Learn the ins and outs of triangles. Half-square triangles and quarter-square triangles look the same when they're finished, but they are cut differently and behave differently when being sewn. Learn which to use and when, as well as the "magic number" for determining what size to cut triangles. Once you've mastered triangles, it's easy to create your own patterns.  

Part 1: What to use and what size to cut:

Half-square triangles and quarter-square triangles look the same when they are finished, but they are cut differently and behave differently when being sewn. The names are logical. A half-square triangle is made by dividing a square in half by cutting it once diagonally. A quarter-square triangle is made by dividing a square in quarters by cutting it twice diagonally. This tutorial explains the difference between the two triangles and how to know the size of square to cut. Part 2 teaches how to use the "magic number" to find unknown measurements for triangles and triangle-based block.

The triangles are the same shape, but how do you know which to use? The key lies in the weave of the fabric. The short sides of half-square triangles are cut on the straight grain of the fabric and won't stretch very much when you sew. The long side is cut on the bias, which easily stretches out of shape.

The short sides of quarter-square triangles are cut on the bias and stretch easily. The long side is cut on the straight grain and is more stable. The bias and straight-grain sides of half-square triangles are the opposite of those of quarter-square triangles

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It is usually easiest to sew the bias sides of the triangles first, keeping the straight-grain sides on the outside of the sewn unit. Often these triangles are sewn together to make a square. A general rule is to cut the square in the same way it will be sewn together. If the finished pieced square is made from two triangles, stat with half-square triangles. If the finished pieced square is made from four triangles, start with quarter-square triangles.

If the units are not square, think about how to position the straight-grain sides on the outside of the unit. In the case of a flying-gees unit, the corner triangles are half-square triangles and the middle triangle is a quarter-square triangle. This positioning allows you to sew the bias edges first. Sew carefully without pulling on the fabric. The stitching stabilizes the bias edges so they will no longer stretch out of shape.

When you cut a square you have to add 1/4" seam allowances all the way around the finished square. This makes the cut size of a square or rectangle 1/2" larger than the finished size.

Triangles are a little different. To make a half-square triangle, begin by cutting a square 1/8" larger than the desired finished size of the short side of the triangle. This gives a 1/4" seam allowance that adds the extra amount needed for the diagonal seam. Then cut the square in half diagonally, from corner to corner. Each square yields two half-square triangles.

To make a quarter-square triangle, begin by cutting a square 1 1/4" larger than the desired finished size of the long edge of the triangle. This gives a 1/4" seam allowance that adds the extra amount needed for the two diagonal seams. Then cut the square twice diagonally, from corner to corner. Each square yields four quarter-square triangles.

Part 2: The Magic Number

You will need a basic calculator and the magic number 1,414. (Note: always start with the finished measurements, when you know the finished sizes, then you can use the numbers in the Part One to determine the cut sizes.)

If you know the length of the short side of a half-or quarter-square triangle, multiply it by the magic number 1,414. This gives you the length of the long side of the triangle. For example, if the short side is 2 1/2" x 1,414=3,535*. Round this number to the nearest 1/8". 3,535* is pretty close to 3 1/2" (Fraction/decimal conversions are at the end of this section.)

If you know the length of the long side of this type of triangle, divide it by the magic number 1,414. This gives you the length of the sort sides of the triangle. For example if the long side is 2 1/2", the short side is 2 1/2" divided by 1,414 = 1.768". That is pretty close to 1 3/4".

If you find that you are getting confused about when to multiply and when to divide by 1,414, it's actually logical. To find the measurement for the longer side of a triangle, multiply you need a larger number. To determine the shorter side, divide you need a smaller number. The magic number gives you all sorts of power fro designing quilts. Take a square in a square.

Let's say you want the finished size of this unit to be 6". How do you know what size pieces to cut? First determine the finished sizes of the center square and corner triangles. 

What is the finished size of a corner triangle? Each short side is half the width of the finished unit. In this example each sort side would measure 3" finished.

What size is the center square? Notice each edge of the center square is sewn to the long edge of a corner triangle. The two measurements are the same. Once you determine the long side of the corner triangle, you know the size of the center square. Multiply 3" (the short side of the corner triangle) by the magic number 1,414.

3" x 1,414= 4,242". That is pretty close to 4 1/4*. The finished size of the center square is 4 1/4".

Add 1/2" for a seam allowance, and you will know to cut the center square 4 3/4".

Now that you know the size, next decide what type of triangles should go on the outside. Which type will put the straight-grain edges on the outside of the square in a square unit? That is the short side of the triangle, so use half-square triangles. The short side finishes to 3", so add 1/8" for the seam allowances, and you will know to cut square 3 1/8". Remember, each beginning square makes two half-square triangles. You need four triangles for each square in a square unit, so you'll need to cut two 3 1/8" squares for every square in a square unit. 

Maybe you want to fussy cut the center square to finish at 4". How do you know what size the corner triangles should be? The same reasoning applies. You know the size of the center square and thus the long edge of the corner triangle is 4". Dived 4" by 1,414 to find the short edge of the triangle: 4" divided by 1,414=2.82". That is not very close to a quarter-inch measurement, but it is close to 1/8". (1/8" is the same as .875.) The short sides of the corner triangles would finish at 2 1/8". The finished square in a square unit would be twice that measurement, or 5 3/4".

The magic number, 1,414, opens u a whole world of quilt design. Experiment a bit. Try designing you own quilt blocks. Soon you will be completely comfortable working with half-square and quarter-square triangles.