Emacs calc is one of my favorite computer algebra systems: it can derive and sum and integrate, numerically or symbolically. It can do unit conversions, graph equations, and do geometry. It's really very neat and useful.
To use this code in any serious capacity, remember the sign conventions: North latitude and East longitude are both positive, South latitude and West longitude are both negative.
It's utterly arbitrary but fairly universal.
If you think about north as up and west as left, then it works out the same as a coordinate plane, so it makes sense.