How many days do you need for Norway?

10 days is definitely not too much! And I wouldn't spend more than 2 nights in Copenhagen, especially since you will spend night 3 in the ferry and thus have a full day in Copenhagen.

We went to Norway in 2018. Family of 4. Spent 10 days and $11,000 dollars, airfare not included. You don’t say how many in your family, but Norway is very expensive, so based on that, 10 days was enough for us.
Here is my trip report.
https://community.ricksteves.com/travel-forum/trip-reports/10-nights-norway-for-family-of-4

Norway is a big country (over 1000 miles south to north) and with multiple climate zones east to west. A 10 day trip would be a sampler tour skipping much of the more rural (and scenic) Norway.

One sampler tour itineary could be:

Multi-city flight itineary to OSL with CPH stopover then return from BGO.

2 fulldays/3 nights Copenhagen

Morning flight to OSL

3 or 4 nights Oslo

Morning train from Oslo S to start Norway in a Nutshell tour (train, boat, bus) via Myrdal and Flam to Bergen. 2 or 3 day with stopover midway through journey.

Arrive Bergen mid-day
2 or 3 nights Bergen

Depart by air from Bergen (BGO)

The above is just a sampel of Southern Norway. There is much more to Norway. See Norway's tourist info wesite: https://www.visitnorway.com/places-to-go/top-10-places-in-norway/

And if you are into slow travel (hiking, skiing)....

Looks like multi-city flight option from ATL to CPH is not very economical if SAS is not a viable option. Best may be to drop CPH and strech Noway.

Norway is a large country and very mountainous. Travel takes a lot of time.

I suggest you consider taking a cruise up the coast of Norway. NCL and Royal Caribbean both have great 11-12 day cruises that go up to the North Cape and stop in several ports.

You get to enjoy the amazing scenic fjords on the ship and then when you get off the ship at the ports, you can take the nutshell tour and others that visit mountains areas.

Norway is very expensive, probably the most expensive country in Europe. In 2019, I remember getting a beer for lunch and it cost the equivalent of $10. It was not a large beer.

By cruising, your lodging and meals are included.

You can do a land tour in conjunction with a cruise, perhaps a shorter cruise that doesn't go to the North Cape. Many cruise lines have them.

Also, in mid-June, the higher elevations have just come out of the snow season where roads are blocked. We visited one port were we were told in mid-June that a week before there was a big snow storm and the roads we used on our ship's excursion were closed.

I don't understand the appeal of the overnight ferry. Why do people take it?

I would fly from Copenhagen out, like Trondheim, Bergen, or Alesund then rent a car and work back to Oslo.

...appeal of the overnight ferry. Why do people take it?

Tax free alcohol. Alcohol is highly taxed in Norway.

We went to Norway in 2018. Family of 4. Spent 10 days and $11,000 dollars, airfare not included.

Adding as a rebuttal to the "it's so expensive" comments:

In 2018 for a family of 5 for 12 days in Norway, 5 days in Stockholm, total cost was $8135 including airfare.

Caveats:
Airfare outbound on points, return on Icelandair very inexpensive at about $330.
2 nights in hotels on points
Cost per day without airfare was $378
Stayed entirely in AirBnBs when paying for lodging
Car rental for 9 days was $630 including a one way charge of $100
Mostly picnicked and cooked for ourselves
Did spring for some large ticket items like the Holmenkollen zip line $260 and frankly just the Nidaros church admission at $80 for all of us was hard to swallow.

So it can be done not very expensively. I cringe when I read about people treating Norway like a radioactive cave, got to limit exposure to as few days as possible or get burned. Yes, Norway and Iceland are more expensive than Germany or France but not really much more expensive than travel in the US.

Yes, you will need 10 days to see a variety of things.

@Tom_MN I stand by my assessment of Norway being expensive. Many others also agree. Can you do it for less than what we spent? Sure. You could sleep in a tent, stay with friends, cook all your own meals, whatever. But, we are not budget travelers and we were not extravagant. Stayed in nice hotels which included breakfast and ate out for other meals. Did the NIN.

Reply:

I am going to be a little contrarian. AirBnb cabins right on the fjords, 3-4 bedroom size and in no way "budget travel", go for about $200/night, at least in 2018. Getting 3 hotel rooms (for 5 it is often required) would have been $600/night or more but not necessarily a better experience. I priced out the NIN and could see that renting a car and spending a week driving through many fjords was going to be about the same cost as a 2-3 day NIN experience so (gasp!) chose to skip it. We drove many fjords and took a ferry through Geiranger which is considered to be the most beautiful. We ate out some dinners maybe 5 total. Frankly I do not go to Europe to sit and wait for the bill, so we often cook for ourselves for the time savings: it's usually less to time to shop, cook, and wash up than to have a restaurant meal. Grocery shopping is a cultural experience I wouldn’t miss.

As to eating out, Norwegians do consider this to be an extravagant activity and prefer to host each other over meeting in a restaurant.

We did not camp, and paid for 10 nights lodging, all AirBnb.

I second Edgar’s plan except I would recommend the ferry. Taking the ferry was a fun new experience for us and we were with friends so we socialized that evening. We also bought some duty free alcohol to bring with us as it is so expensive in Norway. But if your time is limited in Norway then flying to Oslo would make more sense.

Norway can be expensive. San Francisco and New York City can also be expensive.

But if you recreate where Norwegians holiday prices can be less expensive. I looked up our group rate half board (breakfast and dinner) cost at the Radisson Blu Mountain Resort, Beitostølen in Winter 2018. We paid $3000 USD for two in one room to our ski association. That's $300 per day for two of us.

During summer months trekking can be less exepnsive. An example DNT 8 day/7 night tour across the Hardangervidda is priced at 11,000 NOK including the 1,500 non-member surcharge. That's $175 per night per person at 9 NOK/USD.
https://english.dnt.no/aktiviteter/139368/903987/

MASSIV IV HARDANGERVIDDA

8 dyas/7 nights We stay at well-built and charming serviced cabins
along the route and one night at a self-service cabin.

Price: NOK 9.500,- from Finse/to Haukeliseter Non-member surcharge
NOK 1,500,-. .

The package includes: Accommodation, tour leadership, all meals
(breakfast, packed lunch/thermos, normally three-course dinner)
except: First day only dinner and last day only breakfast plus packed
lunch/thermos.

No, 10 days is not enough time in any country…….