It supports all of the basic mathematical operations, although it does not appear to support logic ("and," "or," "not") or bitwise operators (such as "<<", ">>", "|", and "&".) However, it does do some simple natural language-type parsing. Interestingly, "1 and 1" actually does yield an answer, but "and" is treated as addition, not logical and.
It handles several different bases. For example: here is 42 in binary, octal, in hex, and 0x21 in decimal. You can use "base n" notation, but I have not found any bases that work other than 2, 8, 10, and 16.
It knows mathematical constants like pi and e.
It knows the basic mathematical functions such as trig functions, hyperbolic trig functions, the natural logarithm, log base 10, and square root. It also knows about some somewhat more advanced mathematical operations such as factorial, the gamma function, "choose",
Okay, so far so good, but pretty boring you say? It gets better.
It handles imaginary numbers, and it's standard functions all seem to work with complex arguments.
It knows a bunch of scientific constants including:
Given this list, it probably knows many other values, although I have been somewhat surprised to find out some of the constants it does not know.
It also knows about units. For example, here is the radius of the Earth in:
feet,
inches,
miles,
nautical miles ,
meters,
km,
light years,
au,
angstroms,
furlongs, and
Smoots.
(Yes, for those of you who do not know, the Smoot is a unit of length.) My personal favorite way to test a unit converter is to ask for Planck's constant in slug-acres per fortnight, but Google's also happily does stone-Smoot-parsecs per fortnight. This is not just an idle curiosity, of course. It knows there are 2 pints in a quart, 3 teaspoons in a tablespoon, and about 3.79 liters in a gallon. (This should be useful to those of you who like the many food related articles here on K5.)
But for those of you who doubt this calculator can solve all of your life's problems, you will be happy to know that it knows the answer to life the universe and everything, even in binary. However, it still does not seem to know the air-speed velocity of an unladen swallow is.