How do you determine the location of the 16 extreme compass points of the contiguous United States?  I'll describe my methodology here, which I developed in January 2016 while I was planning my trip around America.  My methodology is, I believe, both simple and logical.

First of all, here's a compass rose.  Note that 0 degrees (or 360) is at the top, indicating north and 180 degrees indicates south.  Each of the 16 compass points, in fact, correspond to a specific bearing.

This table lists the bearings of the four cardinal directions (north, south, east and west) and four ordinal directions:

 Direction Bearing North 0 Northeast 45 East 90 Southeast 135 South 180 Southwest 235 West 270 Northwest 315

### The Basic Approach

To determine the location of each extreme compass point in the U.S. (or any country) you use this same basic approach:

 Select an extreme compass point that you want to determine (say, the northernmost point of the U.S., which is 0 degrees).  Calculate the bearing of the line drawn perpendicular to that bearing.  For the northernmost point, that would be a line extending east-west, with a bearing of 90 (or conversely, 270) degrees.  Looking at a map of the U.S., create an imaginary line outside of the U.S. using that bearing.  Move that imaginary line closer and closer to the perimeter of the U.S. in the opposite direction of your extreme point.  For example, if you want to determine the northernmost point, move the line south.  Keep moving the line until it intersects the perimeter of the United States.  The first point it intersects is the location of the extreme compass point for that direction.

That's the basic approach regardless of which extreme point you're trying to determine, whether it's 0 degrees (the northernmost point), 2 degrees, 45 degrees (the northeasternmost point) or any other point on the compass.  However, there's a bit more to it than this, as described below:

### 1. Determining the Extreme Cardinal Points  (i.e., North, South, East, and West)

You may be able to determine the extreme cardinal points of the United States -- or any country -- very easily if you simply look at a map.  It helps if your map uses the Mercator projection because Mercator projections show true directions.  In other words, whatever direction you draw on a Mercator map is the actual, true direction.  This is why Mercator maps have been used by ocean navigators for hundreds of years.

Google Maps, as one example, use the Mercator projection.  Well, technically Google Maps uses what's known as the "Web Mercator" projection, but it's essentially the Mercator projection.

On your map, if the U.S./Canada boundary is a straight line from east to west, it likely uses the Mercator projection.  If the U.S./Canada boundary line is curved, it doesn't use the Mercator projection.  Along with using a Mercator projection, it also helps if your map shows lines of latitude and longitude, because you can use them as a reference.

You can calculate the extreme cardinal points either graphically (simply by looking at the map) or numerically (by calculating the longitude and latitude values for each point on the perimeter of the United States).  To calculate an extreme cardinal point graphically:

 Figure out what point you want to identify -- say, the northernmost point of the contiguous U.S.  Create a line, either imaginary or actually on the map (perhaps by placing a ruler or pencil) that's outside of the United States and perpendicular to that direction.  Then move that line towards the U.S. until it touches the first point on the U.S. perimeter.   For example, to determine the northernmost point of the contiguous United States, look at a map that uses the Mercator projection, then create (or visualize) a line in Canada that runs east-west.  Now move that east-west line southward towards the United States until it touches the first point on the U.S. perimeter.  That’s it:  you've determined the northernmost point of the United States.

You can also calculate this same point numerically, without using any maps or illustrations, if you have access to computer mapping software.  To do this:

 Calculate the longitude and latitude of every point on the perimeter of the United States and put it into a table or spreadsheet.  Geographic Information Systems (or "GIS") software can quickly do this.  If you're trying to locate the northernmost point, look through the table for the point with the highest value of latitude.  If you're trying to locate the southernmost point, look for the lowest value of latitude.  If you're trying to locate the westernmost point, look for the smallest value of longitude (i.e., largest negative value).  Use the same concept to identify the easternmost point.

Either way, graphically or numerically, it’s easy to find an extreme cardinal point, such as the northernmost point or westernmost point of the contiguous United States.

### 2. Determining the Extreme Ordinal Points

But what about the ordinal directions, like northeasternmost or southwesternmost point?  How do you figure out the “southwesternmost” point of the United States?  As it turns out, you use the same methodology as above.

In the case of ordinal directions, like "southwesternmost," both directions -- south and west in this case -- have the same weight or value.  For the direction of southwest, “south” is no more (or less) important than “west.”  That's because the direction of “southwest” is exactly in between the directions of south and west.  The southwestern direction isn’t more (or less) “south” than “west,” just as the northeastern direction isn’t more (or less) “north” than “east.”  Both directions have exactly the same weight.

