How far from San Juan to Florida/NY

Factual Questions
1

My friend swears that the distance between the tip of South Florida to San Juan, Puerto Rico is the same as the distance from NY state to San Juan. Is this true, because on a map and even a globe it looks like it is closer to Florida?

2

Key West, San Juan, New York 40.5N 74W, Miami

Key West - NYC = 1190 mi
Key West - San Juan = 1090 mi
less than 10% difference

Miami - NYC= 1078 mi
Miami - San Juan = 1036 mi
less than 5% difference

3

No no no. Wrong plots. I said the distance from miami to SJ is the same as distance from NY to SJ.

But to play with some geometry… I come up with 1,495 mi. So, they are not the same distances then?

Where did you get those figures? I quick glance at those sites, I didn’t see it.

4

I used the Miami figures, btw.

5

San Juan to NYC 1603 miles
San Juan to Miami 1038 miles

Um, slightly farther to NYC

There are tons of distance calculators out there. Here’s just one:

http://www.indo.com/distance/

6

Easily calculated with a spreadsheet. From some notes I wrote for a course I taught:


  The great circle distance in degrees between
 Point1 (lat1, lon1) and Point2 (lat2, lon2) is easily calculated: 

      cos(D)= Sin(lat1) * Sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 - lon1)

or what is the same:  

     D= arccos(Sin(lat1) * Sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 - lon1))

In this paper we assume the following signs N=+, S=-, W=+, E=- .

cos(D) will always fall in the range
   -1 < cos(D) < 1 
and (D) will be a positive angle: 0° < D < 180°. 
 You can use a formula that will use the arctan function but 
this will give a result in the -90° to +90° range and 
you need to add 180° if the result is negative.

  multiply D by 60 to obtain distance in nautical miles or
  multiply D by 69 to obtain distance in statute miles or
  multiply D by 111.12 to obtain distance in Km
The azimuth or initial course from point 1 (origin) 
 to point 2 (destination) Zn can also be easily calculated. 
 Zn is always measured from North to East from 0° to 360°. 
 First we calculate Z. 
 If we have considered West longitudes as positive we use this formula:
                                   Sin(lon2-lon1)
      Tan(Z) =  ---------------------------------------------------
                 sin(lat1) * cos(lon2-lon1) - cos(lat1) * tan(lat2)

   (If we had considered East longitudes as being positive we 
    would need to change the sign on one side of this equation.)

The function ATAN() returns a value between -90° and +90° so Z needs 
to be adjusted to the right quadrant in order to obtain Zn: 0° < Zn < 360°

    If sign(sin(Z)) = sign(sin(lon2-lon1)) then Zn = Z + 180
    Else, If Z is negative then Zn = Z + 360
            Else Zn = Z

The following formula adds 180° if needed to reduce Zn to the correct quadrant:

            Zn = Z + 90 * (1 + sign( sin(lon2-lon1) * sin(Z) ) )
7

I knew it wasn’t the same. Thanks guys and now I know that truly any piece of info is on the web.