Methodology
All tools share one engine. Intermediate values are not rounded. Purchase quantities always round up.
Pitch
multiplier = √(1 + (rise ÷ run)²)
degrees = atan(rise ÷ run) × 180 ÷ π
percent = (rise ÷ run) × 100
rafter length = √(run² + rise²)
Area and materials
roof area = projected footprint × pitch multiplier
adjusted area = roof area × (1 + waste rate)
squares = adjusted area ÷ 100
bundles = ceil(adjusted area ÷ coverage per bundle)
Assumptions
Phase 1 treats a simple, uniform pitch. Complex roofs with hips, valleys, and dormers should be measured plane by plane. Results are planning estimates, not structural design or a final material order.