InkScape has an area measurement tool that works quite well, it's a bit unrefined, but if Adobe adopted something similar, I'm sure they could improve upon it. (April 2023)

Area of a circle is pi multiplied by a diameter of a circle, no big deal to calculate it. If you want to automate the process — you can use custom plugins like Dynamic Measure by AstuteGraphics.

The other thing is if you want to control the size of the circle by entering the desired area. Like 'create a circle with area x' or 'transform a circle to have the area y'. Is that you want? Plugins can’t do that so far.

Still, there are methods to automate it, like actions to create circle presets, libraries, so on. It’d be easier to understand the request if you provide some examples you want to create.

Anyway, bezier ellipses are not real circles, but a good approximation. So no ACCURACY is possible anyway :)

Please add ability to calculate area of circle (in addition to the existing height/width). This will make it easier for users to create ACCURATE data visualizations/infographics!

This calculation should be included in Photoshop, InDesign, After Effects -- basically, any tool someone may want to use to create a data viz.

could it be possible to get the area of a shape like it is possible to get the length in the "Object" tag of the information panel.

When calculating how much material to buy e.g. architecture and interior design - calculating m² of flooring/cladding/tiling required

When creating emboss dies for label printing we need to know the area of the emboss on the label as the embossing units have maximum area they can emboss in one hit. This calculation (without using a third party script) would be very useful.

Bobby, here's a script I've assembled to quickly get areas and perimeters:
https://www.dropbox.com/s/ujtj1smsvd304rw/6%20Get%20Shape%20Area%20and%20Length.jsx?dl=0
It's based on Bryan's Buchanan and Hiroyuki's Sato scripts, but works on compounds.
Feel free to modify it as you like.

Feature is still required right form the box, in Document Info palette!

Years ago I used Telegraphics' free "Path Area" plug-in to determine the path length of single or multiple selected objects. The plug-in's dialog box would display both the length and area of any selected objects. That plug-in hasn't worked with the last few versions of Adobe Illustrator. It's effectively a dead plug-in.

Currently Illustrator will display Path Length values under the Document Info tab (when Objects are checked in the options fly-out). I would like path area to be added to the values shown for Paths.

Right now my only option for determining path area is using the Dynamic Measure tool, part of Astute Graphics' VectorScribe plug-in. It's a useful tool for certain tasks, but it does not work on multiple selected objects. If I want to determine the physical area of a group of letters I'm going to rout out of a sheet of aluminum I have to select/hover over each object one at a time, write down the values and then add up the results. It's a tiresome, annoying process.

This can be scripted though and this is what I use, I'd like to have it natively; in document chosen units (squared), correctly for compound paths also.