
der Haushalt
household
The entirety of the people who live together in an apartment or house and form an economic unit.
In unserem Haushalt leben vier Personen.
Four people live in our household.
household / budget
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household
The entirety of the people who live together in an apartment or house and form an economic unit.
In unserem Haushalt leben vier Personen.
Four people live in our household.

housework
The activities involved in running a home, such as cleaning, cooking, and doing laundry.
Meine Mutter hat sich immer um den Haushalt gekümmert.
My mother always took care of the housework.

budget
The financial plan of a public institution (such as a state or municipality) or an organization for a specific period; the budget.
Der Bundestag hat den neuen Haushalt für das kommende Jahr verabschiedet.
The Bundestag passed the new budget for the coming year.

balance
In biology or ecology, the balance between intake and output of a certain substance in a system.
Ein ausgeglichener Wasserhaushalt ist für den Körper sehr wichtig.
A balanced water balance is very important for the body.
'Haushalt' is made up of 'Haus' (house) and 'Halt'. The word part 'Halt' is related to the verb 'halten' (to hold) and here means something like 'management' or 'organization'. A Haushalt is therefore the organization of a house or system.
Ein gut organisierter Haushalt spart Zeit und Geld.
A well-organized household saves time and money.
When referring to the people living together, 'Haushalt' (household) is often combined with numbers or size descriptions, e.g. 'Ein-Personen-Haushalt' (single-person household), 'Mehrpersonen-Haushalt' (multi-person household), or 'kinderloser Haushalt' (childless household).
In Deutschland gibt es immer mehr Ein-Personen-Haushalte.
There are more and more single-person households in Germany.
To describe housework, 'Haushalt' is often combined with the verbs 'machen' (to do) or 'führen' (to run). The expression 'den Haushalt schmeißen' (to run the household) is also colloquial and very common.
Wer schmeißt bei euch zu Hause den Haushalt?
Who runs the household at your place?
You can recognize the meaning 'Budget' (budget) from the context. When politics, the state, finances, or a government are being discussed, it almost always means the public financial plan.
Die Ministerin verteidigte ihren Entwurf für den Haushalt.
The minister defended her draft of the budget.
In scientific texts, especially in biology or medicine, 'Haushalt' (balance) refers to a system in equilibrium. It is then usually part of compounds such as 'Wasserhaushalt' (water balance), 'Energiehaushalt' (energy balance), or 'Säure-Basen-Haushalt' (acid-base balance).
Sportler müssen auf ihren Elektrolythaushalt achten.
Athletes have to pay attention to their electrolyte balance.
economy / pub
Both Wirtschaft and Haushalt can refer to managing cooking, cleaning, and household finances. Today, people generally say “den Haushalt führen.” Wirtschaft on its own sounds outdated in this sense and is more likely to occur in older texts.

Heute führen beide Eltern gemeinsam den Haushalt der Familie.
Today, both parents run the family household together.
In dem Roman von 1900 führt die älteste Tochter die Wirtschaft der Familie.
In the 1900 novel, the eldest daughter runs the family household.