Arches & curves
Curved wall / ring volume
- where
- plan area of the ring segment (m²)
- inside radius (m)
- radial thickness (mm)
- angle (degrees)
- gross volume (m³)
- height (m)
Explain this equation
This gives the plan area and gross volume of a curved wall that forms part of a ring, from its inside radius, thickness, angle and height.
R is the inside radius in metres and t is the radial thickness of the wall in mm. φ is the angle of the curve in degrees. A is the plan area of that part of the ring and V is the volume. The calculator also gives the length along the centreline of the wall.
The plan area is a big circle of radius R + t minus a small one of radius R, which is π[(R + t)² − R²]. The fraction φ/360 takes just the part of the ring you want. The thickness is divided by 1000 to convert mm to metres. Multiplying by the height h gives the volume.
A 215 mm wall with a 2 m inside radius, over 180° and 1 m high, has a plan area of about 1.42 m² and a volume of about 1.42 m³.
Watch out: openings are not deducted, and this does not check stability.
Calculate an annular sector in plan and its gross wall volume.
Enter your values to see the result.
Good to know
Inside radius, radial thickness and vertical height. Excludes openings. No stability or retaining-wall design is performed.
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.