The circumvolve is, in my humble opinion, the Queen of the geometric shapes. Don't get me wrong; I similar all those squares, rectangles, triangles, octagons, and whatnot; just the circle is the coolest of the bunch: smooth and pretty and endlessly useful. Notwithstanding, trying to describe a perfect circle without a design 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 tin can consume with a fleck of ice foam. We're hither today to help you lot with the steps yous'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 textile 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

Allow's outset 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

Bore: the distance beyond a circumvolve through its center point

Circumference: the altitude 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 every bit the decimal three.14

How broad to cut material to fit a circle

If you know the diameter of your circle, you tin use a standard formula to effigy 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 footstep-past-step tutorial on how to insert a circle into a tube).

The formula: 3.xiv (π) x diameter = circumference

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

3.14 x 12 inches = 37.68 inches

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

An important step many people miss at this indicate is forgetting to add extra (to both pieces) for the seam allowance. If y'all use a standard ½" seam allowance, y'all demand to add together 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 case, that means:

The circle should commencement as 13″ in diameter.

The fabric should be 38.68″ in width

The height of your fabric cut is variable and dependent on your projection. For instance, a tall duffle handbag might be thirty″ in height whereas a shorter saucepan might be but x″.

Converting a Decimal to a US Ruler Measurement

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

For those of the states in the world of inches, you demand to find a yardage conversion.

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

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

How to Draw a Circle

If you have a supply of big compasses, you're in luck, and can easily draw yourself all sizes of circles. Only you can also easily brand your ain compass to depict a circumvolve.

To start, you demand to know how large y'all 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 higher up in the start department, the radius is one one-half of the diameter. In our instance, i half of xiii″ is half-dozen½".

The full circumvolve method

  1. Use a sail of lightweight paper (graph or design paper works well) that is at to the lowest degree one″ larger all around than the circle you want to draw.
  2. Cut a piece of string near 4″ – five″ longer than your radius. We used a 10″ length of string.
  3. Tie i end of the string to a short pencil.
  4. Place the point of the pencil toward the outer edge of the paper with enough room from the edge to make a total sweep.
  5. Measure from where the point of the pencil touches the paper backwards by the length of the radius (in this instance 6½").
  6. Pin directly through the cord into the paper at that exact bespeak.
  7. Keeping the string taut, draw a perfect circumvolve using your homemade compass.

The folded quarters method

  1. Again, showtime with a square of lightweight paper at least 1″ larger than the circle you lot want to depict.
  2. Fold the paper into quarters. Make certain your original square is even and true! Position the paper with its folded edges forth the bottom and left side and the open edges forth the top and right 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 square, like a pendulum or compass, measuring and marking a dot at the half dozen½" point in three to iv spots. You are creating a semi-circle arc. Make sure the end of the ruler at the corner bespeak doesn't shift position.
  4. Cut along the arc through all the layers and unfold the finished 13″ circle. You can now use this paper pattern to cut your cloth circle.

With your spiffy new circle, you lot tin at present stitch the side seam in the main fabric cutting. Then pin the base of operations to the resulting tube and sew the tube to the circle using a ½" seam allowance. The effect is a 12″ diameter finished base.

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