So to determine an extreme ordinal point, such as the southwesternmost point of the United States, you use the same methodology as you used to determine the extreme cardinal direction points described above.  To find the southwesternmost point:

 Create a line somewhere in the Pacific Ocean that’s perpendicular to that direction.  If north is 0 degrees and south is 180 degrees, southwest has a bearing of 225 degrees.  So in this case, you’d create a line that runs from the northwest to the southeast.  In other words, the line would have a bearing of 135 degrees (i.e., to the northwest or southeast).  Move that line towards the United States until it touches the first point of land on the perimeter of the United States, just as before with cardinal directions.  That point is the southwesternmost point of the contiguous United States.

You can also do this calculation numerically rather than graphically to determine the extreme ordinal location.  In that case, you would determine the latitude and longitude of each point on the perimeter, then you would ADD the x/y coordinate values of each point together.  The point with the highest combined value of x and y is the extreme ordinal point.  Before adding them, though, you might first have to perform a transformation depending on the direction, since latitude gets smaller as you go south and longitude gets smaller (or more precisely, more negative) as you travel west.  Therefore,

 If you wanted to determine the extreme southwestern point, you would add the coordinates of each point on the perimeter of the United States together and look for the smallest combined value If you wanted to determine the extreme northeastern point, you would add the coordinates of each point on the perimeter of the United States together and look for the largest combined value If you wanted to determine the extreme northwestern point, you would first reverse the longitude values (e.g., -124.3 degrees becomes 124.3 degrees) and then add the coordinates of each point together and look for the largest combined value. If you wanted to determine the extreme southeastern point, you would first reverse the latitude values (e.g., 36 degrees becomes -36), add the two coordinates, and the smallest combined value (i.e., the largest negative value) is the southeasternmost point.

So my “point” (heh, heh) is that you can calculate the extreme ordinal points either graphically or numerically, just as with the extreme cardinal directions (north, south, east or west) described above.  And you should come up with the same point as being the most extreme regardless of which way you calculate it, either graphically or numerically.

 Below:  Many people mistakenly believe that San Diego, California is the southwesternmost point of the contiguous United States.  Before I left on my trip around America in 2016 and created this website, I Googled "Southwesternmost point of the U.S." and almost every entry claimed it was San Diego.   But it's not. To determine the southwesternmost point, 1). Create a line in the Pacific Ocean that's perpendicular to that direction (i.e., bearing 135 degrees, or in other words, from northwest to southeast), then 2). Move that line towards the U.S. until it touches the first point of land.  I've done this in this map with the red line. If you create a line bearing 135 through San Diego (blue point and blue line), you'll see that there are many other places in California farther southwest than San Diego, including Santa Barbara and even Big Sur up near Monterey.  In fact, the southwesternmost point in the U.S. is an unnamed point near Lompoc, California (red dot). You can use this same approach to calculate any extreme compass point in the U.S.  Sorry, San Diego.  But congratulations to you, Lompoc!

### 3. Determining the Extreme Interordinal Points

You use the same methodology to determine the extreme interordinal points, such as the south-southeasternmost point or the west-southwesternmost point.  Again, you can do this either graphically or numerically and both ways should yield the exact same location.

 To do it graphically, you create a line perpendicular to the point you’re looking for, just as before.  So for instance, if you’re trying to determine the north-northeasternmost point (north-northeast is an angle of 22.5 degrees), you would create a line in Canada that has a bearing of 112.5 degrees (or conversely, 292.5 degrees), a line that's perpendicular to your bearing of 22.5 degrees.  Then move this line towards the United States until it touches the first point of the United States perimeter.  That’s your extreme point. To do it numerically, you would add the coordinates of each point to determine the point with the largest value.  But in this case, since you’re trying the determine the north-northeasternmost point, you would first double the value of each latitude coordinate and then add it to the corresponding value of longitude for that point, and repeat this for every point on the perimeter of the United States.  If you were trying to determine, say, the west-southwesternmost point numerically, you would double the value of each longitude value and then add them to the latitude value.

But again, you should come up with the exact same interordinal extreme point regardless of whether you’re doing it graphically or numerically.

### Conclusion

Using my GIS (geographic information systems) software, I performed these calculations, both numerically and graphically, in January 2016 as I was planning my trip around America.  By doing this I was able to determine the 16 extreme compass points of the contiguous United States (i.e., the "Lower 48.")  For each of the 16 points, both my numerical calculations and the graphical method yielded the same exact location.

The term "southwesternmost" or "east-northeasternmost" may be a bit fuzzy or nebulous to some folks.  But to me, the southwesternmost or east-northeasternmost points of the United States are just as clearly-defined, exact and identifiable as the northernmost or westernmost points.

You can use this same method to identify all 16 extreme compass points of any land mass -- or 32 points, or even 360 points.  But visiting all 360 extreme compass points of the United States would take a lot more time, so on this trip I decided to limit it to just 16!

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