Has to be free. Has to combine all the stupidly separated modes the Windows 8 calculator has. Has to have better history. Can have a learning curve, but should still feel like an elementary tool. Should be lightweight.

Bonus 1: be able to resolve formulas into graphs

Bonus 2: be able to sketch polygons on a grid, be able to view lengths, angles and name vertices; being able to color stuff by shape would be nice

Bonus 3: based on bonuses 1 and 2, an offline save/load function would be nice

It's 2013 - I don't think it's that much to ask. Apparently it is from Google, anyway.

Well, WolframAlpha (aka "online mathematica") surely qualifies as lightweight, has a bit of a learning curve and is by design easy to use, though it can misinterpret your input if you don't use the commands directly. It can certainly do everything a desktop calculator can. That said, it is unfortunately no longer free, and most of the cool advanced features (data analysis, etc..) are not available to guests...

You could use LaTeX/Tikz to draw polygons and possibly graphs, with no limitations, though the learning curve is quite punishing. You can then save and even share the text scripts everywhere. Not sure it qualifies as an "elementary tool" and it's not exactly lightweight, though I'm sure web services exist. But the "calculator" aspect is obviously lost, unless you are insane and want to use the preprocessor to compute stuff.

What do you mean, wolfram alpha no longer free? It seems to work for free for me :/

Anyway, feel free to hate it, after all I made it for personal use, but maybe the calculator on my website:

http://lodev.org/jscalc/jscalc.html

I tended to just reach for python and a few fairly feature rich libraries. (Can't recall which ones off hand, but my favourite was a math related one with a strong focus on graphing equations)

Run in interactive mode, and coded features as I needed them.

What do you mean, wolfram alpha no longer free? It seems to work for free for me :/

Anyway, feel free to hate it, after all I made it for personal use, but maybe the calculator on my website:

http://lodev.org/jscalc/jscalc.html

Yeah, if you're OK with half the features being reserved to "pro users" and advertisements nagging you every two queries.

Hm - it's actually kind of funny how there is no all-in-one free solution out there. After all there's one for most types of software from OpenOffice to VLC to Linux etc.

Yet no calculator.

In a way this is surreal.

I use the very lightweight and pretty high feature Powertoy calculator for winxp. It can run on windows 7 - best done if you can find somewhere to download the standalone exe and run it in comparability mode. Haven't tried it on Win8 though, so I don't know if it will work.

Microsoft site: http://windows.microsoft.com/en-US/windows/xp-downloads#2TC=powertoys - see the Power Calculator - but I suggest you google for the standalone exe - someone had it posted somewhere. Or you can try to install, or even better if you have an old xp machine, install there and just copy the .exe. If all else fails and you want to try it, I can put up a copy of it on my site

Features: It can graph simple functions, store formulas, has a very good (imo) history, supports binary and hex (entered as ###b for binary and 0x### for hex), has basic functions - trigs/logs, supports up to 512 bit precision, and has unit conversion (which is the only feature I don't use).

This has lately been annoying me too, the windows calculator is just too annoying to use for anything but the most basic operations. Luckily i have my physical calculator i need for school :3

I use SpeedCrunch as my default calculator. I use 0.11-alpha because the release version was missing some important feature--though I can't recall what that was.

Pros:

-Free

-It's like a hybrid of the Windows built-in calculator and the PowerToys calculator.

-Sessions can be saved

-Works on latest versions of Windows

-Hasn't crashed on me

Cons:

-No graphing support

-Hasn't been updated for years

-Limited binary support (No binary operations, but you can view the results as binary.)

Download MS Maths, its free

It solves, draws graphs, solves triangles, etc

You know it has so many features that during my pre-calculus, calculus and physics refresher I never once had to use anything else.

http://www.microsoft.com/en-us/download/details.aspx?id=15702