Jeg sværger, at det er rigtigt.

Sværger means swear or am swearing here. Its infinitive/base form is at sværge = to swear.

In this sentence, sværger is in the present tense:

• jeg sværger = I swear
• jeg svor = I swore
• jeg har svoret = I have sworn

Here, at means that and introduces a subordinate clause:

• Jeg sværger = main clause
• at det er rigtigt = subordinate clause

So the structure is:

• I swear + that + it is true

Be careful: Danish at can also mean the infinitive marker to, as in at spise = to eat. In this sentence, though, it means that.

In standard Danish writing, a comma is often placed before a subordinate clause introduced by at:

• Jeg sværger, at det er rigtigt.

This is a normal Danish punctuation pattern. English is less strict about this kind of comma, but in Danish it is very common and often expected.

Because Danish word order in a subordinate clause normally keeps the verb after the subject:

• at det er rigtigt

Here:

• det = subject
• er = verb
• rigtigt = complement

This is different from main clauses, where Danish often puts the verb in second position. Compare:

• Main clause: Det er rigtigt.
• Subordinate clause: ... at det er rigtigt.

In both of these, the order happens to look the same, but in other sentences the difference becomes clearer.

Det usually means it. In this sentence, it refers to the thing being talked about — basically it in it is true.

Danish uses det very often in the same kinds of places where English uses it:

• Det er godt = It is good
• Det er rigtigt = It is true/correct

Because rigtigt is the neuter singular form of the adjective rigtig.

The adjective changes to match the noun or pronoun it describes. Since det usually goes with a neuter form, the adjective takes -t:

• en rigtig bog = a correct/right book
• et rigtigt svar = a correct answer
• det er rigtigt = it is true/correct

So rigtigt is the form required after det er here.

It can mean all of those, depending on context. In this sentence, rigtigt is best understood as true or correct.

Common uses:

• Det er rigtigt = That’s true / That’s correct
• Du har ret, det er rigtigt = You’re right, that’s correct

So the exact English translation can vary a little, but the Danish word is completely natural here.

Sometimes in spoken Danish, people may drop at, especially in casual speech, but with a verb like sværger, keeping at is the clearest and most standard option:

• Jeg sværger, at det er rigtigt.

For learners, it is best to include at.

Yes, it can sound fairly strong. Jeg sværger is used when someone wants to emphasize sincerity very strongly, like:

• I swear it’s true
• I promise it’s true

In everyday conversation, it may sound more emotional or intense than just:

• Det er rigtigt = It’s true
• Tro mig = Believe me

So it is correct, but it has more force than a neutral statement.

A rough guide is SVAIR-er, but the real Danish pronunciation is softer and more compressed than that.

A few points:

• sv is pronounced together at the start
• æ sounds somewhat like the vowel in care or air, though not exactly
• the r affects the vowel in a typically Danish way
• the final -er is usually a light unstressed ending

If you are learning pronunciation, it is a good word to listen to from native audio, because Danish spelling does not always clearly show the sounds.

You can, but it does not mean exactly the same thing.

• Jeg sværger, at det er rigtigt = I swear that it is true
• Jeg lover, at det er rigtigt = literally I promise that it is true

Jeg lover is possible, but promise is usually used for something you will do, not just for insisting something is true. So in this context, jeg sværger sounds more natural than jeg lover.

It is neutral in grammar, but somewhat strong in tone. It is not especially formal, and it can be used in everyday speech. The emotional force comes from jeg sværger, not from the grammar itself.

So:

• grammatically: normal and standard
• stylistically: emphatic, sincere, a bit dramatic depending on context