Taket är för lågt i källaren.

In Swedish, the definite article is usually added to the end of the noun instead of being a separate word.

• tak = ceiling / roof
• taket = the ceiling / the roof

So -et is the neuter singular definite ending, equivalent to English the.

It can mean either the ceiling or the roof in Swedish, depending on context.

In this sentence, the ceiling is the natural meaning, because i källaren means in the basement, and it makes much more sense to talk about a low ceiling there.

So even though tak can mean both, context tells you which one is intended.

Because taket is a neuter noun.

Swedish adjectives often change form depending on the gender and number of the noun:

• common gender singular: låg
• neuter singular: lågt
• plural / definite plural contexts: låga

Since tak is a neuter noun (ett tak), the adjective becomes lågt.

So:

• ett tak är lågt = a ceiling is low
• taket är lågt = the ceiling is low

Here, för means too.

So:

• lågt = low
• för lågt = too low

This is a very common Swedish pattern:

• för dyrt = too expensive
• för kallt = too cold
• för svårt = too difficult

Be careful: för can mean other things in other contexts, such as for or before, but here it clearly means too.

Because källaren means the basement.

• källare = a basement / basement
• källaren = the basement

Swedish often uses the definite form where English also uses the:

• i källaren = in the basement

If you said i en källare, that would mean in a basement, which is less specific.

This is standard Swedish main-clause word order:

• Taket = subject
• är = verb
• för lågt = complement
• i källaren = place expression

So the structure is basically:

Subject + verb + description + place

This is very similar to normal English word order: The ceiling is too low in the basement.

In practice, it describes the location of the whole situation: the ceiling is too low in the basement.

English works the same way. You would not usually separate those meanings sharply in a sentence like this. The natural interpretation is simply that the basement has a ceiling that is too low.

For the same reason as with taket: Swedish usually adds definiteness to the end of the noun.

• källare = basement
• källaren = the basement

So instead of saying something like the basement, Swedish often expresses this with the ending -en or -et, depending on the noun.

It is an en word:

• en källare = a basement
• källaren = the basement

That is why the definite ending is -en here.

Compare:

• ett tak → taket
• en källare → källaren

A rough guide for an English speaker is:

TAH-ket air fur lohgt ee KHEL-lah-ren

A few notes:

• å in lågt is like a long aw/o sound.
• ä in är and källaren is somewhat like the vowel in air, though not exactly the same.
• g in lågt is not strongly pronounced in normal speech; the word can sound a bit like låt to an English ear.
• The stress is usually on the first syllable of taket and källaren.

Yes. That means The basement's ceiling is too low or The ceiling of the basement is too low.

That version is also grammatical, but it sounds a bit more specific or formal.
Taket är för lågt i källaren is a very natural way to say it in everyday Swedish.

You would say:

Taken är för låga i källaren.

Changes:

• taket → taken = the ceilings
• lågt → låga because the adjective agrees with a plural noun

So adjective agreement changes with number as well as gender.