Geodetic to Geocentric Latitude

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

INSTRUCTIONS:  Choose units and enter the following:

• (φ) Geodetic Latitude

Geocentric 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 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-f)^2 * tan(φ))`

where:

• φ' = geocentric latitude
• φ = geodetic latitude
• f = Earth flattening factor

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 Earth is close to (though not exactly) an oblate spheroid.  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

• Slant Range using Position Vectors
• Slant Range from Elevation Angle (α)
• Slant Range using Subtended Angle (β)
• Distance to Horizon
• Angle of Satellite Visibility
• Grazing Angle
• XYZ to Latitude, Longitude, Altitude
• Earth WGS-84 Equatorial radius in meters: 6378137.0 m
• Earth WGS-84 Polar radius in meters: 6356752.31424518 m 
• Earth Flattening Factor (WGS-84): 0.00335281066474748071984552861852
• Ellipse flattening factor: F = (Er - Pr)/Er  
• Geocentric to Geodetic Latitude
• Geodetic to Geocentric Latitude

Oblate Spheroid Calculators and Data

• Earth WGS-84 Equatorial radius in meters: 6378137.0 m
• Earth WGS-84 Polar radius in meters: 6356752.31424518 m 
• Earth Flattening Factor (WGS-84): 0.00335281066474748071984552861852
• Ellipse flattening factor: F = (Er - Pr)/Er  
• Geocentric to Geodetic Latitude
• Geodetic to Geocentric Latitude
• Slant Range