Quantities
Raking wall / trapezoid
- where
- net wall area (m²)
- length (m)
- heights at each end (m)
- openings (m²)
Explain this equation
This gives the net area of a raking wall: one with two vertical ends of different heights and a straight sloping top, such as a wall stepping up a garden slope or under a lean-to roof.
l is the horizontal length between the two ends. h₁ and h₂ are the heights at each end. A_o is the total area of any openings, subtracted at the end.
Because the top runs in a straight line, the average height of the wall is exactly halfway between the two end heights, (h₁ + h₂) / 2. Multiplying that average by the length gives the area, the same as a rectangle at the mean height. The 2 is just that averaging.
A 5 m wall rising from 1 m to 2 m has an average height of 1.5 m, so 7.5 m². If both ends were 2 m it would be 10 m², a plain rectangle.
Watch out: if the top is stepped, curved or changes slope part way, split the wall into sections and work each one separately.
Measure a straight sloping top between two vertical ends.
Enter your values to see the result.
Good to know
For a stepped or irregular wall, calculate each section separately.
Sources
- Geometry / arithmetic
Estimates are not design approval or British Standards compliance checks. Structural arch, retaining-wall, wind, foundation, lintel and masonry-capacity design are not performed. Use the project engineer’s specification.