The "quick and dirty" math is the diagonal is (approximately) 1.4 times the side of a square. Or if you want a "very approximate" guesstimate -1.5 times.

Example:

A four inch (finished size) square - the "exact" diagonal length is (4 times the square root of two) = 5.656854249...
A close enough approximation (4 x 1.4) = 5.6. Which is close enough for most preliminary design work.
A "quick and dirty" approximation - side of a square times 1.5 -> 4 x 1.5 = 6

But if you are going to get your calculator out, may as well use "side of a square" times 1.414

Graph paper, pencil, and ERASER - for me - are very useful tools.

Wow bearisgray, thanks for the math. Definitely going to bookmark this page for future reference. :)