Is there a rule of thumb as to the number of outlets on a 20 amp circuit. How about a 15 amp. I do understand that 20 amp will carry about 2400 watts and 15amp will carry about 1800 but all of the outlets will not be used at the same time. This is for a residential room expansion with limited space in the main panel.

Most rule of thumb are superseded by building codes. If you have a building department you should check with them first. They will also tell you if their code requires the outlets to be spaced at a certain interval.

You shouldn't exceed 80% of a circuits rating, 1440 watts for 15 amps, and 1920 for a 20 amp. You and add tandem breakers giving you 2 circuits in the space of one. The more copper, the better. You can find a link to the National Electric Code in the sticky at the top of the E&L forum, https://www.askmehelpdesk.com/electrical-lighting/read-first-all-electrical-questions-48863.html Many of our DIY forums now have stickies allowing you to find answers to common questions without waiting for an answer.

Rule is 10 because some home owner is going to plug in one of those 6 pack outlets in every duplex to run all his crap no more than 10 and you won't have any problemos

There is no maximum quantity of outlets for a residential general purpose lighting circuit according to the National Electric Code.

For all other than residential, the maximum is 8 outlets on a 15 amp circuit and 10 on a 20 amp circuit. This is widely used as a guide in residential,but is not mandatory and is flexible.

This is where common sense will come in, not to have too many outlets that will have appliances, computers, TV, etc. all on one circuit.