# Why does the same UTM northing give different values when converted to latitude?

I'm converting two coordinates from UTM to latitude/longitude. The coordinates are:

``````Easting: 657787
Northing: 7795664
``````

and

``````Easting: 658144
Northing: 7795664
``````

Both from zone 23S (EPSG:31998) or 23K (following this reference). Notice that both have the same northing.

The latitudes given for both are slightly different:

``````-19.929034598845494 and
-19.92900563505912
``````

I have tried this using R's `spTransform` function, and also this website. Why aren't they giving me exactly the same latitude, since the northing is the same?

• Accuracy: When using any kind of computer to convert numbers, check out the accuracy (not the same as precision) of your software. Depending on your hardware, language and operating system, if you mix e.g. double and float they will indeed give different answers after the decimal point. Nov 11, 2020 at 12:18
• Precision: I have had this problem with coordinates, and the project leader could not understand why the two numbers looked different. I solved this by docking the displayed number after the decimal point back to roundabout where the difference is 1 metre. This was for ballistics, so 1 metre is quite precise enough. Nov 11, 2020 at 12:21
• @RedSonja Double and Float are a C thing, not R or the website linked. Also, you can see that my difference is on the 5th decimal place (~ 10 m error), but the numbers displayed have 14-15 decimal places. Didn't the answer below convince you? Nov 11, 2020 at 14:01
• The answer is quite correct and answers your question. That is why I only wrote a comment. If you feel this does not apply to you, it may apply to the next person who reads your question. Even if you are not writing code (not only C), just using it, this is a real issue. Nov 12, 2020 at 8:31

This is perfectly normal behaviour in a transverse Mercator projection. The fact that a specific northing does not match a specific latitude (except for the Equator itself) can be easily visualized.

We are used to seeing global maps of the more familiar equatorial-aspect (or normal) Mercator projection, which depicts parallels and meridians as perfectly straight lines parallel to the x and y axes:

So at first, your result may seem surprising, as you noticed differing latitudes for a specific northing in UTM, however UTM uses a transverse aspect. Essentially it's the same projection, but sideways, and check out what it does to parallels and meridians:

The latitude and longitude lines are now curved!

Granted, UTM does not use a single, full extent projection, but it instead uses 60 6-degree bands centered on some central meridians in order to use the area of the projection with minimal distortion, but for the sake of the present visualization, I'm going to use the full projection, but the principle holds for smaller regions too..

Notice how, when we draw straight northing (horizontal) lines on that projection, they do not follow latitude lines anymore (except for the Equator):

Hence, it is perfectly normal that a specific northing corresponds to slightly different latitudes, depending on the easting.

• (Capitalising words: If it is for emphasis, we have italics and bold on this platform. With a few minor exceptions, only proper nouns are capitalised in current versions of English, not common nouns. That was different a few hundred years ago.) Nov 11, 2020 at 18:32
• @PeterMortensen Thank you for the info. This will definitely help me in the future with capital letters in GIS terminology! Nov 11, 2020 at 22:09