The code's flattest gutter is five times steeper than yours
This is the most useful thing on the page and almost nobody says it. The gutter trade hangs to a quarter inch of fall per 10 feet — that is 0.025 inches per foot. IPC Table 1106.6, which is where the published gpm capacities come from, tabulates 4, 5 and 6 inch gutters at one slope only: an eighth of an inch per foot. That is exactly five times steeper than trade practice.
The table does carry a flatter column, a sixteenth per foot, but only for 8 and 10 inch gutters — and even that is two and a half times the trade maximum. So there is no row in the code table describing a residential gutter hung the way residential gutters are actually hung.
That does not make the table useless, and it does not mean your gutters are illegal. Slope and capacity are answering different questions: the trade slope exists to stop standing water and silt, while the table is a hydraulic flow limit. But it does mean the published capacity is an upper bound for your install rather than a promise, and a gutter sized right at the limit will overflow before the number says it should. The calculator flags it when your entered fall is flatter than the tabulated slope, which for a normal install is always.
Why there is no rainfall default here
The rainfall field starts blank and stays blank until you fill it. That is deliberate, and it is the same decision this site made about topsoil density: where a number is genuinely local and getting it wrong is expensive, a stored "typical" value does more harm than an empty box.
Design rainfall intensity in the US runs from roughly 2 inches per hour in the Pacific Northwest to over 9 on the Gulf Coast — a factor of four or more. A national default would undersize gutters across the entire South and oversize them across the Northwest, and the user would have no way of knowing which had happened. The authoritative figure is the 100-year, 1-hour intensity from NOAA Atlas 14, which the plumbing code itself defers to, and it takes about a minute to look up. There is a test in this repo that fails the build if anyone ever adds a rainfall preset to the data file.
Leave it blank and everything else still works — the length, sections, hangers, fall and downspout layout are all independent of rainfall. Only the size check needs it.
Design area is not the roof area
A pitched roof has more surface than footprint, so the instinct is to use the true sloped area for drainage. Every published roof-drainage reference tells you not to. The design factors are lower than geometry: a 12 in 12 roof is exactly 1.4142 times its plan area but designs at 1.30; a 9 to 11 in 12 band designs at 1.20 against a true 1.36 at the top of that range.
The reason is stated plainly in the source — rain does not fall perpendicular to a steep roof except in a driving wind, so "use of the true area of a pitched roof often leads to oversizing of gutters, downspouts, and drains." The divergence widens as pitch increases, which the factors mirror: at 3 in 12 the design factor is about 3% under geometry, at 9 to 11 in 12 it is nearly 12% under. A test in this repo asserts that every factor sits below the true multiplier for the steepest pitch in its band, so nobody can later "fix" the table to match geometry.
If you need the sloped area itself — for shingles rather than drainage — the roof pitch calculator gives the true multiplier, and the roofing shingles calculator works in squares off it. Do not use those figures here.
The downspout everyone buys is undersized
The 2 × 3 inch downspout is what home centres stock for houses. It is 6 square inches of cross-section, and the sheet-metal reference this page draws on says outright that "downspouts of less than 7.00 sq in. cross section should not be used except for small areas such as porches and canopies." The standard residential downspout is below the standard residential minimum.
A 3 × 4 inch is 12 square inches, double the area, and in practice the difference shows up less in capacity than in blockage — twice the cross-section is a great deal more than twice as tolerant of a wad of wet leaves at the elbow. On most houses the downspout count is set by layout rather than by flow anyway, so the upgrade buys reliability rather than a smaller number.
One more thing the published allowances make clear: the roof area a downspout serves per square inch of cross-section rises with diameter — 911 sq ft per sq in at 3 inches, 1,400 at 6. A bigger pipe runs proportionally fuller and with less wall friction, so two small downspouts are not equal to one of twice the area. While you are up there, the soffit calculator covers the ventilation side of the same eave.