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 non the succulent kind you can eat with a bit of ice cream. We're here today to assistance you with the steps y'all've forgotten since high school geometry class (or maybe never learned because you were also busy passing notes with Susan Ellery!). We'll show y'all the parts of a circle, how wide to cut textile to fit a circle, and how to draw a circle without a blueprint. We've too 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 middle of the circle to the outside edge

Diameter: the altitude across a circle through its center point

Circumference: the distance around the outer border of a circle

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

How wide to cut fabric to fit a circumvolve

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

The formula: 3.fourteen (π) x bore = circumference

Example: Yous want a finished 12″ diameter base (a 12″ diameter circumvolve) in a duffle bag.

iii.fourteen x 12 inches = 37.68 inches

(This works with the metric organization too: three.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 yous use a standard ½" seam allowance, y'all need to add 1″ to the diameter of your circle ( the diameter increases by double the seam allowance)and ane″ to the width of your material (½" for both sides of the seam allowance). In our example, that means:

The circle should offset as 13″ in diameter.

The material should be 38.68″ in width

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

Converting a Decimal to a US Ruler Measurement

If you are using Pi, remember it ever 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 lot need to find a yardage conversion.

In our instance we take 38.68 inches. Harumph! The table below will requite you a close-enough ruler friction 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 Describe a Circle

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

To commencement, you need to know how large y'all want your circle (the diameter). For our ongoing instance, we desire a 13″ diameter circle

To draw a circumvolve y'all need to know its radius. Every bit you learned above in the first section, the radius is one half of the diameter. In our example, one half of 13″ is half dozen½".

The full circumvolve method

  1. Utilise a sheet of lightweight paper (graph or design newspaper works well) that is at least 1″ larger all around than the circle you want to describe.
  2. Cut a piece of string nearly four″ – 5″ longer than your radius. We used a 10″ length of string.
  3. Tie ane cease of the string to a short pencil.
  4. Place the point of the pencil toward the outer edge of the newspaper with plenty room from the edge to brand a full sweep.
  5. Measure from where the point of the pencil touches the paper backwards by the length of the radius (in this case six½").
  6. Pin directly through the cord into the paper at that exact point.
  7. Keeping the string taut, draw a perfect circle using your homemade compass.

The folded quarters method

  1. Again, start with a square of lightweight newspaper at least 1″ larger than the circumvolve you want to draw.
  2. Fold the paper into quarters. Brand sure your original foursquare is even and truthful! Position the paper with its folded edges along the lesser and left side and the open edges along the top and right side.
  3. Place a run into-through ruler at the exact center of the lesser left corner of your folded foursquare. Swing the ruler from the pinnacle to the bottom of the foursquare, like a pendulum or compass, measuring and marking a dot at the 6½" betoken in three to four spots. You are creating a semi-circumvolve arc. Make sure the end of the ruler at the corner betoken doesn't shift position.
  4. Cut along the arc through all the layers and unfold the finished thirteen″ circle. You lot can now use this paper pattern to cutting your textile circle.

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

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