A hemisphere is a sphere sliced in half by a flat plane through its center.
About this calculator
A hemisphere is a sphere sliced in half by a flat plane through its center. Volume is (2/3)πr³ — exactly half of a full sphere. The curved outer area is 2πr². If the flat circular base is exposed (like a dome sitting on the ground), add πr² for total surface 3πr².
Domes, bowl interiors, and planet hemispheres use this shape. A radius-5 hemisphere holds about 261.8 cubic units and has curved area 157.1 square units.
Do not confuse with a spherical cap (a slice that is not through the center). For full spheres use the [[sphere]] calculator; for combined pill shapes see [[capsule]]. Link to [[volume]] and [[surface-area]] when comparing several 3D forms.
Common uses
- Dome or igloo interior volume from radius
- Half-sphere bowl capacity in litres (cm inputs)
- Paint area for a curved dome shell plus flat floor
- Compare hemisphere vs full sphere material usage
- Planet or globe half-surface geography estimates
Frequently asked questions
What is the volume of a hemisphere with radius 5?
V = (2/3)π × 125 ≈ 261.80 cubic units. Curved surface = 2π × 25 ≈ 157.08 square units. With flat base, total area ≈ 235.62 square units.
Why is curved area 2πr² and not half of 4πr²?
Half of 4πr² is 2πr² — they match. The curved part is exactly half the full sphere surface.
Is a bowl a hemisphere?
Only if the inner surface is a perfect half-sphere and you measure from the center of the full sphere. Many bowls are shallower spherical caps.
How does this relate to a full sphere?
Double the hemisphere volume to recover (4/3)πr³. Double the curved area to get the full 4πr² sphere surface.