The circle is, in my humble stance, the Queen of the geometric shapes. Don't get me incorrect; I like all those squares, rectangles, triangles, octagons, and whatnot; merely 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 circumvolve can be inserted requires working with Pi (or π), which is not the delicious kind you can eat with a bit of water ice foam. We're here today to assistance y'all with the steps you've forgotten since loftier school geometry course (or maybe never learned considering you were too busy passing notes with Susan Ellery!). We'll show you the parts of a circle, how wide to cut cloth to fit a circle, and how to draw a circumvolve without a pattern. Nosotros've also included a handy conversion from decimals to inches, which is necessary when working with Pi.

The parts of a circle

Let'due south first 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 border

Diameter: the distance across a circumvolve through its center indicate

Circumference: the distance around the outer border of a circumvolve

π or Pi: the name given to the ratio of a circle'south circumference to its diameter, expressed every bit the decimal 3.xiv

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 brand 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 circumvolve into a tube).

The formula: 3.14 (π) ten diameter = circumference

Example: You want a finished 12″ bore base of operations (a 12″ diameter circle) in a duffle bag.

iii.14 x 12 inches = 37.68 inches

(This works with the metric organisation every bit well: 3.14 10 30 cm = 94.2 cm)

An of import step many people miss at this point is forgetting to add extra (to both pieces) for the seam assart. If you employ a standard ½" seam allowance, y'all demand to add 1″ to the diameter of your circle ( the diameter increases by double the seam assart)and ane″ to the width of your cloth (½" for both sides of the seam allowance). In our example, that means:

The circumvolve should outset as 13″ in diameter.

The cloth should be 38.68″ in width

The pinnacle of your fabric cut is variable and dependent on your project. For example, a tall duffle handbag might exist 30″ in summit whereas a shorter bucket might be only 10″.

Converting a Decimal to a US Ruler Measurement

If yous are using Pi, recollect it always returns a decimal number. If you already bargain with the metric system, you stone –  no conversion necessary.

For those of u.s.a. in the earth of inches, you need to discover a yardage conversion.

In our example nosotros have 38.68 inches. Harumph! The tabular array below will give yous a shut-enough ruler match.

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

How to Draw a Circle

If you take a supply of large compasses, y'all're in luck, and tin hands describe yourself all sizes of circles. But you tin also easily make your ain compass to describe a circle.

To commencement, you need to know how big you want your circumvolve (the diameter). For our ongoing example, nosotros desire a 13″ diameter circle

To draw a circle y'all need to know its radius. As y'all learned above in the first section, the radius is ane half of the diameter. In our case, one one-half of thirteen″ is half-dozen½".

The full circumvolve method

  1. Use a sheet of lightweight newspaper (graph or pattern paper works well) that is at least ane″ larger all around than the circumvolve you desire to draw.
  2. Cutting a piece of string virtually iv″ – 5″ longer than your radius. We used a 10″ length of string.
  3. Tie one end of the string to a brusk pencil.
  4. Place the point of the pencil toward the outer edge of the paper with enough room from the edge to make a full sweep.
  5. Measure out from where the point of the pencil touches the paper backwards past the length of the radius (in this example vi½").
  6. Pin direct through the cord into the paper at that exact signal.
  7. Keeping the string taut, draw a perfect circle using your homemade compass.

The folded quarters method

  1. Again, starting time with a square of lightweight paper at least 1″ larger than the circle you want to draw.
  2. Fold the paper into quarters. Make sure your original square is even and true! Position the paper with its folded edges forth the bottom and left side and the open up edges along the top and correct side.
  3. Place a see-through ruler at the exact heart of the bottom left corner of your folded square. Swing the ruler from the top to the bottom of the foursquare, 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 certain the end of the ruler at the corner point doesn't shift position.
  4. Cut along the arc through all the layers and unfold the finished 13″ circle. Yous tin can now utilize this paper blueprint to cut your fabric circumvolve.

With your spiffy new circumvolve, y'all tin at present sew the side seam in the main fabric cutting. Then pin the base to the resulting tube and sew together 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 Apartment Circle Into a Tube.