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# Conversion Coordinates to Distance

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## Conversion Coordinates to Distance

(OP)
We have a project that has key locations defined as N??? degrees, ???.??? minutes (to 3 decimals) and W??? degrees, ???.??? minutes (also to three decimals)

Is there an easy formula to calculate the distance between these coordinate locations, realising the longitude distance varies as you depart the equator?

Dik

### RE: Conversion Coordinates to Distance

I assume you meant latitude...

Depends on what accuracy you need and how far apart they are. Your lat/lon resolves 1.86m

### RE: Conversion Coordinates to Distance

(OP)
IRstuff... yes, the correction is at the latitude level due to the convergence of the longitude lines... thanks for the clarification. The points are several hundred metres apart. The resolution you noted is based on a .??? minute of accuracy? and can you reference something that I can use to determine this? or is there a formula? I can do a rough calculation using spherical trig if necessary, but was hoping for a handy formula.

thanks, Dik

### RE: Conversion Coordinates to Distance

oops, that was my bad, yes, longitude lines converge at the poles, but I'm assuming you're not trying to build a house there?

The standard approach appears to be simply taking the difference in angles and multiplying by the radius of the earth. For more accuracy, you would use basically the same thing, but you'd use the WG84 coordinate transformations to eke out a more accurate effective radius. Attached are some rather old Mathcad files, and their PDFs in a Zip file:
http://files.engineering.com/download.aspx?folder=...

### RE: Conversion Coordinates to Distance

(OP)
Thanks... will look at the files...

With a cold place like that... I want all walls to face south!

Dik

### RE: Conversion Coordinates to Distance

Well, one way to work with latitude and longitude on a local project is to add the same value to all the longitudes so that the local project straddles on the central meridian of a UTM zone. The use any UTM application to convert the latitude and longitude to rectangular plane coordinates.

One problem is that UTM has a scale factor of 0.9996 while similar state plane systems usually have a scale factor of 0.9999 . Of course a simple coordinate scaling could be done (with multiplication or division) instead of a projected difference in scale.

Another problem is that UTM does project from the equator but that's why working near the center of a zone was recommended.

But KBH Local Grid Application can set the point of projection at the center of the local project. Also, it includes geodetic inverse, geodetic forward, grid inverse, and grid forward. And that's fairly good project support. Also, this application accepts a scale factor but then relatse the scale factor to an ellipsoid height. Here's a user link: http://www.kbhscape.com/grid.htm

.

### RE: Conversion Coordinates to Distance

(OP)
Thanks for the added info...
Dik

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