Hemisphere Calculator

The volume of a hemisphere is V = (2/3)πr³, where r is the radius. This is exactly half the volume of a full sphere (which is 4/3πr³). For example, a hemisphere with radius 5 cm has a volume of approximately 261.80 cm³. See also our find Hypotenuse (c) with 45-45-90 Triangle Calculator.

The curved surface area (CSA) is just the dome-shaped top of the hemisphere, calculated as 2πr². The total surface area (TSA) includes both the curved dome and the flat circular base, calculated as 3πr². The base area alone is πr².

A hemisphere is exactly half of a sphere, created by cutting a sphere along a plane through its center. It has one flat circular face (the base) and one curved surface (the dome). The term comes from Greek — 'hemi' means half.

Rearrange the volume formula V = (2/3)πr³ to solve for r: r = ∛(3V / 2π). Simply select 'Given Volume' in the calculator, enter your volume value, and the radius and all other properties will be calculated automatically. You might also find our use the Pentagon Calculator useful.

First divide the diameter by 2 to get the radius (r = d/2), then apply the volume formula V = (2/3)πr³. You can also select 'Given Diameter' in this calculator and enter the diameter directly — it handles the conversion for you.

A hemisphere has two faces: one flat circular face (the base) and one curved face (the dome). It also has one curved edge where the dome meets the base circle, and no vertices (corners).

You can use any consistent unit of length — centimeters, meters, millimeters, inches, feet, etc. Volume results will be in cubic units (e.g. cm³) and surface area results will be in square units (e.g. cm²). Just make sure all inputs use the same unit.

This calculator computes properties of a solid hemisphere. For a hollow hemisphere (like a bowl), you would need to calculate the difference between the outer and inner hemispheres separately — using the outer radius and inner radius — and subtract the results as needed.