Another really rough ball park way of calculating a contractor rate is to take the equivalent yearly salary that you want in $k and use that number as your rate.
EG you want to earn $100k per year, so you charge $100/hour.
This roughly takes care of overheads and downtime when you are not working etc.
However, a more correct calculation is to start with how much you want to net, then add in all the costs of overheads (EG liability insurance, business licensing, equipment costs, 401k matching, health care and any other expenses you may incur), figure out how many hours a year you want to work (and are likely to work, not including EG vacation time, and time spent waiting/looking for work) and divide one by the other.
But then you need to make a judgement call about how your desired rate stacks against the local competition, and what makes you worth the rate that you want to earn compared to them.
Finally if you are being paid $xx/hour for your job, then your company is probably internally billing you as 2 times $xx/hour to cover the overheads of employing you, and that the difference between that and what the customer is actually being billed at is their profit.
But don't begrudge them that amount of $. IMHO unless you are capable of going out and taking directly to clients, then I'd consider it as a finders/agents fee for finding the work for you.
And one last thing .. there is also Freelancing.SE which will have a pile more of theses types of questions.