Pitch is a ratio, not an angle
Roofers write pitch as rise over a 12 inch run — 6:12, 8:12 — and almost never in degrees. The reason is practical rather than traditional: a framing square has 12 inch graduations on one leg, so a ratio against 12 can be transferred straight onto a board without a protractor. Set the square to 6 on the tongue and 12 on the blade and you have marked a 6:12 plumb cut. Degrees would need a bevel gauge and a conversion.
The conversions are all one-liners. Angle is atan(rise ÷ run), so 6:12 is 26.57°. Percent slope is rise ÷ run as a percentage, which is why the IRC describes a 2:12 roof as a "17-percent slope". And the area multiplier — the one that matters for ordering material — is √(rise² + run²) ÷ run, straight out of Pythagoras. None of these is a constant anyone publishes; they are arithmetic, which is why the table below is computed on every build rather than transcribed from another site.
One naming trap. Older carpentry usage sometimes gives "pitch" as a fraction of the whole span — a 6:12 roof over a 24 ft span was a "quarter pitch" — while "slope" meant the rise per 12. Modern US practice uses pitch and slope interchangeably for rise per 12, and that is what this page means throughout. If you are reading an old set of plans, check which convention they use before cutting anything.
Why the overhang is longer than you measured
A rafter tail is the most reliable place to lose an inch. An overhang is specified horizontally — "16 inch eaves" means the roof projects 16 inches past the wall in plan — but the tail itself runs down the slope, so it is longer than its own projection by exactly the pitch multiplier. At 6:12 a 16 inch overhang is 1 ft 5 7/8 in of rafter. Cut 16 inches and your fascia lands short.
That is why the rafter mode above reports three numbers instead of one: the bearing-to-ridge length, the overhang along the slope, and the total. The total is what the board has to be before you make the plumb cut at the ridge, the seat cut at the plate and the tail cut. Those cuts remove material, and the seat cut in particular shortens the effective span, so treat the total as stock length rather than a finished dimension. Deliberately, nothing here rounds up to a purchasable board length — lumberyard stock lengths are a market convention rather than a sourced constant, and rounding is a decision for whoever is holding the saw.
Ridge height is reported the same way, as the vertical distance above the bearing plate rather than above the floor or the ground. For a 24 ft gable at 6:12 that is 6 ft — half the span times the pitch, and nothing to do with the rafter length. If you need overall building height, add the plate height and subtract however much of the ridge board sits below the roof plane.
What the code cares about at low slopes
Pitch is not purely an aesthetic decision — below a certain slope, water stops running off fast enough for a lapped covering to work, and the code draws two lines. Asphalt shingles are permitted only at 2:12 or steeper (IRC R905.2.2). Between 2:12 and 4:12 they are permitted but require double underlayment, per Table R905.1.1(2) — note that this is a different section from the slope minimum, which is a distinction plenty of pages get wrong. The calculator states which side of both lines your pitch falls on.
Two caveats worth more than the check itself. The model code is a floor, not the rule in your jurisdiction: local amendments routinely add ice barrier requirements, wind classifications and inspection stages on top. And the manufacturer's installation instructions are usually a warranty condition, so where they are stricter than the code, they win. Below 2:12 you are looking at a low-slope membrane rather than shingles, which is a different trade with different numbers. How constants here get sourced and checked is on the methodology page.