Volume of a Hemisphere Calculator
Find the volume and all surface areas of a hemisphere — a half-sphere with a flat circular base. Enter the radius to get volume (2/3)πr³, curved surface area 2πr², flat base area πr², and total surface area 3πr².
units
V = (2/3)πr³ — exactly half the volume of a full sphere
V = ²⁄₃πr³
261.7994 units³- 1
r³
5 × 5 × 5 = 125 - 2
Volume
²⁄₃ × π × 125 = 261.7994Exactly half the full sphere volume (4/3)πr³.
How does this calculator work?
Hemisphere volume V = (2/3)πr³ ≈ 2.094 r³ — exactly half the sphere volume (4/3)πr³. Curved surface area = 2πr² ≈ 6.283 r²; flat circular base = πr² ≈ 3.14159 r²; total surface area = 3πr² ≈ 9.425 r². Enter the radius in any consistent unit — the volume result is in the same unit cubed.
Formula
How this is calculated
A hemisphere is exactly half a sphere, cut along a great circle. Its volume is therefore half the sphere volume: V = (1/2) × (4/3)πr³ = (2/3)πr³. This follows from the symmetric cut through the centre — both halves are congruent and each holds exactly half the total volume.
The surface of a hemisphere has two parts. The curved dome area equals half the full sphere surface: (1/2) × 4πr² = 2πr². The flat circular base has area πr². Total surface area = 2πr² + πr² = 3πr². Many textbook problems ask only for the "curved surface area" — that means 2πr² without the base. This calculator reports both separately.
The formula assumes a perfect mathematical hemisphere — a half-ball with a flat circular base of radius r. For engineering applications (domes, bowls, tanks), the shape may deviate from the ideal. Enter the internal radius to find the liquid capacity of a hemispherical bowl; the answer in cubic units can be converted to litres by dividing cm³ by 1000.
Frequently asked questions
A hemisphere's volume is exactly half the full sphere's volume: V_hemi = (2/3)πr³ = (1/2) × (4/3)πr³. The cut is along a great circle, dividing the sphere into two equal halves.
A hemisphere has two surfaces: the dome (curved surface, area = 2πr²) and the flat circular base (area = πr²). Total = 2πr² + πr² = 3πr². If a problem asks only for "curved surface area" it means 2πr² — the base is excluded.
Divide the diameter by 2 to get the radius (r = d ÷ 2), then enter that value. Because the formula cubes the radius, using the diameter directly would give a volume 8× too large.
Also known as
TG we-Calculate Editorial Team. (2026). Volume of a Hemisphere Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/volume-of-hemisphere-calculator
TG we-Calculate Editorial Team. "Volume of a Hemisphere Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/volume-of-hemisphere-calculator.
TG we-Calculate Editorial Team, "Volume of a Hemisphere Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/volume-of-hemisphere-calculator
@misc{wecalculate_volume_of_hemisphere_calculator, title = {Volume of a Hemisphere Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/volume-of-hemisphere-calculator}}, year = {2026}, note = {TG we-Calculate} }
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