Instructional: How to make a Quarter Circle template with a straight ruler

This method is helpful for drawing circles of uncommon widths, or whenever you need a circular curve but have no circular ruler.  To jump ahead, here is a picture of the tool I made to draw the curves in this template.

Both pieces of my template, the 'pie' and the 'crust', overlapped to make a full square with seam allowances.

You will need:

• At least one piece of paper big enough for your quarter circle.  
• A pencil with a sharp point
• Scissors
• A ruler
• A pin
• Thick cardboard that's bigger than your circle (corrugated is good)
• Sticky tape (optional)*

To make:

1. Draw two squares that are the width of your chosen quarter circles.  (Having trouble making a square corner?  See **) 

My squares are 4" wide. (This would make 8" circles.)  You don't have to put seam allowances on these yet.  I did, but to remind me of my pivot corners without marking the square itself. 

Two 4" squares ready for quarter circles

2. Cut out a strip of paper that's at least an inch longer than your squares.  Mine is 6" long. 

3. Rule a line down the strip and mark a zero point near one end.  Measure your square's length from that point, as well as a seam allowance before and beyond that length.  My seam allowance is a quarter inch (6mm), so my marks were at 4", 3.75" and 4.25" respectively.

My completed paper compass.  First hole: Pie seam allowance. 2nd hole: Circle arc.
3rd hole: Crust seam allowance. 4th hole: zero, the pivot point.

If you want to use sticky tape, put a strip on the back to reinforce the paper.

Use a pin to put holes in the measured points.  Make the 'seam & allowance' ones big enough to take the pencil tip. (I used a darning needle for this.)

4. Place your paper on your cardboard.  Take the pin and put it through the strip of paper at the zero point.  Now put it exactly through a pivot corner, pinning the strip and paper to the cardboard. (See pic below)

5. Short version: You're going to use the first and second holes (the top two) to mark two arcs on one square (making the pie piece) and the second and third holes to mark arcs on the other square (making the crust piece).   

Long version:
 

5.a  Poke your pencil through the hole for your circle edge (the middle of the three holes) and a draw corner-to-corner arc on your square, using the strip like a compass.  Here are both my squares with their quarter circles drawn.

Two quarter circles.  Note the pin is stuck through the cardboard.

Choose one to be your 'pie' piece - the quarter circle part - and the other to be the 'crust'.

5.b  On your Pie piece, pin the zero point to the same corner as before and use the outer pencil hole to mark your seam allowance arc.

5.c  On your other square (the 'crust' piece): again, pin the zero point to the same pivot point as before.  Use the inner pencil hole to mark a seam allowance inside (below) the quarter circle edge.

The seam allowances marked on both pieces.

6.  Mark a seam allowances on the corners. Using the same pivot point helps keep track of the pieces.  In the picture below, that's
- the lower and left edges of the top square for the pie, and
- the upper and right edges of the bottom square for the crust.

Seam allowance added to the crust piece (bottom square).

7.  Cut out your template pieces along the seam allowance lines. All done!

Both pieces cut and ready to go.

* I know in the US it's call cellotape, and such, but in Australia we call it sticky tape.  Coz it's sticky and it's tape. 
** If you only have a straight ruler, with no grid or right angle, it can be hard to make a perfectly straight square. The corner of another piece of paper can be a good guide.  However, a piece of firm paper (not wrapping paper, which can warp) folded twice - once to create a straight line and again in exactly the opposite direction - can make a good reinforced right angle to guide you.