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Oblate Spheroid - surface area

vCalc Reviewed
`sA = f( "b" , "c" )`
`(b)"Semi-major Axis"`
`(c)"Semi-minor Axis"`

The Surface Area of an Oblate Spheroid calculator /attachments/3c3d3ab2-7d90-11e4-a9fb-bc764e2038f2/Ellipsoid_OblateSpheroid.pngapproximates the surface area of an oblate spheroid.

INSTRUCTIONS:  Choose units and enter the following:.

  • (b) - This is the semi-major axis, the distance from the oblate spheroid's center along the longest axis of the spheroid
  • (c) - This is the semi-minor axis, the distance from the oblate spheroid's center along the shortest axis of the spheroid

Surface Area of Oblate Spheroid (sA): The area is returned in square meters.  However, this can be a automatically converted to many other area units (e.g. square inches or acres) via the pull-down menu.

The Math / Science

The oblate spheroid is an ellipsoid that can be formed by rotating an ellipse about its minor axis.  The rotational axis thus formed will appear to be the oblate spheroid's polar axis. The oblate spheroid is fully described then by its semi-major and semi-minor axes.

The formula for the surface area of an Oblate Spheroid is as follows:

           sA = 2πb2(1 + (1-e2)/e * tanh-1e)  where e2 = 1 - c2/b2

One important shape in nature that is close to (though not exactly) an oblate spheroid is the Earth.

Ellipsoid Calculator