Bowls, domes, half-ball moulds and some tanks are hemispheres. Their volume is half that of a sphere, and also two-thirds of the cylinder that just contains them.
How to use the Volume of a Hemisphere Calculator
- Radius r
- Every result field is editable: type into Volume or any other result and Radius r plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Enter the radius or type into any other field to work backwards.
What each result means
- Volume = 2÷3×pi×[Radius r]^3
- Base area = pi×[Radius r]^2
- Curved (cap) surface area = 2×pi×[Radius r]^2
- Total surface area = 3×pi×[Radius r]^2
- Diameter = 2×[Radius r]
- Surface to volume ratio = 9÷(2×[Radius r])
Example values
How the main result changes when Radius r changes and everything else stays at the example values above:
| Radius r (cm) | Volume (cm³) |
|---|---|
| 2.5 | 32.7249 |
| 3.75 | 110.4466 |
| 5 | 261.7994 |
| 6.25 | 511.3269 |
| 7.5 | 883.5729 |
| 10 | 2,094.3951 |
Formula
V = 2/3·π·r³
Worked example
Inputs — Radius r: 5 cm.
Results — Volume = 261.799388 cm³; Base area = 78.539816 cm²; Curved (cap) surface area = 157.079633 cm²; Total surface area = 235.619449 cm²; Diameter = 10 cm; Surface to volume ratio = 0.9 cm⁻¹.
Key terms
- Volume
- The space inside a solid.
Frequently asked questions
What is the volume of a hemispherical bowl with radius 10 cm?
2/3·π·1,000 ≈ 2,094 cm³ ≈ 2.09 L.
How is it related to a cylinder?
It is 2/3 of the cylinder with the same radius and height r.
How do I find the radius from the volume?
r = ∛(3V/(2π)).
What is the volume in litres?
Choose L in the unit menu.