Pitch to angle and slope, rafter length, and true sloped roof area — plus the attic volume and net free ventilation area those numbers actually feed into.
Built and verified by Kyle Lorinos, PE — HVAC design engineer. See the method →
Roof
A "6/12" roof rises 6 inches for every 12 inches of horizontal run.
Measured across the span, perpendicular to the ridge.
Advanced — overhang & ventilation
Adds to roof area but not to attic floor area.
Hip volume is approximated as a truncated form; gable is exact.
Geometry
Attic volume & ventilation
Method — and why the ventilation numbers are here
Angle and slope.angle = arctan(rise / 12). Slope percent is rise / 12 × 100. A 6/12 roof is 26.565° and a 50 % slope — note that 45° is 12/12, or 100 %, not 50 %. That confusion is common.
Rafter length is the hypotenuse over the horizontal run: √(run² + rise²), measured from the outside of the wall to the ridge, before any ridge-board or plumb-cut deduction.
True roof area is the plan area multiplied by √(144 + pitch²) / 12. For 6/12 that factor is 1.1180 — a roof over a 1,200 ft² footprint has 1,342 ft² of actual surface. Estimating from footprint alone understates the roof by that margin.
Attic volume for a gable is the exact prism: ½ × width × ridge height × length. Hip roofs are approximated, since the true solid depends on hip run and ridge length.
Ventilation net free area follows IRC R806.2: minimum net free ventilating area is 1/150 of the vented space. The 1/300 exception applies only when both conditions hold — in Climate Zones 6, 7 and 8 a Class I or II vapor retarder is installed on the warm-in-winter side of the ceiling, and not less than 40 % nor more than 50 % of the required area sits in the upper portion of the attic, no more than 3 ft below the ridge, with the balance in the bottom third.
Net free area is not the same as the physical size of the vent. A louvre with insect screen typically delivers only a fraction of its gross opening as net free area, and the manufacturer publishes that figure. Size to the published NFA, not to the hole.
Why a roof calculator computes ventilation: pitch sets attic volume, and attic floor area sets required NFA. Both feed the summer attic temperature that drives duct and ceiling loads. If ductwork runs through that attic, this geometry is a load calculation input, not roofing trivia.