Poplatník vypočítá daň z příjmů.

Poplatník is the subject of the sentence, so it is in the nominative singular.

A native English speaker might also want to know what kind of noun it is:

• it is masculine animate
• singular dictionary form: poplatník
• if it were in the accusative, it would change to poplatníka

So here poplatník means the person who performs the action.

Daň is the direct object, so it is in the accusative singular.

The reason it looks unchanged is that for this noun, nominative singular and accusative singular are the same:

• nominative: daň
• accusative: daň

So the case does change grammatically, but the form happens to stay identical.

Because the preposition z requires the genitive case.

Here:

• z = from / of
• příjmů = genitive plural of příjem (income, receipt, earnings depending on context)

So z příjmů is literally something like from incomes, but in normal English this corresponds to income tax.

This is just how Czech expresses the standard term.

The official and normal Czech expression is daň z příjmů. Even though English uses singular/uncountable income, Czech uses the plural noun příjmy in this set phrase.

So:

• English: income tax
• Czech: daň z příjmů

This is something best learned as a whole expression.

Vypočítá is the 3rd person singular form of the verb vypočítat.

Important point: vypočítat is a perfective verb.

That means:

• it focuses on reaching a result: to calculate, to work out
• its present-tense forms often have a future sense in ordinary Czech

So vypočítá can often mean will calculate in everyday language.

However, in formal, legal, or instructional language, Czech often uses this kind of form to describe procedures in a general way, where English may use calculates.

Because vypočítat and počítat do not mean exactly the same thing.

• počítat is imperfective
  It focuses on the process, repetition, or ongoing activity. It can also mean to count.
• vypočítat is perfective
  It focuses on the completed result: to calculate / work out

In a sentence about determining tax, vypočítá is natural because the idea is arriving at the calculated amount, not just being in the middle of calculating.

Because Czech does not have articles like English.

So poplatník can mean:

• the taxpayer
• a taxpayer
• sometimes just taxpayer in a general sense

The exact interpretation comes from context, not from an article.

The same applies to daň:

• the tax
• a tax
• tax

English forces you to choose; Czech often does not.

No. Czech word order is fairly flexible because case endings show what each noun is doing.

The order here:

• Poplatník vypočítá daň z příjmů.

is the most neutral subject–verb–object order.

But Czech can reorder the sentence for emphasis, for example:

• Daň z příjmů vypočítá poplatník.
  Emphasizes who calculates it.
• Daň z příjmů poplatník vypočítá.
  Can sound more marked or contrastive depending on context.

So the original order is the most straightforward, neutral version.

It is both.

You can understand it word by word:

• daň = tax
• z příjmů = from/of income(s)

But it is also a standard fixed term meaning income tax.

That means it is best to learn daň z příjmů as one vocabulary unit, even though its grammar is completely regular.