The circle is, in my humble opinion, the Queen of the geometric shapes. Don't get me wrong; I like all those squares, rectangles, triangles, octagons, and whatnot; but the circle is the coolest of the bunch: smooth and pretty and endlessly useful. However, trying to draw a perfect circle without a pattern is a challenge, and figuring out the proper size of an opening into which a circle can be inserted requires working with Pi (or **π**), which is not the delicious kind you can eat with a bit of ice cream. We're here today to help you with the steps you've forgotten since high school geometry class (*or maybe never learned because you were too busy passing notes with Susan Ellery!*). We'll show you the parts of a circle, how wide to cut fabric to fit a circle, and how to draw a circle without a pattern. We've also included a handy conversion from decimals to inches, which is necessary when working with Pi.

# The parts of a circle

Let's start with remembering what all the parts of a circle are called and how Pi (**π)** fits into the mix.

**Radius**: the distance from the center of the circle to the outside edge

**Diameter**: the distance across a circle through its center point

**Circumference**: the distance around the outer edge of a circle

**π or Pi:*** *the name given to the ratio of a circle's circumference to its diameter, expressed as the decimal 3.14

# How wide to cut fabric to fit a circle

If you know the **diameter** of your circle, you can use a standard formula to figure out the *width* of the fabric cut needed to make a tube. That width is the **circumference **of the circle that will be inserted into the tube (we have a great step-by-step tutorial on how to insert a circle into a tube)**.**

The formula: **3.14 (π)** x **diameter** = **circumference**

** Example:** You want a finished 12" diameter base (a 12" diameter circle) in a duffle bag.

**3.14** x **12 inches** = **37.68 inches**

*(This works with the metric system as well: 3.14 x 30 cm = 94.2 cm)*

An important step many people miss at this point is forgetting to add extra (*to both pieces*) for the seam allowance. If you use a standard ½" seam allowance, you need to **add 1" **to the **diameter **of your circle ( the diameter increases by double the seam allowance) *and* **1" to the width** of your fabric (½" for both sides of the seam allowance). In our example, that means:

The circle should be 13" in diameter.

The fabric should be 38.68 " in width

The height of your fabric cut is variable and dependent on your project. For example, a tall duffle bag might be 30" in height whereas a shorter bucket might be only 10".

# Converting a Decimal to a US Ruler Measurement

If you are using Pi, remember it always returns a decimal number. If you already deal with the metric system, you rock – no conversion necessary.

For those of us in the world of inches, you need to find a yardage conversion.

In our example we have 38.68 inches. *Harumph!* The table below will give you a close-enough ruler match.

The decimal .68 is closest to .63 or ⅝". We can use 38⅝" as the width of the fabric piece you are cutting for your tube.

# How to Draw a Circle

If you have a supply of large compasses, you're in luck, and can easily draw yourself all sizes of circles. But you can also easily make your own compass to draw a circle.

To start, you need to know how big you want your circle (the diameter). For our ongoing example, we want a 13" diameter circle

To draw a circle you need to know its radius. As you learned above in the first section, the radius is one half of the diameter. In our example, one half of 13" is 6½".

## The full circle method

- Use a sheet of lightweight paper (graph or pattern paper works well) that is at least 1" larger all around than the circle you want to draw.
- Cut a piece of string about 4" - 5" longer than your radius. We used a 10" length of string.
- Tie one end of the string to a short pencil.
- Place the point of the pencil toward the outer edge of the paper with enough room from the edge to make a full sweep.
- Measure from where the point of the pencil touches the paper backwards by the length of the radius (in this case 6½").
- Pin directly through the string into the paper at that exact point.
- Keeping the string taut, draw a perfect circle using your homemade compass.

## The folded quarters method

- Again, start with a square of lightweight paper at least 1" larger than the circle you want to draw.
- Fold the paper into quarters. Make sure your original square is even and true! Position the paper with its folded edges along the bottom and left side and the open edges along the top and right side.
- Place a see-through ruler at the exact center of the bottom left corner of your folded square. Swing the ruler from the top to the bottom of the square, like a pendulum or compass, measuring and marking a dot at the 6½" point in three to four spots. You are creating a semi-circle arc. Make sure the end of the ruler at the corner point doesn't shift position.
- Cut along the arc through all the layers and unfold the finished 13" circle. You can now use this paper pattern to cut your fabric circle.

With your spiffy new circle, you can now sew the side seam in the main fabric cut. Then pin the base to the resulting tube and sew the tube to the circle using a ½" seam allowance. The result is a 12" diameter finished base.

As mentioned above, for more on this technique, see our tutorial: How to Insert a Flat Circle Into a Tube.

Good evening,

As a math teacher, I find this facinating! I will use your creation of circle and all the vocabulary needed to understand the directions as a great learning tool. Thanks for sharing.

P.S. I'm beginning to get the urge to create a duffle bag:)

@Karl - I've never ever gotten a compliment from a math teacher. Thank you. You've made my day. And... you could totally make a duffle!!

