Roof geometry, area, and coordination

Planning workflow

1. Set the footprint, overhang, roof type, and each plane's slope.
2. Locate ridges, hips, valleys, penetrations, low-slope transitions, and drainage paths.
3. Compare the roof with upper-floor walls, stairs, attic use, mechanical routes, and site exposure.
4. Obtain structural, wind, snow, fire, moisture, and product review.

Formula or decision logic

For a simple plane, sloped area = horizontal plan area x sqrt(1 + (rise/run)^2). Complex roofs should sum independently clipped planes instead of applying one global pitch factor. Waste is added afterward and should reflect layout complexity and the selected product, not a hidden constant.

Worked planning example

A 30 by 40 ft gable roof with no overhang has 1,200 sq ft of horizontal plan area. At 6:12, the slope factor is sqrt(1 + 0.5^2) = 1.118, giving about 1,342 sq ft before waste. Valleys, overhangs, openings, starter, ridge, and flashing remain separate.

Limitations and review boundary

• This formula does not design framing or connections.
• Wind, snow, drainage, wildfire, and coastal exposure are site-specific.
• Manufacturer and adopted-code requirements control the finished roof.

Continue in construction systems