# [Proj] Re: Distance measured in Mercator projection

Ed McNierney ed at mcnierney.com
Wed Jul 9 23:59:59 EDT 2008

```Shannon -

First, let me apologize for trying to respond (twice) when I was too rushed to do so properly.

Since you say you're not very familiar with map projections, it might be helpful for you to describe a little bit more about what you're trying to do.  Daan's and Chris's comments are both correct but could be confusing to a novice; the scale factor at a single point is the same in all directions for a Mercator projection, but strictly speaking only at that point.  If you have another point in a different place, the scale factor at that point will be different from the first unless they're at exactly the same latitude.  So if you're measuring the distance between two points at a non-trivial distance apart, a 500-mile line will, for example, change length on a Mercator map depending on its angle with the Equator.  What I was trying to say in my first, poorly-worded reply, is that the set of points that are all 500 miles from a center point on a Mercator map will NOT form a circle on that map.

If your question really is, "How can I measure the great circle distance between two points given their Mercator coordinates" then that's rather tricky.  And it will depend on how far apart those two points are, and how accurate you need your answer to be.

You will find incredibly talented professional expertise on this list, but it's hard for people to answer the question you didn't ask.  If you can describe - in general terms, rather than specific ones - what you're trying to do and what questions you're trying to answer, that will make it easier.  If there are constraints on your solution (e.g. "I have to use Mercator so please don't suggest an alternative projection that would make the math easier") let us know as well.  Thanks.

- Ed

Ed McNierney
205 Indian Hill Road
Groton, MA  01450
ed at mcnierney.com
+1 (978) 761-0049
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