I can't seem to get your circle tutorial to work. thanks

@kimlisa - there are several parts to the information above. If you can give us a bit more detail about which part you are having trouble with, we can try to help fruther.

Thanks for helping me to do my project. It's easy andsimple!

You're welcome - it really is easy.

great tutorial

@Judith - Thanks, so glad you found it helpful.

If this is the case shouldn't 38.68/3.14 = 13?

I believe that the diamater including seam allowance * 3.14 should equal the width of the fabric you want to mach with your circle. So, a 13" circle should fit a fabric width of 40.42".

@Andrew - The formula works with the

finishedcircle. That is always the first step when creating a pattern, you then add the seam allowance to your pieces as the second step. You are no longer working with the formula at that point because your seam allowance "disappears" in constuction. It's like switching from 2D to 3D in a sense. The seam allowance for the circle is actually taken up in theheightof the bag. So, when figuring, work with your desired finished diameter, use the formula to get the circumference, and then add your seam allowances.For adding fabric to a known size circle, I take the diameter and mutliply it by 3.2 and add seam allowance. That way it generally comes out to an easy size and with fabric fits perfectly with no stretching.

@Alice - Thanks for adding your expertise.

What a marvelous tutorial on working with circles within the world of sewing! Thank you, Liz! Unfortunately, the question that brought me here in the first place remains unanswered .

I am

(much emphasis on the trying part) to make a side flap for a messenger bag that I am customizing. The dimensions for the flap are 9 1/2" high by 10" wide and I would like to make a semi-circular (is radius cut also the correct term is sewing?) cut so the corners of the flap are rounded rather than square.tryingIt is at this point I run into trouble.

My question is:How do I determine what the 'best' (most appropriate?) size is for these cuts?Can somebody out there help me?

Please!@Frank - There isn't a "magic formula" for rounding corners. They can be a small/tight curve or a large radius, depending on the look you're after. It might be easiest to cut a paper panel the same dimensions as your flap and then hand draw the approximate look you want. Once it's looking how you want, check around the house for something to trace to give you the same curve. We often use a small glass for tight curves and a bowl or plate for larger curves. You can also use a compass. Trace it using the widest points of your circle to get the smoothest arc.

How do u draw a 1/2 circle?

@Annie - the very easiest option is to make your circle and cut it in half. If using the arc method, you could also simply draw a horizontal baseline and then just draw a half circle from the baseline.

THANK YOU SO MUCH for explaining this so thoroughly. Had I known sewing was going to become a passion of mine I swear I would've paid attention in high school math class. This tutorial has been life changing for me, creatively speaking. I am going to go make some more bucket totes and other circle inspired vessels.

@Misha - You are very welcome! May you have many circles in your life for 2017

Plz can u help me on cutting a perfect circle out of a paper (whether a rectangle or square) without using any thing, I mean only hands. Nothing else, no coin, no scissors, no pencils, nothing. I am actaully applying for an arts university which requires this kind of skill to be used in their entry ecxamination.

The closest you can probably get is by folding a square smaller and smaller and then into triangle - then rip around the bottom in an curve. Not sure this would be "perfect," but if the paper was really thin and you could fold it many times, the smaller the final triangle the better the circle shape will be

@ Ibrahim - I'm so sorry, but we've never tried to cut patterns without any tools at all. Other than starting with what you are sure is a true square and then creatively folding to set creases to cut along... I can't think of any truly good ways to do it. And, I'm not sure why you'd really want to do that anyway

I have never seen any instructions for inserting a flat circle into another piece of flat, unseamed fabric. I would love to make a modern quilt with circles inset into a quilt top, but am a little intimiidated to even try. Ideas?

@ Mommanonna - You still need a seam allowance on both the flat piece and the inset piece to sew them together. One trick to try would be use a line of basting stitches as your folding guide. Let's say your seam allowance is 1/4". Cut your circle "hole" 1/4" smaller than your finished size, then run a basting stitch around the cut edge at 1/4". Cut your circle "fill" 1/4" bigger than your desired finished size, then run a basting stitch 1/4" in from the cut edge all around. Fold along the basting seam on both the hole and the filler. You'll ned to clip to get it to fold smoothly (you might want to try a 1/2"seam rather than 1/4" to make it easier). Press. Set the filler into the hole. Align the basting and the seam allowances and stitch. If it's a big quilt top, you'll have to wrangle the fabric around the holes, but I think it would be possible. Try practicing on an inexpensive sheet or muslin to see how it comes out.

Nicely organized article...will be a great future reference point! Thank you for sharing the "magic formulas" for sewing with circles.

@ izateacher - glad you found it helpful!

Once again, I see that's much easier to live in the "metric world" ;) But sometimes, I like to use my ruler with Inches when I do patchwork... :)

Greetings from Germany

Filippa

@ Filippa - Ha!! Life in the metric world!

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