# Measuring distances when crossing UTM zones?

I like to calculate distance between two UTM coordinates which are in different zones. Could any one point me how I can do this.

I found that we can map these coordinates in to a new projection for solving the problem. Could any one let me know which is the best map projection where cartesian coordinate related calculations are applicable like UTM.

If some points me to extended UTM zones and how it helps, that will also be very helpful.

• Because of distortion it's not as simple as putting the other point in the same zone as the first point. Consider an Albers Equal Area or Lamberts Conformal Conic projection, but you're going to need to enter custom parameters. I have used Lamberts for this and using standard parallels close to coordinates and central meridian between it wasn't too bad. Be aware that you're not going to get high accuracy measuring like this, the longer the distance the more inaccurate it will be. If you need high accuracy use Geodetic distance calculation. – Michael Stimson Jun 19 '15 at 1:07
• @MichaelMiles-Stimson In my early days of GIS I worked on a project related to Port Pirie in South Australia that spans two AMG/MGA/UTM zones (but is largely in one rather than the other) and the advice I was given was that as long as we were within 30 mins (half a degree) of a zone then placing data into that zone would not introduce unacceptable distortion. I guess whether falsing into another UTM zone is better than switching to Albers/Lamberts will depend on how far into each zone the asker is wanting to measure their distances. – PolyGeo Jun 19 '15 at 1:57
• Exactly @PolyGeo, and what kind of accuracy they would be satisfied with. For some states there are known Lamberts like SA_Lamberts (EPSG:3107) and VicGrid (EPSG:3111)... I would imagine other areas of the world that straddle two zones would also have 'special' spatial references to avoid having to split data into UTM zones. – Michael Stimson Jun 19 '15 at 2:29
• @Michaelmiles: Could you please elaborate what are custom parameters and how you solved the problem. – Chaitanya Jun 19 '15 at 16:30
• Search for point in polygon routines. If I search this site using that phrase, I get a bunch of Q&As for different software and languages. I'm not sure you need to calculate distances. – mkennedy Jun 19 '15 at 17:31

First, let's confirm what you already seem to know: If there are two different UTM zones, there are effectively two different coordinate reference systems (CRS), and distances between points across the zones cannot be calculated.

So, you must do one of these first:

• Convert -- or reproject, as it's often called -- one point into the other UTM zone. Or...
• Convert both points into a different, third CRS.

There are many questions on this site about coordinate conversion or reprojection.

Either way, the problem then becomes how to accurately calculate distance given two coordinated points. Again, there are many questions on this site about distance calculation.

Briefly then, you can do one of these:

• Reverse project the two points back onto the ellipsoid and then calculate the great circle distance (or geodesic) from their geographic (lat, long) coordinates. Or...
• Convert the points into the same projected coordinate (N, E) system; calculate the very simple Pythagorean distance; then calculate and apply the scale factor to that "grid" distance to get the "ground" distance.

The easiest solution is probably to use one of the UTM zones, extended to include the outer point.

• As far my understanding, I thought UTM is the only coordinate sytem where I can apply pythogarean theorem for calculating distance. Could you please mention which is the best projection coordination system, I should convert so that I can make use of pythogorean theorem. My problem is not calculating distance. My problem is finding whether one point is inside certain boundary or not. Any suggestions how I can solve this problem. – Chaitanya Jun 19 '15 at 17:02
• Pythagorean distance can be calculated from any projected coordinate system but you must understand they're not survey accurate and you will get slightly different results in UTM, Albers, Lamberts... the Great Circle distance that Martin speaks of is the most accurate. If you don't mind being slightly inaccurate the 2nd option is possibly the easiest. UTM covers areas that are pre-defined and 6 degrees wide but Albers and Lamberts do not have that restriction, using custom parameters to cover your area they need not be too inaccurate.. google search the names and understand why they work. – Michael Stimson Jun 19 '15 at 21:22
• @MichaelMiles-Stimson - It's not so much that a coordinate systems whose accuracy is questioned, only the coordinates or measurements themselves. When referring to surveying and coord systems, you probably mean that conformal projections (such as UTM) are suitable for surveying calculations due to certain geometric qualities unique to conformal projections. (Maybe i'm being overly pedantic.) – Martin F Jun 20 '15 at 3:39
• Without knowing what accuracy is required (or expected) it's hard to say whether you're being pedantic or not, I think it's an excellent answer, providing the user with all the options. All the information is here, it's up to the user to decide. All spatial reference systems and geoids are models, as such they give better or worse approximations of the earths' surface but are not 100% accurate... different models focus on different aspects, UTM for example is good to measure distance but not for bearings - conversely Mercator is good for bearings but not so easy to measure distances off. – Michael Stimson Jun 21 '15 at 21:27
• @MichaelMiles-Stimson: UTM and Mercator are essentially the same projection, so it is not correct to say that one is good for distances and the other for bearings! They both preserve angles, they both distort distances, they both have convergency, etc. – Martin F Sep 15 '15 at 2:54