A friend has a 200amp main breaker in their panel. Their panel is completely full i.e.. No available spaces for additional breakers. They want to add a sub panel for central air and for an eventual hot tub. The central air calls for a 30 amp double pull and the hot tub should be a 50 amp double pull. Also a couple of circuit s will have to moved into the sub panel so that there is room for the subpanel breaker. They have a gas range and hot water tank but their dryer is electric so the loads in the house are nominal.
My questions is what size sub panel break should be used (100amp)? The sub panel will be very close to the main panel.
Thank you in advance for your help and please ask any questions that are necessary to that this is done correctly.

You would have to use a 100 amp subfeed if it was done that way. The existing box can not be changed from wide breakers to skinny ones?

Or why can you not move over some small breakers to the new box and put the 220 breakers in the main box. Then you could get by with a 60 amp sub.

How many spaces do you have in your panel? If it's a smaller 200 amp panel it may have less spaces. You can get 200 amp panels with up to 40 spaces. Just an option if that's the case.

How about holding off on doing any work, until you do a demand load calculation. The added load may require a service upgrade.

Also, the serving utility may notice a peak in your in-home use--requiring you to make changes on their side of the service.