Why a triangle never fills the way a rectangle does
The geometry problem rectangular panels can't solve
Solar panels are rectangles, and a triangular roof plane, common at the ends of a hip roof, has rows that get progressively shorter toward the apex. A rectangular panel grid leaves those narrowing gaps empty, since a panel can't be trimmed to a point, a shape consideration worth factoring in early if a reroof before solar project is already on the table. Most irregular roofs mix triangular, trapezoidal, and rectangular planes, and the multi-roof plane array splitter combines their counts into one system.
What this actually costs in usable area
This calculator places panels row by row from the eave, keeping each panel fully inside the plane. A small 18 by 14 foot triangle fits 4 panels and fills about 57% of its area, a 14 by 10 foot one fits just 1, and a 36 by 16 foot triangle fits 11 and fills about 69%. Trapezoids fill more because they never narrow to a point: a hip side 40 feet at the eave, 20 at the ridge, and 14 up the slope fits 18 panels, about 77%. Roof geometry is only one limit on usable area. NREL's lidar-based rooftop potential assessment found that only 26% of the total rooftop area of small buildings was suitable for PV, even though 83% of those buildings had at least one suitable location. A per-plane fit like this one is a ceiling before setbacks and obstructions, which the usable roof area calculator subtracts.
Why orientation matters even more here
Portrait versus landscape can swing the panel count on a triangular plane, because each row's width shrinks as you climb and the panel's proportions interact with that taper. No simple ratio rule picks the winner, and the better orientation changes with the plane's exact size, so this calculator tries both and reports which fits more. For the 18 by 14 foot example, portrait fits 4 panels and landscape only 3. The compact roof layout tool runs the same comparison on a rectangular plane. Orientation also changes which panels sit in shade during the day, since dormers and vents cast shadows differently across a triangular plane. The shading loss estimator works out how much output that shade costs.
Whether triangular panels are worth the added complexity
Some manufacturers make dedicated triangular and trapezoidal modules to fill these gaps, and they can improve coverage on a genuinely awkward hip or valley section. They add real cost and design complexity, so most residential installs plan around a standard rectangular layout with the packing loss built into the design. The DOE and NREL Solar Ready Buildings Planning Guide favors large contiguous unobstructed roof areas, the opposite of a roof cut into many small hip and valley planes, which is why a simpler roof shape is worth weighing during a reroof.