How to Convert Latitude & Longtitude

Illustration of latitude and longitude

Latitude and longitude measurements provide a unique set of coordinates for any point on Earth. This coordinate system uses imaginary horizontal and vertical lines to form a grid and circle the Earth. A degree of latitude may be easily estimated because it is a fixed distance. However, a degree of longitude is more difficult to estimate because it varies according to the latitude.

Things You'll Need

• Calculator with trigonometry functions

Instructions

1. Define the latitude. Lines of latitude are parallel to the equator; the equator is 0 degrees latitude, and the poles are 90 degrees latitude. Note that this definition means that a degree of latitude is the same distance anywhere on the Earth.

2. Calculate the distance of a degree of latitude. If the Earth were a sphere, a degree of latitude Dl would be Dla = 2π r/360 = π r/180. Because the radius of the Earth varies, a common method for estimating a degree of latitude is to use the mean of the equatorial and polar radii. The equatorial radius is about 6,378,137 meters, and the polar radius is about 6,356,752.3 meters, so we can use (6,378,137 + 6,356,752.3)/2 = 6,367,444 for the radius of the earth. Thus, a degree of latitude is approximately π r/180 = π (6,367,444)/180 = 111,133 meters or about 111.1 kilometers.

3. Define the longitude. Lines of longitude run through the poles. A degree of longitude is therefore 1/360 of the equatorial circumference at the equator and 0 at the poles. If the Earth were a sphere, a degree of longitude would therefore be given by Dlo = (Dla) cos θ = ( π r/180) cos(θ)), where Dlo is the distance of a degree of longitude and θ is the degree of latitude.

4. Calculate the distance of a degree of longitude at the equator. From the equation Dlo = (Dla) cos θ = (π r/180) cos(θ) obtained in step 3, we have Dlo = (π r/180) cos(θ) = (π r/180) cos(0) = π r/180 where r is the equatorial radius. Using r = 6,378,137, we have Dlo = π (6,378,137)/180 = 111,319 meters or about 111.3 kilometers.

5. Use spherical geometry to better estimate a degree of longitude when the latitude is not zero. We can improve on the accuracy of the equation Dlo = (π r/180) cos(θ) by using the substitution r = [(a^4 cos()^2 + b^4 sin()^2)/(a^2 cos()^2 + b^2 sin()^2)]^(1/2) where a is the equatorial radius and b is the polar radius.

References

• Navis.gr