Calculator and formulas for calculating a spheroid (ellipsoid of revolution)
This function calculates the volume and the surface area of a spheroid. A spheroid (ellipsoid of revolution) is an elliptical body, as it arises from the rotation of an ellipse around the axis a. In contrast to a three-axis ellipsoid, axes b and c are the same length.
A distinction is made between:
To calculate the spheroid, enter the lengths of the two semiaxes a and b. Then click the 'Calculate' button.
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To calculate the surface, apply to oblates and prolate ellipsoids different formulas.
Volume |
\(\displaystyle V=\frac{4}{3} ·π · a·b·c\) |
Surface of the oblates ellipsoid (a < b) |
\(\displaystyle S=\frac{2πa^2b}{\sqrt{b^2-a^2}} \left[\frac{b}{a^2} \sqrt{b^2-a^2} +arcsinh\left(\frac{\sqrt{b^2-a^2}}{a} \right) \right] \) |
Surface of the prolate ellipsoid (a > b) |
\(\displaystyle S=\frac{2πa^2b}{\sqrt{a^2-b^2}} \left[\frac{b}{a^2} \sqrt{a^2-b^2} +arcsin\left(\frac{\sqrt{a^2-b^2}}{a} \right) \right] \) |
Surface of a sphere (a = b) |
\(\displaystyle S=4· a ·b·π\) |
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