How Universal Transverse Mercator (UTM) Works

Northing and Easting. Why UTM Uses False Easting

Last Updated: Feb 21, 2018

Universal Transverse Mercator (UTM) Projection

Start with a sphere or ellipsoid because that is the true form of the Earth. Peel it like an orange evenly into sixty segments called “zones”.

Flatten each one of these zones.

What’s the result?

It’s the Universal Transverse Mercator (UTM) projection!

How Universal Transverse Mercator (UTM) works

It’s one of the most common map projections today. But how does the Universal Transverse Mercator work?

A UTM zone is a 6‎° segment of the Earth. Because a circle has 360°, this means that there are 60 UTM zones on Earth. (360 ÷ 6 = 60), right?

The Mercator uses an upright cylinder for its map projection. The Transverse Mercator takes a cylinder and places it on its side (rotates it 90°), as pictured below – which is how the term “transverse” is derived.

However, the Universal Transverse Mercator places this cylinder 60 times for each UTM zone.

This means that all 60 wedges are flattened out with a transverse cylinder. Each time it’s slightly rotated using a different meridian as a central line.

UTM applies a secant cylinder which intersects the ellipsoid along two small circles parallel to the central Meridian. This means that scale is constant north-south along the Meridians. But scale varies east-west along parallels. The two small circles are 180 kilometers east and west of the central Meridian at the Equator. The small circles have a scale factor of 1, meaning a distance of 100 meters in the ellipsoid would be the same on the map projection.

The center line of a UTM grid zone has a scale factor of 0.9996. This means that a distance of 100 meters on an ellipsoid would be 99.96 meters on a map.

What is a false easting and northing?

Instead of using latitude and longitude coordinates, each 6° wide UTM zone has a central meridian of 500,000 meters. This central meridian is an arbitrary value convenient for avoiding any negative easting coordinates. All easting values east and west of the central meridian will be positive.

If you’re in the northern hemisphere, the equator has a northing value of 0 meters.

In the southern hemisphere, the equator starts at 10,000,000 meters. This is because all values south of the equator will be positive. This is called a false northing because y-coordinates in the southern geographic region will avoid negative values.

Which UTM zone do you live in? Because you’ll need a bit of a deeper understanding to specify the position of a point on Earth in that particular UTM zone.

For example, UTM Zone 17S will use a false northing with the equator starting at 10 million. The NAD 1983 UTM Zone 18N will have the equator start at zero meters.

If you are given a set of UTM coordinates, you have to know which zone it is in beforehand because the central meridian is assigned 500,000 meters in each zone.

UTM projection distortions

The UTM projection minimizes distortion within that zone. So this means that when you want to show features in several UTM zone, it starts becoming a poor choice of map projection.

Distortion is small near the central meridian, and as you move away it worsens. So this makes it most fitting for narrow regions and not well-suited for world maps.

Just like every map projection, the Universal Transverse Mercator has its strength and weaknesses. It is up to the map maker to determine what projection is most favorable for its purpose.

…And the Universal Transverse Mercator was really meant to map features in one UTM zone at a time.

READ MORE: Map Distortion with Tissot’s Indicatrix

Flatten the Sphere 60 Times

Universal Transverse Mercator (UTM) coordinate system is a standard set of map projections with a central meridian for each six-degree wide UTM zone.

The transverse Mercator map projection is an adaptation of the standard Mercator projection which flips the cylinder 90 degrees (transverse).

The UTM projection flattens the sphere 60 times by shifting the cylinder central meridian 6° for each zone. This gives cartographers a map to work with always in meters.

The Universal Transverse Mercator is horrible for small-scale (less-detailed) maps like world atlases and perfect for mapping narrow regions

1. Close, but not quite. There’s a few common misconceptions in this post that always need to be unlearned by students and practitioners.

First, the UTM System is not a projection (!!!); rather, it is a global system of narrow mapping zones – each with its own instance of the transverse Mercator coordinate projection method. 120 zones means 120 map projections.

Second, each instance of the transverse Mercator projection method used in this system is a secant type of projection (scale factor along the central meridian < 1.0) and not a tangent type (as illustrated above). Consequently, the distortion pattern created by each includes a swath of deflation between the standard circles, no distortion along the standard circles (scale factor = 1.0), and inflation beyond them.

TRY:
Distortion is small near the central meridian, decreases as you approach a standard circle, and then increases and worsens as you move beyond the standard circle and toward the edge of the zone.

2. andrew says:

You did a good job of describing distance distortion.