Calculate the volume and surface area of a hemisphere. Enter radius or diameter, get volume in multiple units (liters, gallons, cubic feet), curved surface area, base area, total surface area, and...
A hemisphere is half of a sphere — one of the most elegant and commonly encountered shapes in mathematics, architecture, and everyday life. Whether you're calculating the capacity of a dome-shaped structure, determining how much liquid a hemispherical bowl can hold, or solving a geometry homework problem, understanding hemisphere measurements is essential.
This hemisphere calculator lets you instantly compute the volume, curved surface area, flat base area, and total surface area of any hemisphere. Simply enter the radius or diameter in your preferred unit, and the calculator handles the rest. Results are displayed in multiple volume units including liters, US gallons, cubic feet, and cubic inches — perfect for practical applications like tank sizing, cooking measurements, or engineering calculations.
The calculator also provides a side-by-side comparison between a hemisphere and its parent full sphere, clearly showing the mathematical relationships between the two. You'll see that a hemisphere has exactly half the volume and half the curved surface area of the corresponding sphere, but its total surface area (including the flat base) is three-quarters of the sphere's. Visual bars, preset values for quick exploration, and detailed reference tables make this tool both educational and practical. Use it for classroom exercises, architectural planning, industrial design, or any scenario where you need precise hemisphere measurements.
Hemisphere measurements come up whenever you work with domes, bowls, tanks, lenses, or half-sphere molds, and those jobs usually need more than a single volume number. This calculator ties the radius or diameter directly to capacity, curved area, flat base area, and total surface area, which makes it useful for both geometry study and practical sizing decisions.
Volume = (2/3)πr³ | Curved Surface Area = 2πr² | Base Area = πr² | Total Surface Area = 3πr²
Result: Volume ≈ 2094.3951 cm³, curved area ≈ 628.3185 cm², total area ≈ 942.4778 cm²
For a hemisphere with radius 10 cm: Volume = (2/3) × π × 10³ = (2/3) × 3.14159 × 1000 ≈ 2,094.40 cm³ ≈ 2.094 liters. Curved SA = 2π(10²) ≈ 628.32 cm². Base area = π(10²) ≈ 314.16 cm². Total SA ≈ 942.48 cm².
The volume of a hemisphere is exactly half of the corresponding sphere, but surface area requires more care. The curved dome is half the sphere's surface area, yet a real hemisphere also has a flat circular base. That is why the calculator separates curved surface area, base area, and total surface area instead of showing only one area result.
In practical problems, hemisphere volume is often needed in liters, gallons, cubic feet, or cubic inches rather than raw cubic centimeters. A decorative dome might be sized in feet, while a lab vessel or mixing bowl might be measured in centimeters. Converting automatically between those units helps you move from geometric formulas to real storage, fill, or manufacturing decisions without doing a second round of calculations.
Hemispherical shapes appear in skylights, observatory domes, bowls, tank ends, and molded parts because they distribute stress well and look clean. In those applications, the same radius controls both internal capacity and exterior area, so changing the radius even slightly has a large effect. The comparison with a full sphere is helpful because it shows exactly what is lost in volume and what remains in surface coverage when only half the sphere is used.
The volume of a hemisphere is V = (2/3)πr³, where r is the radius. This is exactly half the volume of a full sphere, which is (4/3)πr³.
Divide the diameter by 2 to get the radius, then apply the formula V = (2/3)πr³. Or simply use the diameter input mode in this calculator.
Curved surface area (2πr²) is just the dome part. Total surface area (3πr²) adds the flat circular base (πr²) to the curved surface.
Calculate the volume in cubic centimeters using V = (2/3)πr³ (with r in cm), then divide by 1,000 to convert to liters. Use this as a practical reminder before finalizing the result.
A hemisphere has half the volume, half the curved surface area, and three-quarters (3/4) of the total surface area compared to the full sphere with the same radius. Keep this note short and outcome-focused for reuse.
Yes. For a solid dome, use the outer radius. For a hollow bowl, calculate volumes for both the outer and inner radii and subtract to find the material volume.
First get the volume in liters (cm³ ÷ 1,000), then multiply by 0.264172 to convert liters to US gallons. This calculator does the conversion automatically.