Kostnaden er høy.

Because -en is the definite singular ending for many common-gender nouns in Bokmål.

• en kostnad = a cost
• kostnaden = the cost

So Kostnaden er høy literally means The cost is high.

Kostnad is a common-gender noun in Bokmål, so it takes en in the indefinite singular:

• en kostnad
• kostnaden

That is why you do not see et kostnad.

Er is the present tense of å være (to be).

So:

• er = is / are / am, depending on context

In this sentence, Kostnaden er høy, it simply means The cost is high.

Unlike English, Norwegian verbs do not change according to the subject:

• Jeg er
• du er
• han er
• vi er

It stays er in the present tense.

Because høy is agreeing with a singular common-gender noun.

Here is the basic pattern for this adjective:

• common gender singular: høy
• neuter singular: høyt
• plural: høye

Examples:

• Kostnaden er høy. = The cost is high.
• Nivået er høyt. = The level is high.
• Prisene er høye. = The prices are high.

Even though kostnaden is definite (the cost), the predicate adjective still stays høy because the subject is singular common gender.

Yes, and this is a very common learner question.

In Norwegian, høy is often used with things like:

• pris = price
• kostnad = cost
• lønn = salary
• alder = age
• temperatur = temperature

So Kostnaden er høy sounds very natural.

You can also hear dyrt in related expressions, especially when talking more generally:

• Det er dyrt. = It is expensive.
• Bilen er dyr. = The car is expensive.

A useful rule of thumb:

• high price/cost → often høy / høye
• expensive thing → often dyr / dyrt / dyre

Yes. It is a perfectly complete sentence:

• Kostnaden = subject
• er = verb
• høy = predicate adjective

So structurally it is very similar to English The cost is high.

Because Norwegian normally uses Subject – Verb – Complement in ordinary statements.

So:

• Kostnaden = subject
• er = verb
• høy = complement

That gives:

• Kostnaden er høy.

Norwegian word order is quite strict here, much like English.

Yes. That would turn it into a question:

• Kostnaden er høy. = The cost is high.
• Er kostnaden høy? = Is the cost high?

This is a standard pattern in Norwegian: the verb comes first in many yes/no questions.

Høy contains a sound that can be tricky for English speakers.

A rough guide:

• h is like English h
• øy is a diphthong, something like a rounded vowel sliding into another sound

It is usually pronounced approximately like høy /hœʏ/.

The exact sound does not exist neatly in English, but you can think of it as somewhat similar to saying a rounded vowel and gliding forward. The important part is that it is not pronounced like English hoy with a clear oi sound.

Usually kostnaden refers to the cost in a specific situation or context.

For example:

• Kostnaden er høy. = The cost is high.
• Den totale kostnaden er høy. = The total cost is high.

If you are speaking more generally about costs in the plural, you would use:

• kostnader = costs
• kostnadene = the costs

Example:

• Kostnadene er høye. = The costs are high.

Yes, Kostnaden er høy is standard Bokmål.

In Nynorsk, you might more naturally see:

• Kostnaden er høg.

The main difference here is the adjective:

• Bokmål: høy
• Nynorsk: høg

Both mean high.