Pyramid Roof Calculator

Calculate a square-base pyramid (hip) roof: surface area, four equal triangular faces and four hips meeting at a single apex.

Calculate

A pyramid roof, sometimes called a pyramid hip, sits on a square plan and rises to one apex. It has no ridge. Enter the square base side, the pitch and an equal overhang. The tool returns the sloped surface area, the area of each of the four identical triangular faces, the hip length and the total hip-cap line.

Square base, one apex, four faces

With base side S and overhang O, the eave side is Se = S + 2O. The surface area is Se² × √(1 + p²), and each of the four triangular faces is a quarter of that. Each hip runs from a corner to the apex with length (Se / 2) × √(2 + p²), and the cap line is four times the hip length because there is no ridge to add.

Its own example and cap

For a 20 ft square at 6/12 with no overhang, the area is about 447.21 sq ft, each face is about 111.8 sq ft, each hip is 15 ft and the cap line totals 60 ft. Even with a zero ridge there are four hips to cap, which the ridge cap calculator handles directly.

If your base is rectangular rather than square, use the hip roof calculator instead. This tool enforces a square base on purpose, because a rectangular plan has a ridge and is a different shape.