Spherical Wedge Calculator

Name: Spherical Wedge - Geometry Calculator
Author: Jürgen Kummer

Calculations at a spherical wedge. A spherical wedge, as defined here, is a portion of a sphere bounded by two planes that intersect at the sphere's center. The line of intersection of these two planes, which forms the edge of the wedge, extends between two opposite points on the sphere's surface. Its length is therefore the sphere's diameter or twice its radius. The curved portion of this wedge's surface is an antipodal digon.
Enter radius and angle and choose the number of decimal places. Then click Calculate. Please enter angles in degrees, here you can convert angle units.

Formulas:

A = α \cdot 2 \cdot r^{2} + π \cdot r^{2}

V = α \cdot \frac{2}{3} \cdot r^{3}

(α as Radiant)

pi:

π = 3.141592653589793...

The radius has a one-dimensional 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 volume of the spherical wedge is the proportional volume of a sphere with the same radius, where the proportion corresponds to the angle divided by 360 degrees. The same applies to the surface area of the curved part. Two semicircles, thus forming a full circle with the same radius, are added to the total surface area. At an angle of 180 degrees, the spherical wedge is equal to a hemisphere. So, when 360 degrees is entered as the angle, the volumes of the spherical wedge and the sphere are equal, but the surface area of the spherical wedge is larger because it is considered open, i.e., with the two semicircles on its surface. For larger angles, another spherical wedge is mathematically added to the open full sphere. Geometrically, this can be interpreted as an additional figure.

Real-world objects that have a shape similar to a spherical wedge include, for example, folded spheres or folded domes. These can be extended telescopically from a plane, sometimes even into a full sphere. An example of this is a paper lantern.

Calculation of volume and other dimensions: spherical wedge

Last updated on 03/31/2026. Author: Jürgen Kummer

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