About the Hemisphere
What Is a Hemisphere?
A hemisphere is exactly half of a sphere, formed by cutting a sphere with a plane that passes through its center. The flat circular face where the cut is made is called the base, and the curved part is called the curved surface. Hemispheres are common three-dimensional shapes found in nature, architecture, and engineering.
Volume of a Hemisphere
Since a hemisphere is exactly half a sphere, its volume is half the volume of a sphere. The formula is V = (2/3)πr³, where r is the radius. This comes from halving the full sphere volume (4/3)πr³. The volume is measured in cubic units (cm³, m³, etc.).
Surface Area
A hemisphere has two types of surface area. The curved surface area (CSA) is the area of the dome-shaped part: CSA = 2πr². The total surface area (TSA) includes the curved surface plus the circular base: TSA = 2πr² + πr² = 3πr². It is important to specify which surface area you need for your calculations.
Relationship to the Full Sphere
Every property of a hemisphere can be derived from the corresponding sphere property. The volume is exactly half. The curved surface area is exactly half the sphere surface area. However, the total surface area of a hemisphere is NOT half the sphere surface area, because we must add the circular base that was created by the cut.
Real-World Applications
Hemispheres appear throughout nature and engineering. The Earth is divided into Northern and Southern hemispheres. Domes on buildings are hemispherical. Bowls, cups, and many containers are hemispherical. Satellite dishes use a parabolic shape derived from hemispherical geometry. In medicine, hemispherical shapes are used in prosthetics and implants.
Using This Calculator
Enter the radius of the hemisphere to instantly calculate its volume, curved surface area, total surface area, diameter, and base circumference. The interactive charts visualize the relationship between these properties, and you can download all results as a CSV file for further use.