Spherical Dome Calculator
Enter the base diameter and dome rise (height). This tool calculates the sphere radius, curved surface area, footprint area, and enclosed volume for a spherical cap dome.
How this dome calculator works
This calculator models a spherical cap, which is one of the most common dome shapes used in architecture, greenhouses, observatories, tanks, and small geodesic builds. A spherical cap is defined by two practical measurements: the base diameter and the rise (vertical height from base plane to top of the dome).
From those inputs, we can derive the parent sphere radius and all the core geometry values needed for planning: material coverage, floor footprint, and enclosed air volume.
Formulas used
- Base radius: a = d / 2
- Sphere radius: R = (a² + h²) / (2h)
- Curved surface area (shell): Acurved = 2πRh
- Base area (footprint): Abase = πa²
- Total area (curved + base): Atotal = Acurved + Abase
- Enclosed volume: V = (πh(3a² + h²)) / 6
When to use these outputs
Curved surface area
Use this value when estimating cladding, membrane, insulation, paint, waterproofing, or panel coverage. If your supplier gives cost per square meter (or square foot), multiply by this number.
Base area
Useful for site layout, slab estimation, flooring, and interior usable footprint comparisons.
Volume
Volume helps estimate HVAC sizing, airflow requirements, heating/cooling loads, and acoustic behavior.
Practical tips for better estimates
- Add a waste factor (typically 5% to 15%) for cuts, overlap, and installation errors.
- For framed domes, structural members can slightly reduce internal usable volume.
- If openings (doors/windows/skylights) are known, subtract their area from shell material totals.
- Keep all measurements in the same unit system to avoid conversion mistakes.
Example scenario
Suppose you plan a dome with a 10 m base diameter and 3 m rise. The calculator provides the parent sphere radius, shell area, and internal volume in seconds. That lets you quickly compare material options, budget impact, and HVAC implications before final design.
Frequently asked questions
Is this a geodesic dome calculator?
Not exactly. This tool calculates the geometry of a smooth spherical cap. Geodesic domes approximate this shape with triangular facets and require frequency/strut calculations, which are a separate step.
Can I use feet instead of meters?
Yes. Select your preferred unit before calculating. Outputs will be labeled in the same unit family (square and cubic units included).
Why does shell cost use curved area only?
Most dome shell materials apply to the curved surface. The base is often slab, deck, or another construction system, so it is reported separately.