The circle is, in my humble stance, the Queen of the geometric shapes. Don't become me wrong; I like all those squares, rectangles, triangles, octagons, and whatnot; just the circle is the coolest of the bunch: smooth and pretty and endlessly useful. Nonetheless, 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 lot can eat with a chip of water ice cream. Nosotros're hither today to assistance you lot with the steps you've forgotten since high school geometry class (or maybe never learned because you were as well busy passing notes with Susan Ellery!). We'll evidence you the parts of a circle, how wide to cutting fabric to fit a circle, and how to draw a circle without a pattern. We've as well included a handy conversion from decimals to inches, which is necessary when working with Pi.

The parts of a circle

Permit'due south start with remembering what all the parts of a circle are chosen and how Pi (π) fits into the mix.

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

Bore: the altitude across a circle through its center point

Circumference: the distance around the outer edge of a circle

π or Pi: the proper name given to the ratio of a circle'due south circumference to its diameter, expressed every bit the decimal iii.fourteen

How broad to cut fabric to fit a circle

If you know the diameter of your circumvolve, you can employ 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 volition be inserted into the tube (nosotros have a nifty footstep-by-step tutorial on how to insert a circle into a tube).

The formula: 3.14 (π) 10 diameter = circumference

Case: You lot desire 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 organization equally well: 3.14 x 30 cm = 94.2 cm)

An of import step many people miss at this point is forgetting to add together extra (to both pieces) for the seam allowance. If you use a standard ½" seam allowance, you demand to add 1″ to the diameter of your circle ( the bore 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 circumvolve should commencement as 13″ in bore.

The textile should be 38.68″ in width

The height of your fabric cutting is variable and dependent on your project. For case, a tall duffle purse might be thirty″ in height whereas a shorter bucket might be only 10″.

Converting a Decimal to a U.s.a. Ruler Measurement

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

For those of united states of america in the world of inches, y'all need to detect a yardage conversion.

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

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

How to Draw a Circumvolve

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

To starting time, you need to know how big you want your circle (the diameter). For our ongoing example, we want a thirteen″ diameter circle

To draw a circumvolve you need to know its radius. As you lot learned above in the start section, the radius is i one-half of the diameter. In our example, one half of 13″ is vi½".

The total circle method

  1. Use a sail of lightweight newspaper (graph or pattern paper works well) that is at least i″ larger all around than the circle y'all want to describe.
  2. Cut 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 short pencil.
  4. Identify the indicate of the pencil toward the outer edge of the newspaper with enough room from the border to make a full sweep.
  5. Measure out from where the signal of the pencil touches the newspaper backwards past the length of the radius (in this case half dozen½").
  6. Pivot directly through the string into the paper at that exact indicate.
  7. Keeping the cord taut, draw a perfect circumvolve using your bootleg compass.

The folded quarters method

  1. Again, start with a square of lightweight paper at to the lowest degree one″ larger than the circle you want to depict.
  2. 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 up edges along the top and right side.
  3. Place a see-through ruler at the exact center of the lesser left corner of your folded square. Swing the ruler from the pinnacle to the bottom of the square, like a pendulum or compass, measuring and mark a dot at the vi½" indicate in three to 4 spots. You are creating a semi-circle arc. Make certain the end of the ruler at the corner point doesn't shift position.
  4. Cutting along the arc through all the layers and unfold the finished 13″ circle. You can now use this paper pattern to cut your cloth circumvolve.

With your spiffy new circumvolve, you can now sew the side seam in the main cloth cut. So pin the base to the resulting tube and sew the tube to the circumvolve using a ½" seam allowance. The result is a 12″ diameter finished base of operations.

Every bit mentioned to a higher place, for more than on this technique, see our tutorial: How to Insert a Apartment Circle Into a Tube.