Enter radius to solve the volume and surface areas of a hemisphere.
Start from radius, diameter, volume, surface area, or circumference and solve one consistent hemisphere.
Ready.
Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
Radius, diameter, volume, curved area, total area, base area, and base circumference are related but they are not interchangeable inputs. A reliable solver first identifies the known quantity and inverts the matching formula to recover the radius. That makes it possible to verify every other property from one consistent geometry instead of mixing measurements from different objects.
The curved dome area is 2πr². A closed hemisphere that includes the flat circular base has total area 3πr². A tank shell, dome roof, bowl, coating job, or cut pattern may require one of those areas rather than the other. Record whether the base is included before turning a geometric result into a material or cost estimate.
If radius is entered in centimetres, circumference is in centimetres, areas are in square centimetres, and volume is in cubic centimetres. Converting a volume between unit systems requires cubing the linear conversion factor; area requires squaring it. A unit label is useful context, but it does not rescue a calculation that mixed inches and centimetres in the original measurements.
After solving radius from a known volume or area, substitute that radius back into the original formula. The reconstructed known value should match the input apart from numerical rounding. This residual check is especially useful when a measurement came from another calculator, CAD export, spreadsheet, or field estimate because it exposes formula-selection mistakes without requiring a second independent tool.
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