Learn Hardcore Polish: Planując budżet na miesiąc, liczymy czynsz, rachunki za prąd i gaz oraz bilety na tramwaj. - When planning the budget for the month, we count the rent, the bills for electricity and gas and the tram tickets.

It corresponds very closely to English “(while/when) planning” or “(when we) plan”.
Grammatically, it always refers to the same subject as the main verb of the sentence.
Here: the implied subject is we in liczymy → so planując means “(when we are) planning”.

So the whole beginning Planując budżet na miesiąc is like saying “When (we are) planning the budget for the month…”.

Why is there a comma after Planując budżet na miesiąc?

In Polish, an adverbial participle phrase like planując budżet na miesiąc is treated as a separate clause and is normally separated by a comma from the main clause。

Planując budżet na miesiąc, liczymy…
= When planning the budget for the month, we count/include…

This is a fixed rule: adverbial participles (-ąc, -wszy, -łszy) almost always take a comma before the main clause.

What is the subject of planując? There is no pronoun.

The subject of planując must be the same as the subject of the main verb liczymy.

liczymy is 1st person plural (“we count / we include”).
Therefore, planując implicitly means “(we) planning” or “when we plan”.

Polish does not repeat the subject before the participle; it is understood from the main verb. You cannot use planując with a different subject from the one in the main clause.

Why is liczymy used here, and does it really mean “count”?

Liczymy is the 1st person plural form of liczyć.

Basic meaning: to count (numbers).
In this context it means “to include / to take into account” in the budget.

So liczymy czynsz… is more like “we include the rent…” or “we factor in the rent…” rather than literally “we count the rent”.

Other possible verbs in this context:

wliczamy (we include / count in)
uwzględniamy (we take into consideration)

Why is it budżet na miesiąc and not something like miesięczny budżet?

Both are possible, but there is a nuance:

budżet na miesiąc = budget *for a month
– Focus on the *time span (for one month, monthly period, etc.).
miesięczny budżet = monthly budget
– Sounds a bit more like a fixed type of budget (monthly vs yearly) and is slightly more formal or “label-like”.

In normal speech about practical money planning, budżet na miesiąc is very natural and common.

What case is budżet in, and why?

Budżet is in the accusative singular.

The full underlying structure is:
(Gdy / Kiedy) planujemy budżet na miesiąc, liczymy…
planować takes a direct object in the accusative → budżet.

In the participle form planując, the object budżet remains accusative:

planując (co?) budżet

Why are czynsz, rachunki, and bilety all in the same form? Are they also in the accusative?

Yes, they are all direct objects of liczymy, so they are in the accusative:

liczymy (co?) czynsz – we count/include (what?) the rent
liczymy (co?) rachunki za prąd i gaz – (the) bills for electricity and gas
liczymy (co?) bilety na tramwaj – (the) tram tickets

Forms:

czynsz – masculine inanimate, nominative = accusative sing.
rachunki – masculine inanimate plural, nominative = accusative plural.
bilety – masculine inanimate plural, nominative = accusative plural.

Because for masculine inanimate nouns, nominative and accusative are identical, they look like nominative, but here they function as accusative objects.

Why is it rachunki za prąd i gaz, and not something like rachunki prądu i gazu?

For “bills (for something)”, Polish almost always uses the construction:

rachunek za + accusative = bill for something

So:

rachunek za prąd – electricity bill
rachunek za gaz – gas bill
rachunki za prąd i gaz – bills for electricity and gas

Rachunki prądu i gazu would sound unusual or unclear; it suggests more “accounts of electricity and gas” rather than household bills.

What is the function of na in budżet na miesiąc and bilety na tramwaj? Does it always mean “on”?

Here na + accusative does not mean “on” (physically on top of something). It has other common meanings:

budżet na miesiąc
- na + accusative → “for (a period of time)”
- budget *for a month*
bilety na tramwaj
- bilet na + accusative (środek transportu) → “ticket for (a means of transport)”
- tickets *for the tram*

So na has several uses; “on” is only one of them. Here, it means for (a purpose / period / destination).

Why is tramwaj singular in bilety na tramwaj?

Bilety na tramwaj literally is “tickets for the tram (as a mode of transport)”, not “tickets for trams (individual vehicles)”.

In Polish, when you talk about a type of transport, you usually use the singular with na:

bilet na tramwaj – tram ticket
bilet na autobus – bus ticket
bilet na pociąg – train ticket

The plural trams is not needed; the singular tramwaj already expresses the kind of transport.

What is the difference between i and oraz here? Why use oraz?

Both i and oraz can mean “and”. The difference is mainly in style:

i – the basic, neutral “and”, used everywhere.
oraz – also “and”, but often feels a bit more formal, emphatic, or used before the last item in a list.

Here, czynsz, rachunki za prąd i gaz oraz bilety na tramwaj can be seen as:

group 1: czynsz
group 2: rachunki za prąd i gaz
final item: bilety na tramwaj (introduced with oraz)

You could replace oraz with i and it would still be correct:

… rachunki za prąd i gaz i bilety na tramwaj
Just slightly less “neatly” grouped.

Could we change the word order and say Liczymy czynsz… planując budżet na miesiąc?

Yes, that is grammatically possible:

Liczymy czynsz, rachunki za prąd i gaz oraz bilety na tramwaj, planując budżet na miesiąc.

However:

The original order (Planując budżet na miesiąc, liczymy…) is more natural here because it first states the context/purpose (when planning the budget) and then lists what we include.
Placing the participle at the end is technically fine, but stylistically a bit heavier and less common in everyday language.

Could we say Kiedy planujemy budżet na miesiąc, liczymy… instead of using planując?

Yes, you can say:

Kiedy planujemy budżet na miesiąc, liczymy czynsz…
Gdy planujemy budżet na miesiąc, liczymy czynsz…

This is fully correct and often easier for learners. The meaning is practically the same:

Planując budżet na miesiąc, liczymy…
Kiedy / Gdy planujemy budżet na miesiąc, liczymy…

The planując form is just more compact and slightly more “written-style” or advanced.