Hemisphere Calculator
Volume261.799
Total Surface Area235.619
Curved Surface Area157.080
A hemisphere is exactly half of a sphere, the shape you get by slicing a ball through its center. This calculator takes a single radius and returns the hemisphere's volume, its curved (dome) surface area, and its total surface area including the flat circular base. It is handy for domes, bowls, tanks, and any half-spherical object you need to size or fill.
Formula
V = (2/3) * pi * r^3; curved area = 2 * pi * r^2; total area = 3 * pi * r^2
- V
- Volume of the hemisphere (cubic units)
- r
- Radius of the hemisphere (linear units)
- pi
- The constant approximately 3.14159
How it works
- Enter the radius of the hemisphere. It must be a positive number expressed in your chosen length unit; all outputs use that same unit.
- The calculator applies the half-sphere formulas: two-thirds pi r-cubed for volume, two pi r-squared for the curved surface, and three pi r-squared for the total surface (curved dome plus the flat circular base).
- Results are rounded to three decimal places and shown for volume, curved surface area, and total surface area so you can pick the figure your project needs.
Worked example
Compute the volume and surface areas of a hemisphere with radius 6.
- Volume: (2/3) x pi x 6^3 = (2/3) x pi x 216 = 144 pi, about 452.389.
- Curved surface: 2 x pi x 6^2 = 72 pi, about 226.195.
- Total surface: 3 x pi x 6^2 = 108 pi, about 339.292.
Volume about 452.389, curved surface area about 226.195, and total surface area about 339.292.
Frequently asked questions
- What is the difference between curved and total surface area?
- The curved surface area covers only the rounded dome (2 pi r squared). The total surface area adds the flat circular base (pi r squared), giving 3 pi r squared, which is what you need when the bottom is also a real surface.
- How does a hemisphere relate to a full sphere?
- A hemisphere is half a sphere, so its volume is exactly half the sphere volume of (4/3) pi r cubed, which gives (2/3) pi r cubed. Its curved area is also half the sphere surface area of 4 pi r squared.
- What units does the calculator use?
- It is unit-agnostic. Whatever length unit you use for the radius determines the units of the output: linear units give squared units for area and cubed units for volume.
- Can I enter a diameter instead of a radius?
- The calculator expects the radius. If you only know the diameter, divide it by two first, then enter that value as the radius.