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Add Geometry Attributes—Help | ArcGIS Desktop will get the coordinates in, then you can add a Z field to the table and put your values in. I assume you know how to add a field and assign values to the records.
There are several places where things can go awry. Here's a good article with a process which helps one avoid the common issues. I'd run through this process. If it doesn't work out, let us know what went awry.
Chris Donohue, GISP
I believe your formula should be: degree + min/60 + sec/3600 = DD
Make sure when you do your Display XY Coordinates you choose a geographic coordinate reference system (probably WGS84 or NAD83) to uses degrees as the unit. You can project the data later once you've got them properly defined.
So I have tried to follow the document posted before doing anything new to the data, and it still only displayed 3 points (out of 207) off the coast of Africa. I tried re-calculating the latitude and longitude using the new formula posted in a reply, and that did not help. I also tried saving my excel sheet as a text file before adding to arcmap, and still only got 3 points. I feel like the issue lies with how my excel sheet is being imported into arcmap. I have tried to import it straight from the flash drive it is located on, as well as importing it as a table first into the default.gdb then adding it to the map from that file, and they both have the same result. I have noticed that uploading it as a text file does keep my X (longitude) values from turning into null or 0, but this has not affected the placement of the points. I'm not sure why arcmap is displaying so few points, when they are in fact different locations. I've included a few examples of my data below if that helps any.
Depth (m) X (long) Y (lat)
I know a number of my values may match up, simply because these coordinates were taken from a location with a grid overlay, but I have a lot more than 3 unique locations.
The table I import doesn't have the spaces or parentheses, I just typed those to illustrate what they were for the reply. I originally used WGS 1984, but since that didn't work I've played around. The NAD 1983 state planar for south Louisiana put my coordinates in Mexico, which is the closest I've gotten. Using UTM 15N puts me off the coast of Ecuador. I feel like I'm not proficient enough to fully understand the differences between all of the options. Is that what you're asking, for coordinate reference system?
Your coordinates are lat/long so it is definitely a geographic CRS. Whether you use WGS84 or NAD83 doesn't really matter for now - they are quite similar. If you can't get your points plotted with WGS84, there is a different problem with your data.
the last 4-5 digits of your numbers suggest that something definitely was done wrong ie ending in fractions of 60..
mere coincidence? perhaps the data were calculated with the wrong decimal precision in the first place?
Ok, so since there was a problem most likely with my calculations, I went back to google earth and changed the settings to show coordinates in decimal degrees (did not know this was an option the first go around). This ended up creating individual points, but it was at a 1:0m scale and still off of Africa. The points shouldn't be that close since the pond I'm working from is a scale of 1:3000m. What I ended up doing is adding a shape file, editing point features, and using the absolute XY function to get my 10mX10m intersection points. It was allowing me to do exact coordinates while placing them, but does not show the coordinates in either the attribute table or the sketch properties screen. Is there a way for the coordinates of my points to show up on the attribute table? Also, is there a way to add my depths to their corresponding points to the attribute table? Once I get these values to show up, I know how to create the map I want from there...just didn't realize how big of a mess my points were going to make in the first place! Thanks for all the help.