Earth Radius | Distance to Equator and Pole | Earth's Curvature

# Earth Radius by Latitude Calculator

Calculates radius and diameter of the Earth for a given latitude. The radius of the earth is the distance from the center to the edge. The diameter is the distance from edge to edge through the center, which is twice the radius. Earth isn't a perfect sphere, but is oblate at its poles, due to its rotation. Therefore, the Earth radius isn't constant, but it can be calculated for every location. For this calculation, the longitude isn't needed. Mathematically, Earth is a spheroid.

Earth radius at sea level is 6378.137 km (3963.191 mi) at the equator. It is 6356.752 km (3949.903 mi) at the poles and 6371.001 km (3958.756 mi) on average. The height above sea level of the location is added. Please enter the latitude in decimal degrees, here you can convert coordinates.

## Formula for the calculation

latitude B, radius R, radius at equator r_{1}, radius at pole r_{2}

R = √ [ (r_{1}² * cos(B))² + (r_{2}² * sin(B))² ] / [ (r_{1} * cos(B))² + (r_{2} * sin(B))² ]

*Height above sea level* can be negative, then you are below sea level.

In fact, this calculation is not entirely correct, because the earth is not a perfect spheroid either. The mass is not evenly distributed, there are different types of rock that have different densities. In some parts of the world, therefore, the density is higher than in others. This gives the earth's surface huge and fairly shallow dents and bumps. The shape of the earth, the so-called Figure of the Earth, is a bit reminiscent of a potato. In the western Pacific, for example, the earth has a large bump, while in the eastern Mediterranean it has a dent. Including this figure in the calculation would complicate it extremely and would require the inclusion of thousands of measurement points. Therefore simplified models are used. A slightly more accurate model than a spheroid is an ellipsoid, again the input and calculation would be a lot more complicated than it is here.

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