Po pracy jestem tak zmęczony, że chcę tylko spać.

Because po here requires the locative case.

• praca = work
• locative singular: pracy

So:

• po pracy = after work

This is a very common pattern in Polish:

• po obiedzie = after lunch
• po szkole = after school
• po filmie = after the film

So the form pracy is there because of the preposition po.

In this sentence, po pracy most naturally means after work in the sense of after my work / after the workday.

Polish often uses a noun where English might sometimes prefer a phrase like after working. But here the normal interpretation is simply:

• Po pracy = after work

If you wanted to emphasize the activity of working, Polish might use a different structure, but in everyday speech po pracy is the standard expression.

Polish often drops subject pronouns like ja, but it normally keeps the verb to be in the present tense.

So:

• jestem zmęczony = I am tired

You would usually not say just zmęczony as a full neutral sentence meaning I am tired, although in conversation people can shorten things informally. The standard full sentence needs jestem.

What Polish often drops is the pronoun:

• Ja jestem zmęczony = I am tired
• Jestem zmęczony = I am tired

Both are correct, but the second is more neutral because Polish usually does not need ja unless you want emphasis.

Yes. Zmęczony must agree with the person it describes.

For a man:

• jestem zmęczony

For a woman:

• jestem zmęczona

For a mixed group or a group of men:

• jesteśmy zmęczeni

For a group of women:

• jesteśmy zmęczone

So if a female speaker says this sentence, it becomes:

• Po pracy jestem tak zmęczona, że chcę tylko spać.

Tak ... że means so ... that.

In this sentence:

• tak zmęczony, że... = so tired that...

This is a very common structure in Polish:

• Było tak zimno, że nie wyszliśmy. = It was so cold that we didn’t go out.
• Jestem tak głodny, że zjem wszystko. = I’m so hungry that I’ll eat anything.

So the sentence structure is:

• tak
  • adjective/adverb + że
    • result

Because in Polish, że introduces a subordinate clause, and such clauses are normally separated by a comma.

So:

• Po pracy jestem tak zmęczony, że chcę tylko spać.

That comma is required in standard Polish spelling.

This is very common with że:

• Wiem, że masz rację. = I know that you’re right.
• Było tak późno, że wróciliśmy do domu. = It was so late that we went home.

Because after chcę (I want), Polish uses the infinitive.

• chcę spać = I want to sleep
• chcę jeść = I want to eat
• chcę odpocząć = I want to rest

The form śpię means I sleep / I am sleeping, which is a finite verb form, so it cannot directly follow chcę here.

So:

• correct: chcę spać
• incorrect: chcę śpię

Here tylko means only or just.

So:

• chcę tylko spać = I only want to sleep / I just want to sleep

It emphasizes that the speaker wants nothing else.

Word placement with tylko can matter a little, but in this sentence it naturally modifies the verb phrase spać. The idea is:

• the only thing I want to do is sleep

Sometimes yes, but the meaning or emphasis may shift.

The natural version is:

• chcę tylko spać

This usually means:

• I just want to sleep
• sleep is the only thing I want

If you move tylko, it may sound marked or emphasize a different part. For example:

• tylko chcę spać — possible in context, but less neutral
• chcę spać tylko — usually sounds incomplete unless something follows

So the sentence as given is the most natural everyday order.

Because the second part is a result, not just another separate statement.

• tak zmęczony, że... = so tired that...

The że clause explains the consequence of being tired.

If you said:

• Po pracy jestem tak zmęczony i chcę tylko spać

that would sound wrong or at least badly connected, because tak strongly expects że in this structure.

So że is necessary to complete the meaning so tired that...

Spać is imperfective.

That makes sense because sleeping is seen here as an activity or state, not as a completed single result. After chcę in this kind of sentence, Polish often uses the infinitive that expresses the action naturally:

• chcę spać = I want to sleep

There is no normal perfective partner used in the same straightforward way here to mean sleep as a complete one-time result. So spać is exactly the right verb.

Yes. Both are possible in English.

• I just want to sleep sounds more natural in everyday English.
• I only want to sleep is also correct, but it can sound slightly more formal or more strongly contrastive.

The Polish chcę tylko spać can cover both ideas, depending on context and tone.

Yes, it is completely natural and idiomatic.

It sounds like something a Polish speaker would really say in everyday conversation. The structure is very common:

• time/context first: Po pracy
• main statement: jestem tak zmęczony
• result clause: że chcę tylko spać

So this is a very good model sentence for learning everyday Polish.