A hemisphere is exactly half a sphere, the shape of a dome, a bowl, a half-round tank end or the cap on top of a silo, and this calculator gives you its full geometry from a single measurement: the radius. Enter the radius and it returns the volume enclosed, the curved surface area of the rounded part, the total surface area including the flat circular base, and the area of that base, all in matching units. Each of those answers earns its place. The volume tells you the capacity of a dome roof, a hemispherical bowl or the rounded end of a pressure vessel. The curved surface area is what you need for cladding, painting, coating or working out heat loss across the dome. The total surface area adds the base for when the flat face matters too, and the base area is simply the circle the hemisphere sits on. Hemispheres appear constantly in architecture, engineering, manufacturing and design, from planetarium domes and stadium roofs to gauges, lenses, tank caps and decorative features, yet the formulas are awkward enough to get wrong in a hurry because they involve cubing and squaring the radius and carrying pi through every step. This tool removes that friction and recalculates instantly as you adjust the radius, so you can size a dome to a target volume or compare the material needed for different sizes at a glance. Whether you are an engineer sizing a vessel, an architect costing a dome, a maker planning a project or a student checking homework, it gives a fast, accurate answer. The exact formulas and a worked example are explained clearly below.
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452.3893
volume (cubic units)
Curved surface226.1947
Total surface339.292
Base area113.0973
How it works
The volume of a hemisphere is two thirds of pi times the radius cubed, half the volume of a full sphere. The curved surface area is two pi times the radius squared. The flat circular base has area pi times the radius squared, so the total surface area, curved plus base, is three pi times the radius squared.
Worked example
For a radius of 6, the volume is two thirds times pi times 216, about 452.4 cubic units. The curved surface is two pi times 36, about 226.2. The base area is pi times 36, about 113.1, and the total surface area is three pi times 36, about 339.3.
