Døren er lukket, så jeg kan ikke komme ind.

Because døren is the definite form: the door.

In Danish, the definite article is usually added to the end of the noun:

• en dør = a door
• døren = the door

So Døren er lukket means The door is closed.

Lukket means closed or shut here.

It comes from the verb at lukke, which means to close.

So:

• at lukke = to close
• lukket = closed

In this sentence, lukket describes the state of the door.

It means closed, not necessarily locked.

That is an important difference:

• lukket = closed / shut
• låst = locked

So Døren er lukket does not automatically mean the door is locked. It just means it is closed.

Because Danish often uses er + past participle/adjective to describe a state.

So:

• Døren er lukket = The door is closed

This focuses on the result or condition of the door, not the action of someone closing it.

English does the same thing: The door is closed.

Yes.

• er lukket = is closed / is in a closed state
• bliver lukket = is being closed or gets closed

So in your sentence, er lukket tells us the door is already closed.

Så means so here.

It connects the two ideas:

• Døren er lukket = The door is closed
• så jeg kan ikke komme ind = so I cannot come in

So så shows a result or consequence.

Because here så is being used as a conjunction meaning so, linking two main clauses.

After this kind of så, the second clause keeps normal main-clause word order:

• jeg kan ikke komme ind

The subject jeg comes before the finite verb kan.

A learner often notices that Danish sometimes inverts word order, but not in this structure.

In a Danish main clause, ikke usually comes after the finite verb.

So:

• jeg kan ikke komme ind

Here:

• jeg = subject
• kan = finite verb
• ikke = negation

This is very normal Danish word order.

A useful comparison:

• Main clause: Jeg kan ikke komme ind
• Subordinate clause: ... at jeg ikke kan komme ind

So ikke moves depending on the clause type.

Because kan is a modal verb, and modal verbs in Danish are followed by the bare infinitive.

So you say:

• jeg kan komme ind

not:

• jeg kan at komme ind

This is similar to English:

• I can come in
• not I can to come in

Other common Danish modal verbs work the same way:

• vil
• skal
• må
• bør

Because komme ind is a verb phrase meaning come in / get in / enter.

In Danish, words like ind, ud, op, and ned often work as particles that go after the verb:

• komme ind = come in
• gå ud = go out
• løbe op = run up

So kan ikke komme ind is the normal way to say cannot come in.

The basic form is kunne, which means can / be able to.

Here are the forms you are most likely to notice first:

• kan = present tense
• kunne = past tense / dictionary form

So:

• jeg kan ikke komme ind = I cannot come in

They are both vowels that do not match English exactly.

• ø in døren has no exact English equivalent. It is somewhat similar to the vowel in French deux or German schön.
• å in så is roughly like the vowel in law or saw for many English speakers.

These are only rough guides, but they are a good starting point.