Rain gutters' primary function is to move water away from structures. The U.S. Department of Housing and Urban Development (HUD) in its summary of recommendations for constructing moisture resistant homes specifically includes designing roof drainage systems based upon gutter sizing, downspout sizing, roof pitch, and the intensity of local rains (See Reference 2). Although gutters and downspouts form the backbone of common roof drainage systems, there is much more to be considered when designing those systems.
Download Moisture Resistant Homes from the link in Resources.
Scroll to the Rainfall Intensity Map (Figure 11) on page 22 and determine the design rainfall intensity based upon the building's location.
Calculate the square footage of roof on one side of the building by multiplying the length of the roof by the distance from the fascia to the ridge.
Find the nearest square footage of one side of the roof under the applicable Design Rainfall Intensity column in Table 6 - Maximum Allowable Tributary Roof Plan Area on page 23. This will narrow down the gutter size and type that can be used in your area, for the size of your roof. Roofs that are less than 5:12 pitch will use one of the Suggested Downspouts for that area of the roof.
Multiply the square footage of the one side of the roof by 0.85 if the pitch is equal to or greater than 5:12. Divide the result into the square footage of one side of the roof. Round up this result to determine the number of additional downspouts needed for the steeper roof.