What is hemisphere volume?
V = (2/3)πr³, half the volume of a full sphere.
Hemisphere Calculator
Get volume and surface measures for a solid hemisphere from its radius.
Enter radius
Provide a positive radius for the hemisphere.
About this calculator
How to use Hemisphere Calculator, plus the formulas and logic behind the results.
Tool description
A hemisphere is half a sphere. Volume is half the sphere volume; curved area is half the sphere surface; total area also includes the flat circular base.
How to use
- Enter a positive radius.
- Select Calculate.
- Read volume, curved surface, and total surface.
- Compare with the related full-sphere values if needed.
Formulas & reference
Volume = (2/3)πr³Curved surface = 2πr²Total surface = 3πr²
Hemisphere facts
- Volume is half of (4/3)πr³
- Curved area is half of 4πr²
- Base area πr² added for total
- Radius must be positive
Calculation logic
Uses π = M_PI with the standard solid-hemisphere formulas including the base disk in total surface area.
Total surface assumes a closed solid hemisphere (curved face + circular base).
Hemisphere Calculator FAQ
Common questions about this calculator and how to use the results.
What is curved surface area?
The dome only: 2πr².
What is total surface area?
Curved area plus the flat circular base: 3πr².
Is the base included?
Yes in total surface; no in curved surface.
Can r be zero?
Zero is rejected; enter a positive radius.
How does this compare to a sphere?
Volume and curved area are half of the corresponding sphere measures.