Enter the roof area draining to one gutter, the roof pitch, your local rainfall intensity, and a downspout size to see how many downspouts that run needs and how much the gutter should drop over its length.
Estimate only — local rainfall intensity and gutter profile vary; check your jurisdiction's drainage table.
We multiply the roof's plan area by a small slope factor — a steeper roof throws rain into the gutter faster, so it behaves like a larger flat area. Standard practice allows about 1 square inch of downspout cross-section per 100 square feet of roof at a 4 in/hr design storm, scaled up for higher rainfall intensity. Dividing the required downspout area by your chosen downspout's cross-section gives the count, with a minimum of one.
Gutters are pitched about 1/4 inch of fall for every 10 feet of run toward a downspout, so a 40-foot run drops roughly an inch end to end. Long runs are usually split to drain both ways from a high point in the middle, which halves the effective length each downspout has to carry.
As a rule of thumb, one downspout per 600–800 square feet of roof for a 3x4 in downspout. High-rainfall areas or small 2x3 downspouts need one every 300–400 square feet.
About 1/4 inch of drop per 10 feet of run toward the downspout. Too little and water stands; too much and the gutter looks crooked and can overshoot in heavy rain.
Split any run over about 40 feet so it drains both directions from a center high point. That keeps each downspout's load and the required slope reasonable.