How this calculator works
Split each half-span into a lower and upper horizontal run. Each pitch gives its segment rise and rafter length. Eaves extend the lower slope; gable overhangs extend both roof faces along the building. The attic volume integrates the piecewise-linear roof profile across the interior width and excludes overhangs. The half-octagon construction gives lower and upper slopes of 67.5 and 22.5 degrees.
Formula
lower rise = lower run x tan(lower angle); upper run = width/2 - lower run; upper rise = upper run x tan(upper angle); roof area = 2 x extended roof length x (extended lower rafter + upper rafter).
Worked example
For a 6 m span with both segments at 45 degrees, total rise is 3 m regardless of break position. At 10 m building length without overhang, roof area is 84.853 m2 and geometric attic volume is 90 m3.
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Frequently asked questions
Does the half-circle method make a curved roof?
No. Four straight equal segments follow points on a semicircle, giving a regular half-octagon profile.
Is attic volume usable living volume?
No. It includes low headroom and excludes framing, floor thickness and access constraints.
Can this select rafter sizes?
No. It provides geometry and covering area. Loads, connections, thrust and member sizes require structural design.