I am putting an addition on my house I has a 200 amp siemens panel in it now I want to install a sub panel in the addition mainly because the preent panel does not have room for more breakers. I will be moving the washer and dryer and heat pump and central air to sub panel, also I will be adding 2 bedrooms, a bathrom and mudroom in the sub. Was wondering how to determine what size sub panel I need for addition.

Without doing any calculations because you don't have numbers. He washer, dryer, heat pump can run at the same time and it's very likely that the max breaker you can get for the panel is 100 A, maybe 125A, but I doubt it.

Isn't the AC the Heat Pump?

SO lets say 40, 15, 15, 20 for HP, washer, dryer and bathroom and that's 90 A. Loads are going to be less. The breakers don't have to total to 100 A.

The NEC can be read online with registration for free. See the sticky under Electrical and Lighting at the link at the top left of this page.

Your breaker panel can be either a main lug or main breaker panel. You can even put in a 200 A panel with a 100 A breaker in the main. In this case the 200 A main breaker in the sub acts as a local disconnect.

Wiring from main to sub would be rated at the feeded breaker size.

So a guestimate is 100 A. Hopefully someone will confirm this.
Loads that are expected to be on for more than 3 hours at a time, such as the heat pump are deemed as continuous loads. So if the HP is 30 A, then you use 1.25*30 as the load value.

You really want to look for a panel with an available number of spaces, so you may at least be loooking at a 125 A panel.

I do see breakers for washer, dryer, heat pump, bathroom.
Put the ceiling lighting on a separate circuit.

And I'd do each bedroom as separate circuits.

When you put the lighting on a separate circuit, you don't risk being in the dark while vacuuming or whatever.

Remember to put in hall circuits for easy plugging in of a vacuum cleaner. Those circuits being separate also prevent neucense trips, say using a hair dryer in a bedroom.

Using a hair dryer in a bedroom is likely the biggest load seen in the bedroom.

So, there are some ideas.

100 Amp feeder using #2 - 4 wire aluminum SER cable will be fine.

Don't forget smoke detectors, one in each bedroom and one in a common are outside the bedrooms. Also need Arc fault breakers for the bedrooms and mud room, not needed for bathroom.