You already know what your right hourly price is. However many clients are going to request a fixed price. Some may request this even before they have a specification.

You can give a fixed price if

• The specifications are well defined.
• You know how to handle change requests.
• You are good with estimating time
• You are comfortable with the client. (It requires experience and git feeling to decide which client will demand a lot of changes and insist they are part of the original specifications.)

If ALL of these do not exist, you should be very wary of committing to a fixed price quote and instead insist on a hourly/weekly pricing.