Fabrikanın bacasının çapı üç metre.

-ın is the genitive ending, meaning of the factory.

• fabrika = factory
• fabrikanın = of the factory / the factory’s

In Turkish, when one noun belongs to another, the owner often takes the genitive ending, and the thing owned takes a possessive ending.

So here, fabrikanın bacası means the factory’s chimney.

Because bacasının contains two things at once:

1. baca-sı = its chimney / the chimney of it
2. baca-sı-nın = of its chimney

So this word is doing double duty:

• it is possessed by fabrikanın
• and it is also the possessor of çapı

Structure:

• fabrikanın = of the factory
• bacasının = of its chimney
• çapı = its diameter

So the full chain is:

fabrikanın bacasının çapı
= the diameter of the factory’s chimney

This is the 3rd person possessive ending.

• baca = chimney
• bacası = its chimney / the chimney
• çap = diameter
• çapı = its diameter / the diameter

In Turkish, this ending is used in noun phrases where one noun belongs to another.

Examples:

• evin kapısı = the house’s door
• arabanın rengi = the car’s color
• bacanın çapı = the chimney’s diameter

So in your sentence:

• bacası = the factory’s chimney
• çapı = the chimney’s diameter

Because bacasının is part of a nested possession structure.

Break it down:

• baca-sı = its chimney
• baca-sı-nın = of its chimney

The -sı shows that the chimney belongs to the factory.
Then -nın shows that this chimney is itself the possessor of diameter.

So the grammar is:

• fabrika-nın = of the factory
• baca-sı-nın = of its chimney
• çap-ı = its diameter

This kind of stacking is very normal in Turkish.

That n is a buffer consonant.

When a noun already has a 3rd person possessive ending like -sı, and you add another case ending after it, Turkish often inserts n to connect them smoothly.

So:

• bacası = its chimney
• bacasının = of its chimney

The n is not a separate meaning by itself here; it helps attach the genitive ending.

You will see this often:

• evi = his/her house
• evinde = in his/her house
• evinden = from his/her house

Because Turkish marks these noun relationships more explicitly than English.

In English, we can say:

• the diameter of the chimney

In Turkish, that relationship is shown with possessive marking:

• bacanın çapı
• literally: the chimney’s diameter

So çapı has -ı because it belongs to bacasının.

This is one of the most important patterns in Turkish noun phrases.

It is understood, not spoken.

Turkish often omits the verb to be in present-tense noun sentences.

So:

• Fabrikanın bacasının çapı üç metre.
• literally: The diameter of the factory’s chimney three meters.
• natural English: The diameter of the factory’s chimney is three meters.

This is completely normal in Turkish.

If you want a more formal or emphatic style, you might sometimes see:

• Fabrikanın bacasının çapı üç metredir.

But in everyday Turkish, üç metre is enough.

Both are possible, but they are slightly different in style.

• üç metre = neutral, common, everyday
• üç metredir = more formal, more definite, sometimes more written or explanatory

So your sentence is perfectly natural as:

• Fabrikanın bacasının çapı üç metre.

Adding -dir is not necessary here.

Because in Turkish, nouns after numbers normally stay singular.

So:

• bir metre = one meter
• üç metre = three meters
• on baca = ten chimneys

You do not usually say üç metreler in this kind of sentence.

This is different from English, where plural is required after most numbers.

The sentence has this structure:

[topic / noun phrase] + [predicate]

• Fabrikanın bacasının çapı = the diameter of the factory’s chimney
• üç metre = three meters

So literally:

The diameter of the factory’s chimney — three meters.

This is a very normal Turkish sentence pattern, especially with noun sentences.

Yes, depending on context.

A simpler version could be:

• Bacanın çapı üç metre. = The chimney’s diameter is three meters.

If it is already clear which factory you mean, you may not need fabrikanın.

But if you want the full meaning the diameter of the factory’s chimney, then Fabrikanın bacasının çapı üç metre is correct and precise.

Yes. In fact, it contains that pattern twice.

First layer:

• fabrikanın bacası = the factory’s chimney

Second layer:

• bacasının çapı = its chimney’s diameter

Together:

• fabrikanın bacasının çapı = the diameter of the factory’s chimney

This is a very useful pattern to learn, because Turkish uses it constantly:

• arabanın kapısı = the car’s door
• okulun bahçesi = the school’s garden
• binanın çatısının rengi = the color of the building’s roof

You can for learning purposes, but it will sound unnatural in normal English.

A very literal breakdown is:

• Fabrikanın = of the factory
• bacasının = of its chimney
• çapı = its diameter
• üç metre = three meters

Literal sense: Of the factory, of its chimney, its diameter: three meters.

Natural English: The diameter of the factory’s chimney is three meters.

So the Turkish grammar is more layered than the English translation.