DOME DESIGNER
Draw a dome, switch units, and check it stands up. Give only a diameter and the dotted lines show the stable height range - give only a height and they show the stable diameter range.
Only the base is set - dotted lines show the stable height range (min / max), solid line is the most likely rise.
- Radius
- 10 m
- Circumference
- 62.8 m
- Area
- 314 m²
- Radius of curvature
- 10.3 m
- Surface distance
- 13.8 m
- Surface area
- 515 m²
- Volume
- 1,525 m³
- Rise : span
- 0.400 (1:2.5)
Stability is estimated from the rise-to-span ratio of a thin spherical shell: a stable pure-compression dome lies between about 1:8 (shallow, the minimum before base thrust gets excessive) and 1:2 (a full hemisphere). The most-likely figure uses a rise-to-span of 0.4. These are guideline figures, not a substitute for structural engineering.
About the dome calculator
A dome is modelled here as a spherical cap. From the base diameter (span) and the rise (height) the tool derives the radius of curvature, the curved surface area, the surface distance from crown to base edge, the enclosed volume and the floor area - the same figures used by spherical dome builders - and renders the profile to scale on the canvas. Every value and the drawing update instantly when you change a number or switch units between metres, feet, yards, kilometres and miles.
Not sure how tall a dome should be? Enter just the diameter and the designer fills in the structurally stable height range with dotted guides, based on the rise-to-span ratio that keeps a thin shell working in compression. Know the height but not the footprint? Enter only the height to see the stable diameter range instead.
Frequently asked questions
How do I calculate the radius of curvature of a dome?
For a spherical dome with base radius r (half the diameter) and rise/height h, the radius of curvature is R = (r² + h²) / (2h). The Dome Designer computes this automatically as you type.
What is a stable height-to-diameter ratio for a dome?
A pure-compression spherical dome is generally stable between a rise-to-span ratio of about 1:8 (a shallow saucer dome, the minimum before base thrust becomes excessive) and 1:2 (a full hemisphere). A rise-to-span of roughly 0.4 is the structurally efficient sweet spot.
Can I find the stable height range if I only know the diameter?
Yes. Enter only a diameter or radius and the designer draws the most-likely dome as a solid line with dotted lines marking the minimum and maximum structurally stable heights. Enter only a height and it shows the stable diameter range instead.
What units does the dome calculator support?
You can switch the whole drawing and all results between metres, feet, yards, kilometres and miles at any time.
