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 depict a perfect circle without a design is a challenge, and figuring out the proper size of an opening into which a circle tin can be inserted requires working with Pi (or π), which is non the succulent kind you tin can eat with a flake of ice cream. We're here today to assist you lot with the steps you've forgotten since high school geometry class (or mayhap never learned considering yous were too busy passing notes with Susan Ellery!). We'll bear witness y'all the parts of a circumvolve, how wide to cut fabric to fit a circumvolve, 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 kickoff with remembering what all the parts of a circle are chosen and how Pi (π) fits into the mix.

Radius: the altitude from the center of the circle to the outside edge

Diameter: the distance across a circle through its center betoken

Circumference: the distance around the outer edge of a circle

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

How wide to cut textile to fit a circle

If you lot know the diameter of your circle, you can use a standard formula to effigy out the width of the cloth cut needed to brand a tube. That width is the circumference of the circle that volition exist inserted into the tube (nosotros have a great stride-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 purse.

3.fourteen 10 12 inches = 37.68 inches

(This works with the metric arrangement as well: three.14 10 30 cm = 94.ii cm)

An important step many people miss at this point is forgetting to add extra (to both pieces) for the seam allowance. If you apply a standard ½" seam allowance, you demand to add ane″ 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 case, that means:

The circle should start as xiii″ in diameter.

The fabric should be 38.68″ in width

The height of your fabric cutting is variable and dependent on your project. For case, a tall duffle handbag might be 30″ in height whereas a shorter bucket might be but 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 united states in the world of inches, you lot need to detect a yardage conversion.

In our example we take 38.68 inches. Harumph! The tabular array below will give you lot a close-enough ruler match.

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

How to Draw a Circle

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

To start, you demand to know how big you lot want your circumvolve (the diameter). For our ongoing example, we desire a 13″ diameter circle

To describe a circumvolve you lot demand to know its radius. As yous learned in a higher place 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

  1. Use a sheet of lightweight paper (graph or pattern newspaper works well) that is at least ane″ larger all around than the circumvolve you desire to depict.
  2. Cutting a piece of cord about 4″ – 5″ longer than your radius. We used a 10″ length of string.
  3. Tie one end of the string to a curt pencil.
  4. Identify the betoken of the pencil toward the outer edge of the paper with enough room from the edge to make a full sweep.
  5. Mensurate from where the point of the pencil touches the paper backwards past the length of the radius (in this example 6½").
  6. Pivot straight through the string into the paper at that verbal point.
  7. Keeping the string taut, draw a perfect circumvolve using your homemade compass.

The folded quarters method

  1. Again, start with a foursquare of lightweight newspaper at to the lowest degree one″ larger than the circle you desire to describe.
  2. Fold the paper into quarters. Brand 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 tiptop and right side.
  3. Place a run into-through ruler at the exact center of the lesser 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 marker a dot at the half dozen½" point in three to 4 spots. Yous are creating a semi-circle arc. Make sure the cease of the ruler at the corner indicate doesn't shift position.
  4. Cut forth the arc through all the layers and unfold the finished xiii″ circle. You can now use this paper pattern to cut your fabric circumvolve.

With your spiffy new circumvolve, you can now sew the side seam in the main fabric cut. Then pivot the base of operations to the resulting tube and sew the tube to the circle using a ½" seam assart. The result is a 12″ bore finished base.

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