Quarter Sphere Calculator

Calculations at a quarter sphere. A quarter sphere is a hemisphere halved in the middle. Its two straight surfaces are two semicircles of equal size. Radius and diameter of the quarter sphere refer to the original sphere.
Enter one value and choose the number of decimal places. Then click Calculate.

	Radius (r):
	Diameter (d):
	Surface area (A):
	Volume (V):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Radius and diameter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The curved part of the surface of a quarter sphere has twice the area of ​​one of the semicircles and thus the same area of ​​both straight surfaces together. And since the area of ​​two semicircles is of course the same as that of a circle, the area of ​​the curved part of the surface of a quarter sphere has the same area as the circle, namely pi multiplied by the radius squared, πr². The surface of the quarter sphere is also just as large as the calotte area of ​​the hemisphere.
If you halve a quarter sphere again in the middle through both straight surfaces, you get a spherical corner or eighth sphere. For each further halving, the volume is of course halved. The surface area of ​​the curved part of the surface is also halved, but new flat side surfaces are added, so that the total surface area of ​​the halved shape is larger than half the surface area of ​​the previous shape.
The quarter sphere is a spherical wedge with an angle of 90 degrees. Another possible halving of the quarter sphere would be to form a spherical wedge with an angle of 45 degrees. The quarter sphere is mirror-symmetrical to the two planes, which create a halving to form an eighth sphere or a 45-degree spherical wedge.

Last updated on 04/01/2026. Author: Jürgen Kummer

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