How to Calculate the Boundaries of an UTM Zone

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Calculating the eastern and western boundaries of a UTM is very straightforward.  

What is the Universal Transverse Mercator (UTM) Map Coordinate System?

Developed by the U.S. Army, the Universal Transverse Mercator (UTM) is an international plane (rectangular) coordinate system for the map projection, Transverse Mercator, on which it is based.

In this coordinate system, the world is divided into 60 zones of 6 degrees longitude. UTM zones are numbered from 1 to 60, with the first zone being 180 degrees longitude with each subsequent zone increasing eastward.

Each zone extends 3 degrees east and west from its central meridian and are numbered consecutively west to east from the 180-degree meridian.

Map showing the ten zones that cover the contiguous United States with the UTM map projection.
Map showing the Universal Transverse Mercator grid that covers the conterminous 48 United States comprises 10 zones—from Zone 10 on the west coast through Zone 19 in New England. Map: USGS, public domain.

Transverse Mercator projections may then be applied to each zone.

The Northern and Southern Hemispheres are separated by the Universal Transverse Mercator (UTM) convention. The northern hemisphere’s UTM zone is designated as UTM North, which is represented by a positive value. The UTM zone has a negative value in the Southern Hemisphere, and is therefore known as UTM South.

Units for the Universal Transverse Mercator (UTM) Coordinate System

The distance in each zone is measured in meters. Distance in meters to the east are known as the easting and distance in meters to the north are known as the northing.

Calculating the Boundaries of a UTM Zone

Difficulty Level: Easy    Time Required: 1 minute


Here’s How:

  • UTM zones are all 6 degrees wide and increase from west to east starting at the -180 degree mark.
  • Calculate the eastern boundary of any UTM zone by multiplying the zone number by 6 and subtracting 180.
  • Subtract 6 degrees to obtain the western boundary.
  • Therefore to find the eastern boundary of UTM zone 11: Eastern boundary of zone 11 = (11 * 6) – 180 = -114 degrees.
  • Western boundary of zone 11 = -114 – 6 = -120 degrees.

References

The Universal Transverse Mercator (UTM) Grid. (n.d.). U.S. Geological Survey Publications Warehouse. https://pubs.usgs.gov/fs/2001/0077/report.pdf

This post was originally published August 25, 2006 and has since been updated.

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4 thoughts on “How to Calculate the Boundaries of an UTM Zone”

  1. Eric is asking how to determine the zone boundaries for a given UTM coordinate for which the zone number is unknown. This requires some math, considering the distortion of the projection at the equatorial and polar regions. All the basic equations you need are located here… rotate the pieces put the puzzle together – it’s good exercise for your brain!

    http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.HTM

  2. Eric, you can calculate max X and Y for a particular UTM zone, these numbers will be the same across all UTM zone, except non-standard ones. The results will also depend on which geo ellipsoid you are using.

    To lookup zone, based on the geodetic coordinate, you can use this online tool:
    http://www.apsalin.com/utm-zone-finder.aspx

    Please clarify the question, what are you trying to find, what do you been under the boundaries – is it max/min values of X, Y?

  3. This is well and good but how do you do it the other way? How do you calculate the boundaries of a UTM Zone given a UTM coordinate?

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