calc is just insane. From the manual:
"Calc was originally started as a two-week project to occupy a lull in the author’s schedule.
...
Emacs Lisp would surely reach its limits long before the project got too far out of hand.
To make a long story short, Emacs Lisp turned out to be a distressingly solid implementation of Lisp, and the humble task of calculating turned out to be more open-ended than one might have expected.
Emacs Lisp didn’t have built-in floating point math (now it does), so this had to be simulated in software. In fact, Emacs integers would only comfortably fit six decimal digits or so (at the time)—not enough for a decent calculator. So I had to write my own high-precision integer code as well, and once I had this I figured that arbitrary-size integers were just as easy as large integers. Arbitrary floating-point precision was the logical next step. Also, since the large integer arithmetic was there anyway it seemed only fair to give the user direct access to it, which in turn made it practical to support fractions as
well as floats. All these features inspired me to look around for other data types that might be worth having.
Around this time, my friend Rick Koshi showed me his nifty new HP-28 calculator. It allowed the user to manipulate formulas as well as numerical quantities, and it could also operate on matrices. I decided that these would be good for Calc to have, too. And once things had gone this far, I figured I might as well take a look at serious algebra systems for further ideas.
... (and on and on and on) ...
Final thanks go to Richard Stallman, without whose fine implementations of the Emacs editor, language, and environment, Calc would have been finished in two weeks."
If you look at its feature set, it is amazing how much can be done with it. It has nifty features like evaluating formulae inline in any buffer, and replacing the expression with the result. Expanding things to their LaTeX representation, etc.
I spent a lot of time trying to learn it. I use it for simple calculations, but ultimately decided it is not worth my time to go much further. That same effort would be better spent learning Sage, with a lot less cognitive load. And there is decent integration between Sage and Emacs.