Learn Hardcore German: Ich bin innerlich ruhig, obwohl der Tag stressig war. - I am calm inside, although the day was stressful.

Obwohl is a subordinating conjunction in German. Subordinating conjunctions (like weil, dass, wenn, obwohl) send the conjugated verb to the end of the clause.

So:

Der Tag war stressig. – normal main clause: verb in position 2
… obwohl der Tag stressig war. – subordinate clause: war goes to the end

This is a general rule:

Ich bleibe zu Hause, weil ich müde bin.
Ich glaube, dass er Recht hat.
Sie kommt, wenn sie Zeit hat.

Could I say obwohl der Tag stressig ist instead of war?

You can, but it changes the nuance slightly.

obwohl der Tag stressig war
– The speaker sees the day as something that is (more or less) over or as a completed unit. The stress is viewed as something that happened earlier in the day.
obwohl der Tag stressig ist
– The speaker is talking about the stress as something that is still going on right now.

In everyday speech, war is very natural even if the day is not completely finished yet, because you are talking about how the day has been up to now.

Why is it der Tag and not den Tag or some other form?

Here der Tag is the subject of the subordinate clause:

der Tag (subject, nominative)
war (verb)
stressig (predicative adjective)

So it must be nominative der Tag, not accusative den Tag.

Compare:

Der Tag war stressig. – subject in nominative
Ich fand den Tag stressig. – Ich = subject; den Tag = object in accusative

Why is there a comma before obwohl?

German always separates a full subordinate clause from the main clause with a comma. Since obwohl der Tag stressig war is a complete subordinate clause (it has its own subject and verb), you must write a comma:

Ich bin innerlich ruhig, obwohl der Tag stressig war.

If you put the obwohl‑clause first, you also need a comma:

Obwohl der Tag stressig war, bin ich innerlich ruhig.

If I start with obwohl, why is it bin ich innerlich ruhig and not ich bin innerlich ruhig?

When a subordinate clause comes first, the main clause that follows still has the verb in second position. The entire subordinate clause counts as “position 1”, so the finite verb of the main clause comes right after the comma:

Obwohl der Tag stressig war, – whole clause = position 1
bin – verb of main clause = position 2
ich innerlich ruhig. – the rest of the main clause

So:

Obwohl der Tag stressig war, bin ich innerlich ruhig. ✔
Obwohl der Tag stressig war, ich bin innerlich ruhig. ✘ (verb is not in second position)

What exactly does innerlich ruhig mean? How is it different from just ruhig?

ruhig by itself can mean:
- calm (emotionally)
- quiet (not making noise)
- peaceful (environment)
innerlich ruhig narrows the meaning to inner, emotional calm. It says explicitly that the calmness is on the inside, in contrast to outer chaos or stress.

So:

Ich bin ruhig. – I’m calm / I’m being quiet (context decides).
Ich bin innerlich ruhig. – Inside I feel calm, even if things around me are hectic.

It emphasizes an inner emotional state, not just external behavior.

Is innerlich an adjective or an adverb here, and why is it before ruhig?

Grammatically, innerlich is an adjective that is used adverbially here to modify ruhig.

Ich bin ruhig. – ruhig describes ich (predicate adjective).
Ich bin innerlich ruhig. – innerlich further specifies what kind of calmness: calm on the inside.

The usual pattern in German is:

sein + [adverb] + [adjective]
Ich bin innerlich ruhig.
Ich bin sehr müde.
Ich bin völlig sicher.

Putting innerlich after ruhig (Ich bin ruhig innerlich) is grammatically possible but sounds unusual and very marked; in normal speech you put innerlich before ruhig.

Could I leave out innerlich and just say Ich bin ruhig, obwohl der Tag stressig war?

Yes, that is perfectly correct:

Ich bin ruhig, obwohl der Tag stressig war.

The difference:

With innerlich: You emphasize your internal emotional state, possibly in contrast to external stress or even your outward behavior.
Without innerlich: You just say you are calm/quiet, and context decides whether that is inner or outer calm.

What is the difference between stressig and gestresst?

stressig describes something that causes stress (an event, a situation, a day, a job):
- Der Tag war stressig. – The day was stressful.
- Mein Job ist stressig. – My job is stressful.
gestresst describes a person who feels stressed:
- Ich war gestresst. – I was stressed.
- Sie ist heute sehr gestresst.

So:

Der Tag war stressig, ich war gestresst. – The day was stressful, I was stressed.

Why is it Ich bin innerlich ruhig and not Ich habe innerlich ruhig?

In German, when you describe a state or characteristic of a person with an adjective, you normally use sein (bin, bist, ist, etc.), not haben:

Ich bin müde. – I am tired.
Wir sind glücklich. – We are happy.
Er ist nervös. – He is nervous.
Ich bin innerlich ruhig. – I am calm inside.

Haben is used for possession or for some fixed expressions, but not for simple state adjectives like ruhig, müde, glücklich, etc.

Could I use trotzdem instead of obwohl to say the same thing?

Yes, but the grammar changes slightly because trotzdem is an adverb, not a conjunction.

Original with obwohl (subordinate clause):

Ich bin innerlich ruhig, obwohl der Tag stressig war.

With trotzdem (two main clauses):

Der Tag war stressig, trotzdem bin ich innerlich ruhig.

Notice:

With obwohl, the verb in that clause goes to the end: …stressig war.
With trotzdem, both parts are normal main clauses, and trotzdem takes the first position, so the verb follows it in second position: trotzdem bin ich….