Hemisphere Calculator
Volume and surface area of a hemisphere.
Half a sphere — volume and total surface (curved + flat).
How the Math Works
The Hemisphere Calculator uses two key formulas: Volume (V) = (2/3)πr³ and Surface Area (SA) = 3πr². The volume formula derives from halving the sphere's volume (4/3 πr³), representing the space inside a hemisphere. The surface area includes both the curved outer layer (2πr²) and the flat circular base (πr²), totaling 3πr². These equations rely on the radius (r) as input, with π approximated as 3.14159 for precise calculations.
Practical Applications
This calculator is essential in engineering and architecture for designing hemispherical structures like domes, storage tanks, or acoustic shells. Manufacturers use it to determine material quantities for hemispherical components, such as pressure vessels or sports balls. In physics, it helps model phenomena involving half-spheres, like fluid dynamics in curved containers or celestial hemispheres in astronomy.
Day-to-Day Use
You might use this calculator when working on DIY projects involving dome-shaped objects, like estimating paint for a hemispherical ceiling or materials for a garden cloche. It also applies to everyday items like measuring the capacity of a bowl or determining the surface area of a planetarium dome. Hobbyists building model rockets or geodesic domes can quickly compute dimensions for their projects using this tool.
Worked example
Radius 5 → volume 261.8.
FAQ
Dome only?
The curved area alone is 2πr².