Flow and grade logic
Peak flow uses roof area x rainfall intensity x 0.01039 x capture factor. Target fall uses extension length x target slope x 12.
Roof discharge path
Estimate peak downspout flow, short-burst volume, and target fall for an extension or drain line.
Peak flow uses roof area x rainfall intensity x 0.01039 x capture factor. Target fall uses extension length x target slope x 12.
A 600 sq ft roof section in a 2.5 in/hr burst produces about 14.8 gpm at 95% capture. Over 20 ft, a 2% target slope needs about 4.8 inches of fall.
Use the roof area that feeds one downspout, not the whole house. That keeps the flow and grade check close to the problem corner you are trying to fix.
Slope helps, but the line still needs cleanouts, discharge space, and enough downstream capacity. If the yard stays wet, pair this with a French drain or storage page.
Questions
Downspout lines care about how fast water arrives during the burst, not only the total inches over a whole storm.
That is a common failure path. A flat or reverse-pitched line can hold water, clog, or freeze.
Shorten the run, change the outlet, switch to surface conveyance, or combine the line with storage before the outlet.