. Find the radius of circle and change inches to stitches. Radius = 1⁄2 the diameter of the circle.
    40 inches divided by 2 = 20
    20 x 2 stitches per inch = 40 (this is what you will cast on).
  5. Shape this by short rows so that it will become a pie shaped piece.
    Each section will be short rowed down to the next to the last group. The last group will not be worked. Then 2 rows are knitted over all needles.Since short rows are done only on alternate rows, divide the number of rows by 2. 50 rows divided by 2 = 25 rows.
  6. Distribute the stitches evenly over these rows. You have 40 stitches to shape in 25 rows. Since the answer you want is stitches, divide rows into stitches.25 rows divided into 50 = 2 stitches to short row.Magic Formula for Circle step 6 math

Therefore you will short row 2 stitches every other row.

So you will cast on 40 stitches and knit back but don’t do peg 1 and 2. Lift stitch 2 off peg and wrap yarn on it. Replace stitch and knit back to peg 40 then knit to peg 5 and then back to peg 40. You will short row 2 stitches every other row when you get to the last 2 stitches you will knit over all the stitches.

Then change to 2nd color or keep it in one color. Remember there are no knitting police out there so let you imagination run wild and do as many colors as you prefer and as many panels as you want.

Lets say your stitches were 7 stitches and 10 rows per inch and you wanted it 46 inch circle.

Using 10 panels.

Here is how you would do it.
46 inches x 3.14 (pi) = 144.44 = 144 using the 4 is lower then 5.
144 inches x 10 rows =1440 rows around the entire edge.
Radius = 1⁄2 the diameter.
46 inch divided by 2 = 23 inches x 7 stitches per inch =161 stitches to cast on. Now shape the short rows.
144 divided by 2 =72 rows

so now we have 161 stitches to shape in 72 rows.


magic Formula for circles math example


Therefore you will short row 3 stitches 17 times then 2 sts ever other row 55 times.

Now to prove it
17+55= 72rows
23 inches x 7 stitches = 161 stitches.

I hope you can understand this Magic Formula for flat circles.

– Alles (and Joann)


Note from Kristen:

I have done the math using Lion Brand Hometown USA knitting gauge for size 13 needles.  Here is my math for a 36″ diameter circle across with 8 wedges (like a pie)


Gauge 9 sts (stitches) x 12 rows 4×4 swatch.  So that is 2.25 sts per in. x 3 rows per in.

36 in is the width (diameter) I want.

8 is the number of panels I want to knit up. Say I want to use 8 colors and change on every “panel” or wedge.

  1. 36 dia x 3.14 (# for Pi) = 113.04 –> 113
  2. 113 x 3 rows per in = 339 sts around edge
  3. 339 / 8 panels = 42.375 –> 42 rows
  4. 36 dia / 2 = 18 radius –> 18 rad. x 2.25 sts per in. = 40.5 –> 41 sts cast-on
  5. Short rows will be every other row. Work these rows short. –> 42 rows / 2 = 21 rows shaped with short rows
  6. Shape 41 sts over 21 rows every __ stitches on each row. 42 / 21 = 2 sts (so every even stitch will be wrapped for a short row)

The following would happen:

Cast on 41 pegs.  (the word “work” can function as a knit or a purl stitch; short rows are in groups of 2 here.)

row 1: Work back to peg 3 and wrap peg 2

row 2: Work to peg 41

row 3: Work to peg 5 and wrap peg 4.

Even rows repeat Row 2.

Odd rows repeat working back to 1 peg before even peg higher than previous row. Wrap that even peg. Continue until 1 full group (of 2) is left empty.  Will have +1 left in this example.

Work last remaining stitches to 41.

End of 1st “panel”. Change color as desired.

Repeat 7 more panels.

Have fun making your own magic formula circles!


Thursday 26th of January 2017

Do you have any samples of your knitting in which you used this formula? Love to see it if so!


Thursday 26th of January 2017

Do you have any samples of your knitting in which you used this formula? Love to see it if so!


Tuesday 1st of November 2016

I can't wait to try this formula on a loom!


Tuesday 1st of November 2016

I can't wait to try this formula on a loom!