If you are asking how to calculate the maximum capacity of the chainrings and cogs, based on looking at the derailleur, then it's not going to be as easy as just looking at them.
Finding a derailleur to fit your chainrings/cogs based on just the chainrings/cogs is going to be a lot easier than finding chainrings based on looking at your derailleur.
HOWEVER, there are some standards for manufacturer, I have listed them below.
I have also included the formula to find out your capacities, since I misread your question initially and decided to answer the part you weren't concerned with.
I am not deleting it because, well, it took a while to type.
According to United Bicycle Institute: Determine Maximum Chainring Difference by subracting the number of teeth in the smallest chainring from the number of teeth in the largest chainring Determine Maximum Cassette Cog Difference by subtracting the number of teeth on the smallest cassette cog from the number of teeth on the largest cassette cog Determine Total Drivetrain Capacity by adding Maximum Chainring Difference to the Maximum Cassette Cog Difference Record
the Maximum Cassette Cog
(the number of teeth on the largest Cassette Cog) For Shimano: SS - Short Cage Road Double - Maximum Cassette Cog is 27 and Total Capacity is 29 GS - Medium Cage MTB/Road Triple - Maximum Cassette Cog is 34(MTB)/27(Road) and Total Capacity is 33(MTB)/37(Road)
SGS - Long MTB - Maximum Cassette Cog is 34 and Total Capacity
is 45 For SRAM: Short - Maximum Cassette Cog is 34(MTB)/28(Road) and Total Capacity is 32(MTB)/31(Road)
Medium - Maximum Cassette Cog is 34 and Total Capacity
is 37 Long - Maximum Cassette Cog is 34 and Total Capacity
is 45 For Campagnolo: Short - Maximum Cassette Cog is 26 and Total Capacity
is
27 Medium - Maximum Cassette Cog is 29 and Total Capacity
is 36 Long - Maximum Cassette Cog is 29 and Total Capacity
is 39 NOTE -
THIS INFORMATION IS SUBJECT TO CHANGE BY MANUFACTURER And
a great source for all of this is Sutherland's 7th edition http://www.sutherlandsbicycle.com/7th_Edition.html Hope that helps
bicycles.stackexchange.com/users/2946/mister_ed
You should be able to estimate the tooth capacity of a rear derailer by installing it on a bike, threading a chain through (and over a cluster), anchoring one end of the chain so it can't move, and pulling on the other end.
You'd first pull just enough to achieve "minimum" tension, then pull until the derailer was stretched close to tight.
Count the chain links that are pulled past a fixed spot
(ie, don't just count how many links roll off the jockey wheel) as you pull between these two positions.
You'd probably want to try this 2-3 times on different cogs of the cluster.
Definitely takes a bit of judgment, but should come within 1-2 teeth of the "right" answer.
bicycles.stackexchange.com/users/1584/Daniel R Hicks
Some nice detail in the big answer there.
However I should add that on my fancy road bike, I'm running a Shimano Ultegra 6700 SS (i.e. short cage)
Derailleur on a 10 speed cassette that is 12-30.
(I have a compact 50-34 at the front.)
Not that I do, but crossing the chain isn't a problem either, except for rubbing on the front derailleur.
So I don't understand the limits that Shimano give, except for - either covering their asses if somethign does go wrong- or more likely, wanting to sell more kit on the back of incompatibility.
bicycles.stackexchange.com/users/23525/Simon Rushton
I'm building a new touring bike and finding the capacity specs far below what I've used on the old one I put together.
The crank is 44-20 and the cassette is 36-11, which is a 49 capacity.
It works perfectly with old friction shifters, and an extra long derailleur screw.
and yes, this low gearing really has been useful/necessary with a loaded bike in the mountains.
bicycles.stackexchange.com/users/24885/sastrugi
I have found that the length of the derailleur from the bolt centre (rear axle) to the first jockey-pulley's outer edge (when the derailleur is in its lowest gear), must be greater than the radius of the largest rear cog (with the chain on it), i.e. an RD M592 9-speed will work on a 40 tooth maximum cog but not on a 46 tooth maximum cog.
Thank you
bicycles.stackexchange.com/users/43393/Dunstan Dunstan
The manufacturer's specs are total BS.
The max cog sizes and capacties can he extended ALOT!
Flipping the B tension screw over can get a Shimano Short Cage RD up to 36t max cog size (vs 27t spec) and
39t is the real capacity (vs. 29t spec).
The Specs are leaning WAY TOO PARANOID on the safe side.
The manufacturers are TERRIFIED of lawsuits.
So in essence you are lost and at the mercy of blogs and youtube videos to find THE REAL SPECS.
Lacing up a chain so the chain doesn't drag or drags just a tiny bit in small/small combo, then flipping the B tension screw so the head of the screw leans against the derailer hanger stop and max extending it, and then experimenting with the max tooth count cassette cog that'll fit w/o the upper jockey pulley grinding the largest cassette in small/big and the chain not jamming in big/big shift will determine your true RD max cog size and total tooth capacity.
It's that simple.
bicycles.stackexchange.com/users/36068/Michael Greene
It's easy to calculate what capacity of a rear derailleur will be needed based on the size of the big and small chainring and the big and small cog. What about the converse question, how to calculate the capacity of a derailleur?  I was comparing some short-cage rear derailleurs I have lying around, and I noticed that the cage length and pulley sizes varied enough that they probably had different capacities.  Related question: is there a fairly comprehensive place to look these up?
How to calculate the capacity of a rear derailleur
bicycles.stackexchange.com
<derailleur><math>
bicycles.stackexchange.com/questions/7264
bicycles.stackexchange.com/users/2824/Darth Egregious
There are a number of explanations on how to calculate the capacity of a rear derailleur based on the cogs and chainrings. However, they are extremely complicated and difficult to follow and a better solution may be to find a youTube video or a blog for a clearer picture. It is easier to find a derailleur to match your chainrings/cogs rather than the other way around. You can estimate the capacity by comparing the radius of the largest cog to the length of the extended derailleur and by installing it on the bike and experimenting with the high and low gears that can be used without grinding or jamming. The official specifications are more cautious than the true capacity, so some users find that these can be exceeded significantly.
It is easier to find a derailleur to match your chainrings/cogs rather than the other way around. You can estimate the capacity by comparing the radius of the largest cog to the length of the extended derailleur and by installing it on the bike and experimenting with the high and low gears that can be used without grinding or jamming. The official specifications are more cautious than the true capacity, so some users find that these can be exceeded significantly.