Stämningen är lugn i vardagsrummet.

Stämningen here means “the atmosphere / the mood” (of the room).

• The basic noun is stämning = mood, atmosphere
• Swedish often puts “the” at the end of the noun instead of in front:
  • stämning = a mood / mood
  • stämningen = the mood / the atmosphere

So -en is the definite ending for most common-gender nouns (the ones that take en in the indefinite: en stämning → stämningen).

Lugn is an adjective meaning calm.

In Swedish, adjectives agree with the gender and number of the noun they describe:

• en stämning → stämningen (common gender, singular)
  → adjective form: lugn
• ett rum → rummet (neuter, singular)
  → adjective form: lugnt
• plural (any gender): lugna

So:

• Stämningen är lugn. – The atmosphere is calm.
• Rummet är lugnt. – The room is calm.
• Barnen är lugna. – The children are calm.

No. In Swedish, you normally don’t use a separate word for “the” together with the noun in this way.

You say:

• ett vardagsrum – a living room
• vardagsrummet – the living room

So “the living room” is almost always just vardagsrummet, not det vardagsrum.

Correct options:

• Stämningen är lugn i vardagsrummet.
• Stämningen är lugn i det här vardagsrummet. – in this living room
  (Here det is part of det här, this, which is fine.)

Vardagsrummet is a compound noun:

• vardag – weekday / everyday life
• rum – room
• vardagsrum – living room (literally “everyday room”)
• vardagsrummet – the living room

So the pattern is:

• ett vardagsrum → vardagsrummet
  (neuter noun, definite form with -et)

Both i and på can mean “in / at / on”, but they’re used in different types of expressions.

• i is used for inside places or rooms:

  • i vardagsrummet – in the living room
  • i köket – in the kitchen
  • i huset – in the house

• på is used for:

  • surfaces: på bordet – on the table
  • some institutions/places: på jobbet – at work, på skolan – at school

A room of a house is something you are in, so i vardagsrummet is the natural choice.

Yes, that’s correct Swedish, just a slightly different emphasis.

• Stämningen är lugn i vardagsrummet.
  → neutral, states the situation; focus a bit on the mood.

• I vardagsrummet är stämningen lugn.
  → puts more emphasis on the place: In the living room, the mood is calm (maybe in contrast to somewhere else).

Both are grammatically fine and natural.

This mostly has to be memorized; there is no simple rule that predicts it.

• en stämning (common gender) → stämningen
• ett vardagsrum (neuter) → vardagsrummet

Some rough tendencies exist (for example, many -ing words are en-words), but you still have to learn the gender with each noun:

• en stämning, en tidning, en räkning
• ett rum, ett hus, ett bord

Stämning has several meanings; in this sentence it clearly means “mood / atmosphere”:

• stämning = mood, atmosphere
  
  • Det är bra stämning här. – There’s a good atmosphere here.

Other meanings (not relevant here, but useful to know):

• stämning = tuning (music)
  
  • gitarrens stämning – the tuning of the guitar
• stämning = summons (legal)
  
  • en stämning – a legal summons

Context decides the meaning. With i vardagsrummet, the natural interpretation is the atmosphere in the room.

Approximate English comparisons:

• ä (in Stämningen) – similar to the vowel in “ten” or “bed”, but often a bit more open.

  • stäm- sounds roughly like “stem” (but with Swedish accent).

• å is not in this particular sentence, but in general:

  • å sounds a bit like the “o” in “more” (British) or “or” in “born”, but often a bit shorter and more rounded.

So Stämningen is roughly: STEHM-ning-en, with stress on STÄM.

Different verbs give slightly different meanings:

• är lugn – is calm

  • Just describes the current state.

• blir lugn – becomes calm / gets calm

  • Focuses on a change: it wasn’t calm before, but now it is.

• känns lugn – feels calm

  • Focuses on how it feels to someone.

In this sentence we simply want to state a fact about the atmosphere, so är lugn is the neutral, most direct choice.

Yes, that is also correct and very natural:

• Stämningen i vardagsrummet är lugn.

Now the phrase i vardagsrummet directly describes stämningen (“the mood in the living room”), instead of describing where it is calm. The meaning is nearly the same; it just slightly changes the structure:

• Stämningen är lugn i vardagsrummet.
  → The mood is calm in the living room.

• Stämningen i vardagsrummet är lugn.
  → The mood in the living room is calm.

Both are fine in everyday Swedish.

Yes, you could replace lugn with other adjectives, depending on the nuance:

• Stämningen är stilla i vardagsrummet. – The atmosphere is still/quiet.
• Stämningen är avslappnad i vardagsrummet. – The atmosphere is relaxed.
• Stämningen är harmonisk i vardagsrummet. – The atmosphere is harmonious.

But lugn is the most common, neutral way to say the atmosphere is calm.