Sunday, October 6, 2013

Katy Explains The Maths Behind The Perfect Zippy Pouch - a 2013 FAL Tutorial

she can quilt

Today, Katy from The Littlest Thistle is going to show us how to make perfect zippered pouches. I have been lucky enough to meet Katy in real life, and she is fun, interesting and generous. Don't be put off when her tutorial starts talking about math - and seemingly complicated math at that - you have all the calculating power you need on your cell phone or computer to lick this bit of math in an instant. And with Katy's help, you will be sewing prettier and technically complicated zippy pouches too. Read on.

Hi I'm Katy from The Littlest Thistle, and I'm here today with a FAL tutorial to help with an oft puzzled over conundrum - how to create a zippy pouch with a flat bottom and vertical sides.

So lets take a look at the 'traditional' zippy pouch, where you squish the sides down to meet the base, sew along a line and chop the extra off:

You can see the sides slope down to meet the base, which is not necessarily a bad thing, it's just that with patterned fabric with any kind of horizontal or vertical pattern you'll lose the effect with things wrapping oddly round the side.  The angle of the sides depends on how far up the seam you go before stitching the line across, and it's not easy to see what the effect will be until the pouch is turned through.

The next option is to cut a square out of the bottom corners of the rectangles you're using to make the sides.  You sew the sides and base together, leaving the square openings free, then you squish the sides down to meet the base again, but this time you have a cut edge to sew along the seam allowance for:

You can see the sides are at less of an angle, but they're still not vertical.

Now I do have to break the news to you that there's maths involved in the ultimate solution, good old Pythagoras and his theorem in fact, sorry!  The good news is, it's easy, and you can do it on the calculator on your computer :oD

Taking the 2nd example from above as a starting point, we're going to use the cut out corners method, but instead of vertical sides on the fabric we start with, we're going to angle it up to the top.  By doing this, when the right angled triangle at the side is folded round and the base is folded up, they will meet to push the front out, leaving the sides vertical.

A right angled triangle is one where the side and the base are at a 90 degree angle to each other, or thinking about a clock face, the big hand (side) is at 12 and the small hand (base) is at 3.  We need a right angle between the side and the base to keep the base flat otherwise you would end up with a rocking pouch!

Because we're using a right angled triangle, to work out how to get the height and the depth we want we need to use Pythagoras:

In the diagram above:

a = the height we want the pouch to be + seam allowance top and bottom
b = half the depth we want the pouch to be (as there is a front and back) + 1/2 seam allowance
c = ?

Pythagoras says:

a2 + b2 = c2

So since I've decided that I want a height of 7 1/2", a depth of 4 1/2" and a seam allowance of 1/2" I get:

a = 7 1/2 + 1/2 + 1/2 = 8 1/2
b = 2 1/4 + 1/4 = 2 1/2

c2 = (8 1/2)2 + (2 1/2)2 = 78 1/2  (that is, c2 = 72.25 + 6.25 = 78.5)

c = √(78 1/2) = 8.86 which we round to the nearest 1/8 inch, making 8 7/8  (8.875)

(** For those who have forgotten a few math things: c2 means c multiplied by c. When you know the value for c2  you then have to take the square root of that value to get c and you can do that by putting the value of c2 into your calculator and hitting the square root button that looks like this:  √. The calculator will tell you the square root and you can check by multiplying that number times itself to see if you get the c2 number you started with.)

Are you still with me?  I hope so...

In the diagram above, there are some unlabelled measurements, so for the depth to work correctly the bit below c must be the same length as b, ie 2 1/2".  The width of the pouch is entirely up to you, but I went for 10".

If you are going to create your pattern using paper and pencil, I suggest you draw the triangle sides on a separate piece of paper with side a vertical and side b horizontal to ensure you have your right angle, then you can connect the 2 and double check that c is correct by measuring it.  Once you're happy that you have all the right measurements, cut them out, and tape them to the main body.  Gridded paper, like graph paper, can be really useful for this kind of thing.

If you want to use a program like Illustrator to create your pattern, as I did, I suggest you also draw your triangle with a vertical and b horizontal, joined by c, then group the lines together and rotate the shape until c is vertical.  Using the grid functions available on most drawing programs should help ensure that your measurements are correct, and that you have managed to get c vertical

Here are a few step by step shots to show you how the construction works:

Front of pouch piece cut out

Having added the zips, I'm now constructing the pouch.  Note that the cut out bits are unstitched

Stitching the corners closed

Finished front on (that left side is vertical, honest!)

Side on shot

This actually allowed me to tick off one of my Q3 finishes, so thanks for helping me out with that Leanne!

And thank you Katy

Don't forget to link up your Q3 finishes - the Q3 post-quarter link is open here and it will close at midnight MST, October 7, 2013. And if you still have some UFOs I hope you will join us for Q4 of the FAL, Q4 FAL lists can be posted starting on October 8.


  1. What a great idea. I am trying to pretend that it really doesn't look complicated!

  2. Love it! But I can hear screaming coming from from others around the globe!!!

  3. Great tutorial - thank you for working it all out for us. No screaming here!

  4. I'm trying to pretend I understand this! Maybe when I'm not so tired... Pretty pouch though!

  5. Yes! Katy you genius, I was trying to figure this out yesterday! Of course, my theories didn't involve algebra but me and Pythagoras? We're good pals. Sorted!

  6. Well that a tute you don't want to lose. How incredibly helpful!!! I knew I liked that Katy Girl for a reason!

  7. I've never made a pouch with this shape - thank you Katy and Leanne!

  8. You are SOOO clever
    Thanks for teaching me something useful!

  9. *worships those who are not scared of maths and angles*

  10. The Pythagorean theorem is actually "a^2 + b^2 = c^2" -- that may have been what you did in your calculations (I didn't check) but not what's listed in your tutorial.

    (Hugs from a geometry teacher)

  11. La, la, la.I can't hear you..........

  12. The p theory is pretty well known and it's neat to see how it works in this bag. I would love to get a ready-made pattern with about 50 different shapes and sizes--call me lazy. And just get at it. I keep thinking there must be an easier way to draft these shapes. It seems like the 2 lines with the same measurement are the key.

  13. Why doesn't "the geometry teacher" do what comment #16 suggests--give us a chart of inches and measurements for a bunch of sizes--that would make my day.


Thank you for stopping to comment and I will try to respond individually to to you if you have an email attached to your profile. If you don't hear back from me you might be a no-reply commenter and I encourage you to change that.