# Distance between latlongs varies in different projection systems?

I have shapefiles with correct projections. The SRS is EPSG 32735 (WGS 1984 UTM 35S)

Now, I have these two coordinates from this projection system:

(31.3751,-23.4388) and (31.3779,-23.4355).

Obviously the coordinates (format and value) will vary on different projection systems, and there in lies my confusion.

I used the following link to calculate the distance between the two points: http://www.movable-type.co.uk/scripts/latlong.html

I copy pasted the lat/longs exactly as shown above and the distance it gives me is 0.313 meters. But I'm not sure if this is correct at all, since the calculator didn't ask me for any projection system? So:

1. Does this mean the projection doesn't matter to calculate the distance?
2. Does it differ between different projection systems?
3. Is the tool I'm using incapable?

Thanks,

Kaushik

• 0.313 meters is incorrect. When I use the web site you link to I get 441.7 meters and, indeed, this is the geodesic distance on the surface of the ellipsoid. In fact, a more accurate distance is 441.504 meters. However, the geographic coordinates are only specified to the nearest 0.0001 degree, about 10 meters, so interpret the distance accordingly. (BTW, I interpreted your coordinates as (lat,lon). If you meant (lon,lat), the distance is 464.158 meters.) – cffk Sep 18 '13 at 14:19
• P.S. The more accurate geodesic calculator I used is geographiclib.sourceforge.net/cgi-bin/GeodSolve – cffk Sep 18 '13 at 14:26

## 2 Answers

When you find distance using latitude and longitude, the tool would be calculating Geodetic distance between the two points, so it does not need a projection. However it will need the datum or ellipsoid, say WGS84 etc. Since it is not asking for a datum, it signifies a default system datum which generally is WGS84, the world datum.

Once you apply a projection system, then the co-ordinate system changes to planar co-ordinates and the distance can be calculated by applying Cartesian co-ordinate geometry. The distance if measured in planar co-ordinates will change if you change the projection system. But the distance between two points when using Geodetic distance will change only when you change the datum/ellipsoid, projection will have little difference or may be nil.

• Please do not use the url of your website as a signature. That can be construed as self promotion and spam. – Conor Sep 18 '13 at 14:06
• Sorry, saw it on my other post now. – mapsandlocations Sep 18 '13 at 14:10

The tool you linked calculates distances on a sphere. You see that in the formulae beneath, where R instead of a and b is used. Note that the sites wants lat, lon; so the negative value should be first (supposed to be in South Africa, right?).

For your points, 0,465km is calculated.

QGIS calculates 464,109m in UTM 35S on the ellipsoid, which is not that far away from the sphere result.