Hemisphere Volume Calculator
A hemisphere with a radius of 6 has a volume of about 452.39, exactly half the matching sphere's 904.78. This hemisphere volume calculator uses V = (2/3) pi r cubed and also reports the curved surface area, the flat base area, and the total surface area, the three measures that trip people up because a hemisphere gains a circular face a sphere never had.
Quick answer
A hemisphere is half a sphere, cut through the center, so its volume is half the sphere formula.
Volume
452.3893
Curved surface area
226.1947
Base area
113.0973
Total surface area
339.292
What this tells you
- •A hemisphere is half a sphere, cut through the center, so its volume is half the sphere formula.
- •Volume = (2/3) x pi x radius cubed.
- •The curved (dome) surface is 2 pi r squared, half the sphere's skin.
- •Total surface area adds the flat circular base: 3 pi r squared altogether.
How to Use
- 1Enter the radius of the hemisphere.
- 2Read the volume as the main result.
- 3Check the curved, base, and total surface areas below.
- 4For a dome measured across its widest point, halve that diameter to get the radius first.
How It Works
Formula
V = (2/3) pi r^3, total surface = 3 pi r^2A full sphere has volume (4/3) pi r cubed, and slicing it in half through the center halves that to (2/3) pi r cubed. For radius 6, that is (2/3) x pi x 216 = 452.39. The surface splits into the dome, 2 pi r squared, plus the newly exposed circular base, pi r squared, giving 3 pi r squared in total.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Radius 6 hemisphere
Two thirds of pi times 216. The total surface area is 339.29.
A 10 cm mixing bowl (radius 5 cm)
A hemispherical bowl of radius 5 cm holds about 262 ml when filled to the brim.
Dome with a 12 m span (radius 6 m)
The dome skin alone is 2 pi r squared, what you would paint or tile.
Hemisphere Volumes by Radius
Volume and total surface area for common radii.
| Radius | Volume | Total surface area |
|---|---|---|
| 1 | 2.09 | 9.42 |
| 2 | 16.76 | 37.70 |
| 3 | 56.55 | 84.82 |
| 5 | 261.80 | 235.62 |
| 6 | 452.39 | 339.29 |
| 10 | 2094.40 | 942.48 |
Common mistakes
- Halving the sphere's surface area for the total. Cutting a sphere exposes a new circular face, so the total is 3 pi r squared, not 2 pi r squared.
- Using the diameter as the radius. A dome spanning 12 meters has a radius of 6, and cubing the wrong one is an 8x volume error.
- Forgetting the cube. Volume grows with r cubed, so doubling the radius gives 8 times the volume, not 2 times.