Hi Jim - good question.
As someone who uses/hires freelance and contractor developers and designers here's my take...
So many factors at play here:
Do you plan to work on evenings and weekends and or during the day? Standard day for day/hour rate calculations is 8 hours and an average month is around 21/22 working days.
Location you live in, in the UK, and will be remote or on site? Also, how much do you need to survive a month and do you have a regular job and this is extra earning power?
Remember it's not only your time because as a freelancer you have your laptop costs to consider, any software licence costs you have to do your job technically, issue invoices, timekeeping etc. etc. You will also have to pay tax.
Also, who is the client and what do they want you to do? They may match up to your ethics and ideals or offer you chance to work on something cool so will make you amenable to take a lower rate.
All of the above should be considered when pricing yourself and they are things I consider when hiring... As ahfarmer said, have a range.