Calculate total surface area, curved surface area, base area, and volume of a hemisphere. Includes full sphere comparison bars, unit selection, presets for bowls and domes, and a reference table.
A hemisphere is half of a sphere, created by cutting a sphere along a great circle (a plane through the center). Hemispheres appear everywhere in architecture and daily life — from domed ceilings and planetariums to salad bowls, contact lenses, and igloos. Understanding their surface area and volume is essential for construction, packaging, and manufacturing.
The surface area of a hemisphere consists of two parts: the curved dome surface and the flat circular base. The curved surface area is 2πr² (exactly half the full sphere's surface), while the flat base adds another πr². Together, the total surface area is 3πr². The volume of a hemisphere is (2/3)πr³, exactly half the volume of the corresponding sphere.
This calculator lets you work from any starting measurement — radius, diameter, curved surface area, or volume — and derives all properties. It also includes a full-sphere comparison visualization showing how hemisphere measurements relate to the complete sphere, making it especially useful for students learning 3D geometry and engineers designing dome structures.
Hemisphere calculations require careful attention to which surface area is needed — curved only, or total including the base. Engineers designing dome roofs need the curved area for material estimates, while manufacturers of hemispherical containers need the total surface area. This calculator breaks down both and provides an instant full-sphere comparison, avoiding the common mistake of using the wrong formula.
Curved Surface Area = 2πr² Base Area = πr² Total Surface Area = 3πr² (curved + base) Volume = (2/3)πr³ Solving from different inputs: From diameter: r = d / 2 From curved SA: r = √(CSA / 2π) From volume: r = ∛(3V / 2π) Relation to full sphere: Hemisphere SA = 75% of sphere SA (3πr² vs 4πr²) Hemisphere Volume = 50% of sphere volume
Result: Total SA = 942.4778 cm², Curved SA = 628.3185 cm², Volume = 2094.3951 cm³
When Solve From is set to Radius and the input is 10 cm, the curved dome surface is 2π × 10² ≈ 628.3185 cm² and the flat base contributes π × 10² ≈ 314.1593 cm². Adding them gives a total surface area of 942.4778 cm². The volume is (2/3)π × 10³ ≈ 2094.3951 cm³, and the sphere comparison confirms that this is exactly half the volume of the matching full sphere.
The most important hemisphere distinction is whether you need only the curved dome or the entire outside including the flat base. A bowl, dome roof, or radar cover often needs the curved surface area because the bottom is open or attached to another surface. A molded plastic shell or enclosed half-sphere part may require the total surface area because the circular base is part of the finished piece. This calculator separates those outputs clearly so you can choose the correct measurement for coating, cladding, packaging, or manufacturing work.
In practice, you do not always start with the radius. Sometimes you know the diameter across the opening, sometimes the curved area from a material estimate, and sometimes the internal volume of a bowl or dome. The solve-from menu reflects those real starting points. Once one measurement is entered, the calculator derives radius, diameter, curved area, base area, total area, volume, and base circumference in a consistent unit system, which is much faster than manually rearranging several formulas.
The sphere comparison panel is more than a visual extra. It helps explain why a hemisphere has 50% of the sphere's volume but 75% of its total surface area. Half of the spherical shell gives 2πr², but the cut creates an additional circular base worth πr², so the total becomes 3πr². Seeing those percentages side by side is useful for students learning solid geometry and for designers deciding whether a dome should be analyzed as an open shell or as a closed half-sphere.
Total surface area = 3πr², which includes the curved dome surface (2πr²) and the flat circular base (πr²). Use this as a practical reminder before finalizing the result.
The curved surface area = 2πr². This is exactly half the surface area of a full sphere (4πr²) and represents just the dome portion.
Volume = (2/3)πr³. This is exactly half the volume of a sphere with the same radius.
Because cutting a sphere in half creates a new flat circular surface (the base). The curved part is half the sphere (2πr²), but adding the base (πr²) gives 3πr², which is 75% of the sphere's total.
Rearrange the formula: r = ∛(3V / 2π). For example, if V = 2000 cm³, then r = ∛(6000 / 2π) ≈ 9.85 cm.
Salad bowls, dome buildings (like the U.S. Capitol dome), igloos, planetarium screens, contact lenses, wok pans, and geodesic dome tents.
A hemisphere of radius r has volume (2/3)πr³. A cone with base radius r and height r has volume (1/3)πr³ — exactly half the hemisphere's volume.
Yes. For roofing material, use the curved surface area (2πr²). For total material including the floor, use the total surface area (3πr²). Multiply by a waste factor (typically 10-15%) for practical estimates.