Hemisphere Volume Calculator
Enter a radius and read the volume, curved surface, and total surface of a half-sphere instantly — from domes and bowls to tank caps.
Three results at once
A single radius gives the volume it holds, the curved dome area, and the total surface including the flat base.
Unit-agnostic
The radius can be in any unit — the volume comes out cubed and the surface areas squared in that same unit.
What is a hemisphere volume calculator?
One radius, the whole half-sphere
A hemisphere is exactly half a sphere — a sphere sliced cleanly through its centre, leaving a domed top and a flat circular base. A hemisphere volume calculator turns the single radius measurement into the three numbers that describe that shape: how much space the dome holds, how large the curved skin is, and how large the total surface becomes once you add the flat base. The volume follows V = 2/3 × π × r³, the curved surface follows A = 2 × π × r², and the total surface is 3 × π × r². Because every formula depends only on the radius, a bowl, an igloo, a dome roof, and a hemispherical tank end all obey the same three rules.
Enter the radius and read the volume, curved surface, and total surface at once — no formula juggling required.
Cube the radius for the volume and square it for the surface areas, then scale each by its constant.
V = 2/3 × π × r³ · A = 2 × π × r² · total = 3 × π × r²The volume formula multiplies the cube of the radius by π and by 2/3 — exactly half a full sphere's 4/3, because a hemisphere is half a sphere. The curved surface squares the radius, multiplies by π, then by 2: it is half a sphere's outer skin. The total surface adds the flat circular base, π × r², on top of that dome, which turns the 2 into a 3 and gives 3 × π × r². The only value you ever change is the radius.
Suppose you have a hemisphere with a radius of 5.
Cube the radius
5³ = 5 × 5 × 5 = 125.
Find the volume
2/3 × π × 125 = 261.799388 cubic units.
Find the curved and total surface
2 × π × 5² = 157.079633 square units for the dome; adding the base π × 5² gives 3 × π × 5² = 235.619449 square units total.
The three numbers answer three different questions, and knowing which one you need is the whole game. The volume is the half-sphere's contents: it is exactly half a full sphere of the same radius, so a hemispherical bowl holds half what a complete ball would. Reach for it when you care about capacity — litres in a bowl, concrete in a dome, fluid in a tank cap. The curved surface is just the dome's outer skin, the same as half a sphere's surface; use it when you are coating, painting, or insulating only the rounded part. The total surface adds the flat circular base on top, so it is always larger than the curved figure by exactly π × r²; reach for it when the shape is solid and every face counts, such as a paperweight or a sealed half-ball. As a sanity check, the total surface is always 1.5 times the curved surface, and doubling the radius makes the volume eight times larger while the surfaces only quadruple.
The formulas are exact, but they describe an ideal shape.
Perfect hemispheres and display rounding
The calculation assumes a perfect, mathematically smooth half-sphere with a flat circular base. Real objects — slightly oval bowls, dented dome roofs, or uneven tank caps — deviate from the ideal, so treat the result as a close estimate for anything that is only roughly hemispherical. Results are rounded to six decimal places, so values with long decimal tails may round the last digit, and the radius must be a positive number for the geometry to be defined.