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Geocentric to Geodetic Latitude

φ=tan-1⋅(1(1-f)2⋅tan(φ′))
(φ′)Geocentric Latitude

The Geocentric to Geodetic Latitude calculator computes geodetic latitude from the geocentric latitude.

INSTRUCTIONS:  Choose units and enter the following:

Geodetic Latitude (φ): The latitude is returned in degrees.  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

Latitude is know as the angle from Equator (equatorial plane) to a point on the surface of the Earth.  This is ideally known as the geocentric latitude.   However, local measurement of the elevation of the Sun above the horizon is not perfectly analogous to that angle because the Earth is not a perfect sphere.  It is more accurately modeled as oblate spheroid where there is a bulging at the Equator.  The localized latitude is known as the geodetic latitude.  Fortunately, there is an easy conversion.

The formula for the converting geocentric latitude to geodetic latitude is:

  φ=tan-1⋅(1(1-f)2⋅tan(φ′))

where:

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.

One important shape in nature that is close to (though not exactly) an oblate spheroid is the Earth.  The force of gravity alone would pull the matter of the Earth into a sphere.  But the rotation of the Earth causes an outward (centripedal) force along the equator creating a bulge.

Earth Model Calculators

Oblate Spheroid Calculators and Data