Hemisphere Calculator
Calculate the volume and surface areas of a hemisphere.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Hemisphere Calculator
This tool calculates all key measurements of a hemisphere from the radius.
- Enter the radius. Type a positive number.
- View the results. Volume, total surface area, curved surface area, and base area update automatically.
- Copy or share. Use the buttons to save or share your result.
About the Hemisphere
A hemisphere is half of a sphere, cut by a plane through its center. The volume is (2/3) * pi * r^3, exactly half the volume of a full sphere. The curved surface area is 2 * pi * r^2 (half the sphere's surface), and the flat circular base adds pi * r^2, giving a total surface area of 3 * pi * r^2. Hemispheres appear in architecture (domes), geography (Earth's hemispheres), and engineering.
Frequently Asked Questions
What is the volume formula for a hemisphere?
Volume = (2/3) * pi * r^3. This is exactly half the volume of a sphere with the same radius.
Does the total surface area include the base?
Yes. The total surface area includes the curved dome surface (2 * pi * r^2) plus the flat circular base (pi * r^2), totaling 3 * pi * r^2.
How is a hemisphere different from a half-sphere?
They are the same thing. A hemisphere is the mathematical term for exactly half of a sphere, divided by a plane through the center.