Volume of a Hemisphere Calculator

A hemisphere is exactly one half of a sphere cut through its centre. Its flat face is a circle, while its curved surface extends from the circular rim to the pole. Hemispherical forms appear in bowls, domes, tanks, observation instruments, architectural roofs, and the end caps of industrial vessels. The defining measurement is the radius, which runs from the centre of the flat circular face to any point on its rim and also equals the distance from that centre to the highest point of the curved surface. The volume formula is V = two-thirds times pi times r cubed. It comes directly from the sphere formula, four-thirds times pi times r cubed, because a hemisphere occupies half of a complete sphere. Cubing the radius is important: volume grows in three dimensions, so doubling the radius multiplies the volume by eight rather than two. A hemisphere with radius ten therefore holds eight times as much as one with radius five, assuming identical units. This calculator uses the mathematical value of pi supplied by the browser and displays a rounded decimal result. Enter a radius in any unit and interpret the answer in the matching cubic unit. A radius entered in centimetres produces cubic centimetres, while metres produce cubic metres. The radius must be positive. If the measurement you have is a diameter, divide it by two first because the diameter spans the complete circular face through its centre. For practical capacity questions, distinguish inside and outside measurements. A metal bowl may have an outside radius larger than its usable interior radius because of wall thickness. A building dome may also be only a hemispherical shell rather than a solid volume. The calculator returns the full ideal enclosed volume, not material volume or curved surface area. To estimate material in a shell, calculate outer and inner hemisphere volumes separately and subtract the smaller result. Measurement precision controls result precision. Since radius is cubed, a small radius error becomes magnified in the final volume. Measure from the true centre, keep units consistent, and avoid reporting more significant digits than the original radius supports. For a rough estimate, rounding the final answer may be appropriate; for engineering work, retain additional digits and apply project-specific tolerances. The formula remains useful for comparing designs, checking homework, estimating liquid capacity, and understanding how curved three-dimensional objects scale.