🌎💻 Converting Lat Lng to XY Coordinates: A Guide

As someone who works with geographic data, I often need to manipulate latitudes and longitudes. Recently, a researcher requested that I convert a list of latitudes and longitudes to XY coordinates to obscure the actual location of the points while still allowing for analysis of the distance relationship between them. Here’s how I did it, complete with formulas!

🔍 Step 1: Drop the Lat Lngs into Excel
First, I needed to get the latitudes and longitudes into a spreadsheet. I simply copied and pasted them into Excel.

📝 Step 2: Calculate the X and Y Coordinates
I used the following formulas to calculate the X and Y coordinates, using a common latitude and longitude as a reference point:

X:

=(lon1 - lonconstant) * 40000 * COS((lat1 + latconstant) * PI() / 360) / 360

Y:

=(lat1 - latconstant) * 40000 / 360

These formulas use the distance from the reference point (in degrees) to calculate the distance in kilometers or miles, depending on the constant used.

📐 Step 3: Calculate the Distance Between Points
Next, I needed to calculate the distance between the points. I used the following formula:

=SQRT((x2-x1)^2+(y2-y1)^2)

This formula calculates the Euclidean distance between two points, which is the straight-line distance between them. To check that the values were correct, I also calculated the distance using only the latitudes and longitudes with the following formula:

=6371*ACOS(COS(RADIANS(90-Y1))*COS(RADIANS(90-Y2))+SIN(RADIANS(90-Y1))*SIN(RADIANS(90-Y2))*COS(RADIANS(X1-X2)))

This formula calculates the great-circle distance between two points, taking into account the curvature of the Earth.

🤔 Step 4: Compare the Two Distances
To check that the values were correct, I compared the two distances to see how close they were. Then I measured the distance on Google Maps. Bingo! Keep in mind that they will never be perfect due to the way things are projected, but they should be relatively close.

🌟 And that’s it! Converting latitudes and longitudes to XY coordinates can be a useful technique when you need to obscure the actual location of the points while still allowing for analysis of the distance relationship between them. I hope this guide helps you in your own work with geographic data!

For anyone interested, here is a js version of the code below: