Here's a little table of cake pan sizes in inches and square inches:
Cake pan sizes, with square and circular areas
inches square circular
5 25 19.6
6 36 28.2
7 49 38.4
8 64 50.2
9 81 63.6
10 100 78.5
11 121 95.0
12 144 113.0
13 169 132.7
Columns:
- inches is the length of a side of a square, or the diameter of a circle.
- square is the area (in square inches) of a square with inches sides.
- circular is the area (in square inches) of a circle with a diameter of inches.
Example: If a recipe called for for a 9" circular pan, (63.6 sq. inches), and the only pan that was available was an 8" square pan, (64 sq. inches), that'd be a close match.
Generally substituting an n" square for an n+1" circle, for area gives a +/-10% margin of error.
Perimeters are less interesting for cake, but might be of interest with pizza crust.
Equivalent diameter circles always have 21% less perimeter than squares.
Not so for an n" square and and n+1" circle, where the perimeter percent difference increases with size. For example an 8" square pan has a 32" perimeter, a 9" circle has a 28" perimeter, a 12% difference; but the perimeter of a 9" square is 13% larger than that of a 10" circle. This perimeter percent increase gradually slows down and levels off at 21% at and above 83".