Calculating quilt block sizes is one of the least enjoyable parts of being a quilter. You could rely on published patterns for your patch sizes, but if you want to stray into something original, you're stuck with complicated math. If you're going to make a quilt including Square-in-a-Square or any variation such as Bow Tie or Snowball, skip the complex triangle measuring and go with a quick-piecing trick using only squares. Popularized by Mary Ellen Hopkins, this method eliminates the need for sewing on bias edges while creating perfect points.
Calculate your inner square patch by taking the finished size of the inner patch and adding 1/2 inch in each direction for seam allowances. If you want the inner square to measure 6 inches across, cut 6 1/2-inch squares.
Divide the inner square finished size in half, then add a seam allowance, to find the size of the smaller corner squares. For the original 6-inch inner square, you would divide it by two to reach 3 inches, then add seam allowances to end up with 3 1/2-inch squares.
Cut one larger square and four smaller squares for each completed Square-in-a-Square quilt block.
Pin one smaller square on each corner of a larger square with the right sides together. Stitch a diagonal line across each smaller square, sewing across each corner of the larger square. Cut off the excess outside fabric and open up the squares to reveal the finished block plus seam allowance of 1/4 inch all around.
Mark the diagonal lines with a fabric marking pencil for more accurate piecing.