Math Formulas > Geometry > Surface Area of an Ellipsoid
Surface Area of an Ellipsoid
a, b and c defines the vertical distances from the origin of the ellipsoid to its surface.
According to wikipedia.org the surface area of a general ellipsoid cannot be expressed exactly by an elementary function. However an approximate formula can be used and is shown below:
Where p ≈ 1.6075 yields a relative error of at most 1.061% (Knud Thomsen's formula)
Π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used.
Example: determine the surface area of a ellipsoid that has following properties:
a = 2 m
b = 3 m
c = 4 m
SA = 4 ∙ Π ∙ ((a1.6075b1.6075 + a1.6075c1.6075 + b1.6075c1.6075)/3)1/1.6075 = 111.604 m2
Online Surface Area Calculator, click on the link will open a new window.
