Kompensationen er høj.

Because Danish usually puts the definite article at the end of the noun.

• kompensation = compensation
• kompensationen = the compensation

The ending -en is the definite ending for many singular common-gender nouns.

So Danish often does this:

• en bog = a book
• bogen = the book

The same pattern gives:

• en kompensation = a compensation
• kompensationen = the compensation

It is a common-gender noun in Danish.

You can tell because:

• the indefinite form is en kompensation
• the definite form is kompensationen

A useful pattern: many nouns ending in -tion are common gender in Danish, for example:

• en situation
• en nation
• en produktion

So en kompensation fits a very common pattern.

They do different jobs:

• kompensation = compensation in a general or uncountable sense
• en kompensation = a compensation / one compensation
• kompensationen = the compensation / a specific compensation already known from context

Examples:

• Kompensation er vigtig. = Compensation is important.
• Han fik en kompensation. = He got a compensation / some compensation.
• Kompensationen er høj. = The compensation is high.

So in your sentence, kompensationen refers to a specific compensation.

Er is the present tense of at være, which means to be.

So:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• vi er = we are

Unlike English, Danish uses the same form er for all persons in the present tense.

In this sentence, er simply means is.

Because the subject kompensationen is singular common gender, and predicate adjectives agree with gender and number.

After er, Danish adjectives usually behave like this:

• common gender singular: høj
• neuter singular: højt
• plural: høje

Examples:

• Kompensationen er høj.
• Beløbet er højt.
• Udgifterne er høje.

So høj is the correct form because kompensation is a common-gender singular noun.

Yes. The difference is that these are two different sentence structures.

In Kompensationen er høj, the adjective comes after er because it is a predicate adjective:

• The compensation is high

If you want the adjective directly before the noun, you can do that too:

• høj kompensation = high compensation

So:

• Kompensationen er høj. = full sentence
• høj kompensation = noun phrase

Both are correct, but they are used in different structures.

Because Danish normally does not use den when the noun already has the definite ending.

So:

• kompensationen = the compensation

Not normally:

• den kompensationen

However, den is used in other situations, especially when there is an adjective before a definite noun:

• den høje kompensation = the high compensation

This is a very common Danish pattern:

• bilen = the car
• den røde bil = the red car

So with no adjective, kompensationen is enough by itself.

In this simple sentence, the word order is very similar to English:

• Kompensationen = subject
• er = verb
• høj = adjective

So it is basically:

subject + verb + complement

But Danish also follows the verb-second rule in main clauses. That means the finite verb usually stays in the second position.

For example:

• Kompensationen er høj.
• I år er kompensationen høj.

In the second sentence, I år comes first, so er still stays in second position.

Høj is one syllable.

A helpful rough guide for English speakers:

• h sounds like English h
• ø has no exact English equivalent; it is somewhat like the vowel in bird or her, but with rounded lips
• then it glides toward a y sound, a bit like the start of yes

So høj is roughly something like hoy, but with a more rounded vowel than normal English oy.

If you want a practical learner tip: listen carefully to native audio, because ø is one of the vowels that usually needs imitation rather than spelling-based guessing.

In Danish, høj is very commonly used for amounts, levels, prices, salaries, taxes, compensation, and other measurable quantities.

So Danish says things like:

• høj pris = high price
• høj løn = high salary
• høj skat = high tax
• høj kompensation = high compensation

Stor usually means big, large, or sometimes great in a different sense.

So in this sentence, høj is the natural choice because the idea is that the compensation is at a high level/amount, not physically big.