What is a hemisphere?
A hemisphere is exactly half of a sphere — picture a ball sliced cleanly through its center. The cut produces a flat circular face (the base) and a domed curved surface. This calculator works out every geometric property of a hemisphere from just one known measurement: the radius, the base circumference, the volume, the curved surface area, or the total surface area.
How to use it
Pick what you already know from the dropdown, type that value, choose a length unit (purely a display label — no unit conversion is performed), set how many significant figures you want, and optionally override the value of pi. The tool first solves for the radius, then derives the base circumference, volume, curved surface area, base surface area, and total surface area. Each result is also shown "in terms of pi" as a coefficient multiplied by pi.
The formulas explained
For radius \(r\) and pi the relationships are: base circumference \(C = 2\pi r\); volume \(V = \frac{2}{3}\pi r^3\); curved surface area \(A = 2\pi r^2\) (half the full sphere area \(4\pi r^2\)); flat base area \(B = \pi r^2\); and total surface area \(K = A + B = 3\pi r^2\). When a non-radius value is given, the calculator inverts the matching formula: $$r = \sqrt[3]{\frac{3V}{2\pi}},\quad r = \sqrt{\frac{A}{2\pi}},\quad r = \sqrt{\frac{K}{3\pi}},\quad r = \frac{C}{2\pi}.$$
Worked example
Take radius \(r = 5\) with \(\pi = 3.14159265359\) and 6 significant figures. $$C = 2\pi (5) = 31.4159.$$ $$V = \frac{2}{3}\pi (125) = 261.799.$$ $$A = 2\pi (25) = 157.080.$$ $$B = \pi (25) = 78.5398.$$ $$K = 3\pi (25) = 235.619.$$ Notice \(K = A + B = 157.080 + 78.5398 = 235.619\), confirming the total surface area.
FAQ
Does it convert units? No. The unit dropdown only labels the answers — linear results carry the unit, areas carry unit squared, and the volume carries unit cubed, all in whatever unit you entered.
Why can I change pi? Some textbooks use 3.14 or 22/7. Overriding pi lets your answer match a specific assignment, though the default gives the most accurate result.
What does "in terms of pi" mean? It is the exact symbolic value, e.g. a volume of 261.799 equals 83.3333 multiplied by pi, which avoids rounding error in further calculations.
