# [Proj] Re: Distance measured in Mercator projection

Ed McNierney ed at mcnierney.com
Wed Jul 9 16:45:53 EDT 2008

```Shannon -

Your question implies you are only interested in measuring east/west distances, and Daan's answer is helpful for that purpose.  But that answer ONLY applies to measuring a line that runs due east/west.  A line running north/south, of the same length on the Earth as the east/west one, would be a different length on a Mercator projection.  If you wish to measure an arbitrary line on a Mercator projection you need to also take into account the angle of that line to the Equator (as well as the latitude, and whether you're assuming a spherical Earth).

This is one of the many reasons Mercator projections are most useful to 17th-century mariners.

- Ed

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

On 7/9/08 4:21 PM, "strebe at aol.com" <strebe at aol.com> wrote:

If you assume a spherical earth, the length of a meter on the Mercator equatorial aspect is

1m / cos (phi)

where phi is the latitude and "cos" is the cosine function. Be careful to set the calculator to degrees or else to convert the latitude to radians. The calculation is more complicated on an ellipsoidal earth.

Regards,
-- daan Strebe

-----Original Message-----
From: Shannon Scott <sscott at locationinc.com>
To: Proj at lists.maptools.org
Sent: Wed, 9 Jul 2008 10:52 am
Subject: [Proj] Distance measured in Mercator projection

Hello,
Please forgive my ignorance, I know very  little about map projections.  I apologize if this list is not the appropriate place to post this question.
If I understand correctly, in the Mercator projection, 1 unit of space is equal to 1 meter at the equator.
As you move away from the equator, the longitudinal lines are stretched to make the lat and long intersect at 90 degree angles.
How would I calculate the length in meters of 1 unit of space in the Mercator projection at a specific latitude?
Any advice of pointers are appreciated.
Thank you.
Shannon

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