Learn Hardcore Croatian: Hvala, račun je spreman.

a restaurant check: Račun, molim.
a store invoice or receipt: Trebam račun za povrat.
an account (bank/online): bankovni račun, korisnički račun. In your sentence, it means the bill/invoice is ready.

Why is there a comma after Hvala? Could I use a period instead?

Hvala works like an interjection here, so it’s set off with a comma. Both are fine:

Hvala, račun je spreman.
Hvala. Račun je spreman. The comma makes it feel like one smooth utterance; the period makes it two short sentences.

Is Hvala alone polite enough? What about Hvala vam or Hvala ti?

Hvala is polite and perfectly fine on its own.
Hvala vam adds politeness/formality (speaking to one person politely or to more than one person).
Hvala ti is informal/singular (to a friend). You’ll also hear Puno hvala, Hvala lijepo/lijepa. In formal emails, you may see capitalized Vam: Hvala Vam.

Why is it spreman and not spremna or spremno?

Adjectives agree with the noun’s gender and number. Račun is masculine singular, so:

masculine: spreman → Račun je spreman.
feminine: spremna → Narudžba je spremna.
neuter: spremno → Piće je spremno. Plural masculine mixed: spremni; plural feminine: spremne; plural neuter: spremna.

Could I say Račun je gotov instead of spreman? Any nuance?

Yes. Common options and nuances:

spreman = ready/available (emphasizes readiness)
gotov = finished/done (very common in service contexts)
izdan = issued (more formal/administrative)
pripremljen = prepared (focus on the preparation process) All are grammatical; pick based on tone and context.

Where does je go, and can it move? Why not Račun spreman je?

Je (is) is a clitic and wants 2nd position in its clause. Natural options:

Račun je spreman.
Spreman je račun. (emphasis on spreman) But not Račun spreman je in standard speech. When you add words, je still goes right after the first stressed element:
Vaš račun je spreman.

How do I turn this into a question: “Is the bill ready?”

Use je li:

Je li račun spreman? Colloquial speech often contracts it to Je l’ račun spreman? You’ll also hear Da li je račun spreman? in the region, but standard Croatian prefers je li.

Can I drop je and say Račun spreman?

Not in normal sentences. You need je in the present tense. Omitting it is telegraphic style (headlines, labels, notes): Račun spreman might appear on a status screen, but it’s not full standard prose.

Why is there no word for “the” in račun? How do I say “the bill” vs “a bill”?

Croatian has no articles. Definiteness is understood from context, or you can specify:

ovaj/taј račun (this/that bill)
vaš račun (your bill)
neki račun (some bill, a bill) In your sentence, context makes it “the bill.”

What’s the plural of račun, and how does the adjective change?

Plural is računi. Agreement:

singular: Račun je spreman.
plural: Računi su spremni. With a possessive: Vaši računi su spremni.

What case is račun in here?

Nominative singular, because it’s the subject: Račun je spreman.
For reference: after Hvala na… you’d use locative: Hvala na strpljenju.

Is the sentence natural in real life? In what situations would I hear it?

Yes, especially in messages from a service or shop: a repair is done, an invoice is prepared, etc. In a restaurant you’re more likely to hear:

Vaš račun je gotov.
Evo računa.
Or you might ask: Račun, molim.

Any quick pronunciation tips for these words?

Hvala: pronounce the initial cluster as one unit: HVA-la. Croatian h is stronger than English h; r is tapped/trilled.
račun: č = ch in English “church”; u = oo in “food” → ra-CHOON.
spreman: stress early; rolled r; all vowels short and clear.

How could I make the opening Hvala sound more specific or polite?

Add a reason or courtesy:

Hvala na strpljenju, račun je spreman. (Thank you for your patience…)
Hvala vam, račun je spreman. (more polite)
In formal emails: Poštovani, račun je spreman za preuzimanje.