(NOTE: this software is at the testing stage. There will be bugs and the reporting of them will be appreciated)
Math Minion is a general purpose calculation tool that runs completely in the browser and is completely free and private.
It combines a mind map style diagram of the relationships between a range of calculation tools, with a formula system that operates transparently on scalars, arrays and matrices. It also includes a comprehensive conversion unit system that performs dimensional analysis on all calculations.
Best of all, if you have a reasonably recent browser and can wait a few seconds for it to load, you can try it right now by tapping on Run.
iPad Mouse and Trackpad
There is some strange behaviour when you mix trackpad (or mouse) use with touch dragging or pinching on the screen. The latter will always work, but disables the trackpad on the diagram, graphs and result tables. Also pinch zooming on the trackpad doesn't work and should be avoided. Use the + and - zoom icons on the diagram instead. Reloading will restore things.
Any thoughts on the cause of this would be most welcome.