Hemisphere Calculator
Find radius, diameter, base area, surface area, and volume from any one hemisphere measurement
By Drew Budwin · Last updated July 2026 · Methodology
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Results
Radius
Diameter
Base Circumference
Base Area
Curved Surface Area
Total Surface Area
Volume
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Hemisphere Calculator Formula
Volume of a hemisphere:
V = (2/3) × π × r³
r = radius.
Curved (dome) surface area:
A = 2 × π × r²
r = radius.
Total surface area (dome + base):
A = 3 × π × r²
r = radius.
Base (equator plane) area:
A = π × r²
r = radius.
Radius from volume:
r = ∛(3V / 2π)
V = volume.
How to Use This Calculator
- Choose what you already know: Radius, Diameter, Base Circumference, Base Area, Curved Surface Area, Total Surface Area, or Volume.
- Enter your known value in the field.
- Click Calculate to see all seven hemisphere measurements instantly.
Frequently Asked Questions
Can I find the radius of a hemisphere from its volume?
Yes. Rearranging V = (2/3)πr³ gives r = ∛(3V / 2π). Enter the volume in the Volume tab and this calculator solves for the radius, diameter, surface areas, and base measurements at once.
What is the difference between curved and total surface area?
The curved (dome) surface area is 2πr², just the rounded top. The total surface area is 3πr², which adds the flat circular base of πr². This calculator reports both, plus the base area on its own, so you can pick whichever your problem needs.
What is the flat face of a hemisphere?
The flat circular base is the equator plane where the sphere was sliced. It has radius r and area πr², and its perimeter is the base circumference, 2πr. Enter either one to solve for every other measurement.
What units does this calculator use?
This calculator is unit-agnostic. If you enter the radius in feet, the volume is in cubic feet (ft³) and the surface areas in square feet (ft²). Use whatever unit matches your measurement.
How is a hemisphere different from a sphere?
A hemisphere is exactly half a sphere, sliced through its center. Its volume is (2/3)πr³, half the sphere's volume of (4/3)πr³. For the full sphere, use the sphere calculator.
Where are hemisphere calculations used in real life?
Hemisphere volumes and surface areas come up when sizing dome-shaped structures, mixing bowls, igloo interiors, planetarium domes, and pressure-vessel end caps.
How is a hemisphere used in dome structure calculations?
A dome modeled as a hemisphere has interior volume (2/3)πr³ and a floor area of πr². For a dome with a 5-meter radius, the interior is about 261.8 m³ with a 78.5 m² floor. The volume-to-footprint ratio improves as radius increases, so large domes are more space-efficient.
Further Reading
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