Rectangular Downspout diameters are sized according to the roof area they drain.
The following is the rule of thumb used in the industry:
2x3 inch downspout for 600 sq. ft. of roof
3x4 inch downspout for 1200 sq. ft. of roof
4x5 inch downspout for 2000 sq. ft. of roof
The typical downspout size for a 5” K-style gutter is 2x3 inches, but 3x4 inches is preferable because it is less likely to become clogged and is easier to clean out.