Spheroid Calculation
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:
- the oblate ellipsoid, a < b, c (shape of a lens)
- the prolate ellipsoid, a > b, c (shape of rugby ball)
To calculate the spheroid, enter the lengths of the two semiaxes a and b. Then click the 'Calculate' button.
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oblates ellipsoid
prolate ellipsoid
Formulas for the spheroid
To calculate the surface, apply to oblates and prolate ellipsoids different formulas.
Volume (\(\small{V}\))
\(\displaystyle V=\frac{4}{3} ·π · a·b·c\)
Surface of the oblates ellipsoid (a < b) (\(\small{S}\))
\(\displaystyle S=\frac{2\cdot π\cdot a^2\cdot b}{\sqrt{b^2-a^2}} \left[\frac{b}{a^2} \sqrt{b^2-a^2} +arcsinh\left(\frac{\sqrt{b^2-a^2}}{a} \right) \right] \)
Surface of the prolate ellipsoid (a > b) (\(\small{S}\))
\(\displaystyle S=\frac{2\cdot π\cdot a^2\cdot b}{\sqrt{a^2-b^2}} \left[\frac{b}{a^2} \sqrt{a^2-b^2} +arcsin\left(\frac{\sqrt{a^2-b^2}}{a} \right) \right] \)
Surface of a sphere (a = b) (\(\small{S}\))
\(\displaystyle S=4· a ·b·π\)
Round solids functions
Sphere • Spherical cap • Spherical sector • Spherical segment • Spherical ring • Spherical wedge • Spherical corner • Spheroid • Triaxial ellipsoid • Ellipsoid volume • Spherical shell • Solid angles • Torus • Spindle torus • Oloid • Elliptic Paraboloid