Squaring of Circle | Ellipse | Rectangle | Polygon || Square Multiplication

Cubing of Sphere | Ellipsoid | Cuboid || Cube Multiplication

Cubing the Ellipsoid - Calculator

Calculator for the edge length of a cube and the semi axes of an ellipsoid, if both have the same volume. The cubing of the ellipsoid is the three-dimensional equivalence to the squaring of the ellipse. Please enter three of the five values, at least two of them semi axes. The other values will be calculated.

	Cube	Ellipsoid
Length:
1. semi axis:
2. semi axis:
3. semi axis:
Volume:

Round to decimal places.

The unit is the same for the lengths. The volume has this unit to the power of three. For example, length in centimeters, volume in cubic centimeters. The volume V of an ellipsoid is calculated using this formula: V = 4/3 * π * a * b * c, where a, b and c are the lengths of the three semi-axes. The volume of a cube is, of course, its edge length to the power of three.

Example: cube and ellipsoid with almost equal volumes. The edge length of the cube is 100 pixels, the semi axes of the ellipsoid are 81, 60 and 49 pixels long, because there are no fractions of pixels.

An ellipsoid is the three-dimensional equivalent of an ellipse. It has three distinct semi-axes. A somewhat simpler form of the ellipsoid is the spheroid, in which two semi-axes are equal. Our Earth, like all celestial bodies above a certain size, is approximately a spheroid.

Constructing a two-dimensional representation of an equally sized cube from an ellipsoid using only a compass and straightedge, in other words cubing the ellipsoid, is generally impossible. There are no special cases where this would be feasible. This is because calculating the ellipsoid requires the mathematical constant pi (π), which is transcendental. This means that π cannot be expressed algebraically, so it cannot be calculated using basic arithmetic operations or roots. Therefore, such a length cannot be constructed.