Fallout – How many caps can you earn with Fortune Finder

You can wear an armor piece for each limb plus your chest and head and then a thin garment underneath. This means you can wear your vault suit or some other clothing and have a piece of armor on each arm/leg and your chest/head, and these will be rendered on top of each other when you zoom out. You can also wear some eye wear which can add a further minor boost to stats.

Note that some items of armor will completely remove all other armor (for example the Haz Mat Suit will remove everything and you'll have to put it all back on again afterwards).

I found the solution while tediously studying the pip boy.
While it doesn't give an exact number, there is a gauge to the right of the main pip boy screen that reflects how much radiation you've contracted.

You cannot really determine it down to the exact rad, but should be able to guess to within 10 or so rads. As far as I can see, there is no rads bar or anything in the actual pip boy screen itself (as there was in FO3 or New Vegas).

If anyone finds it difficult to read the gauge, zooming in a bit (with the touchpad on a dualshock) makes it a little easier.
And as rpmerf commented, right click zooms on PC.