Der Tag ist heute ruhig.

Because Tag is a masculine noun in German. Its basic form is der Tag.

German nouns have grammatical gender:

• der = masculine
• die = feminine
• das = neuter

So:

• der Tag = the day

You usually just have to learn the gender together with the noun.

Yes. Der Tag literally means the day. German often uses the definite article where English might or might not.

In this sentence, der Tag is the subject:

• Der Tag = the day
• ist = is
• heute = today
• ruhig = calm / quiet

It does sound like it refers to today as a day in a general descriptive way.

Because German main clauses usually follow the verb-second rule (V2). The finite verb normally comes in the second position.

In this sentence:

• Der Tag = position 1
• ist = position 2
• heute ruhig = the rest

That is standard German word order.

Because ruhig is being used after the verb ist, so it is a predicate adjective.

In German:

• attributive adjectives (before a noun) take endings
  
  • ein ruhiger Tag = a calm day
• predicate adjectives (after sein, werden, bleiben, etc.) do not take endings
  
  • Der Tag ist ruhig = the day is calm

So ruhig stays unchanged here.

Here, ruhig means something like:

• calm
• quiet
• peaceful

For a day, it usually means the day is not hectic, not stressful, not full of activity.

It does not necessarily mean completely silent. It can describe the general atmosphere of the day.

Yes, heute can move, but the verb still stays in second position.

Current version:

• Der Tag ist heute ruhig.

Also possible:

• Heute ist der Tag ruhig.

Both are grammatically correct, but the emphasis changes:

• Der Tag ist heute ruhig. → focus starts on the day
• Heute ist der Tag ruhig. → focus starts on today

German often moves time expressions like heute for emphasis or style.

It is grammatical, but it may sound a bit less neutral in everyday use, depending on context.

Most neutral:

• Der Tag ist heute ruhig.

Also very natural in many contexts:

• Heute ist es ruhig. = It’s quiet today.
• Heute ist der Tag ruhig can work, but it may sound more marked or literary unless the context clearly contrasts today with other days.

Because all nouns are capitalized in German.

So:

• Tag = noun → capitalized
• heute = adverb → not capitalized
• ruhig = adjective → not capitalized

This is one of the most noticeable spelling rules in German.

It is understandable and grammatical, but in everyday speech Germans might often choose a more natural phrasing depending on context, such as:

• Heute ist es ruhig.
• Es ist heute ein ruhiger Tag.
• Der Tag ist heute sehr ruhig.

Your sentence is fine, but it can sound a little more descriptive or written than the most common spoken option.

A rough guide:

• Der ≈ dehr
• Tag ≈ tahk
• ist ≈ ist
• heute ≈ HOY-tuh
• ruhig ≈ roughly ROO-ikh or ROO-ig depending on accent

A few pronunciation notes:

• eu in heute sounds like oy
• r in German is often different from English r
• g at the end of ruhig is not pronounced like hard English g

Yes, you could, but it is more formal or stylistically heavier.

• Der Tag ist heute ruhig. = simple, direct
• Der heutige Tag ist ruhig. = The present/today’s day is calm, which sounds more formal or literary

In normal conversation, Germans would usually prefer the simpler version.

It is in the nominative case because it is the subject of the sentence.

You can identify it by asking:

• What is calm today?
• Der Tag.

So:

• der Tag = nominative singular masculine
• ist agrees with that singular subject