Jeg gætter på, at hun kommer for sent til mødet.

In this sentence, at gætte på is a very common fixed expression meaning to guess / to suppose / to figure that.

So:

• Jeg gætter på, at ... = I guess that ...
• Jeg gætter ... by itself usually feels incomplete unless you are directly guessing something, like an answer.

Examples:

• Jeg gætter på, at det regner senere. = I guess it will rain later.
• Kan du gætte tallet? = Can you guess the number?

So here, på belongs to the expression gætte på.

At introduces a subordinate clause, just like that in English.

So the sentence has two parts:

• Jeg gætter på = I guess
• at hun kommer for sent til mødet = that she is arriving late for the meeting

In everyday English, that is often omitted: I guess she’s late. Danish can also sometimes omit at in speech, but in writing it is very common to include it.

The comma marks the start of the subordinate clause.

In Danish, you will often see:

• Jeg gætter på, at hun kommer for sent til mødet.

This comma is very normal. However, modern Danish also allows writing this without the comma before at:

• Jeg gætter på at hun kommer for sent til mødet.

So both can be acceptable, depending on the comma style being used. A learner should mainly recognize that the comma is separating the main clause from the at-clause.

Because after at, Danish uses subordinate clause word order.

In a main clause, Danish normally follows the verb-second pattern:

• Hun kommer for sent.

But in a subordinate clause introduced by at, you do not do inversion the way you might in some main-clause structures. The subject normally comes before the finite verb:

• at hun kommer ...

So hun kommer is the expected order.

Danish very often uses the present tense to talk about the future, especially when something is expected, planned, or likely.

So:

• hun kommer for sent til mødet

can mean:

• she is arriving late to the meeting
• she will be late for the meeting

English does this too in some cases, compare:

• She’s coming late
• She comes tomorrow (less common, but possible in certain contexts)

If you want to make the future more explicit in Danish, you can also use vil in some situations, but the present tense is extremely natural here.

For sent means too late / late in the sense of being later than one should be.

It is two words because:

• for = too
• sent = late

Examples:

• Jeg er for sent på den. = I’m too late.
• Hun kommer for sent. = She is arriving late.

A useful point: for sent is not the same as English too late in every context, but they often overlap.

• Hun kommer for sent til mødet = She will arrive late for the meeting.
• Det er for sent = It is too late.

Danish uses til with events like meetings when talking about arriving at them or being late for them.

So:

• til mødet = to/for the meeting

In English, we say late for the meeting, but Danish uses til in this expression:

• komme for sent til noget = to arrive late for something

Examples:

• Han kom for sent til timen. = He arrived late for class.
• Vi kom for sent til festen. = We arrived late for the party.

So this is something you should learn as a set expression:

• at komme for sent til ...

Yes. That would be very natural.

The difference is mostly one of nuance:

• Jeg gætter på, at ... = I guess / I’m guessing that ...
• Jeg tror, at ... = I think that ...

Jeg gætter på can sound a bit more tentative, like you are making an informed guess rather than stating a belief.

So both are possible, but gætter på gives a slightly stronger feeling of I’m not certain; this is my guess.

Yes, especially in speech and informal writing.

You may hear or see:

• Jeg gætter på hun kommer for sent til mødet.

That is natural in conversation. But for learners, it is often best to learn the fuller version first:

• Jeg gætter på, at hun kommer for sent til mødet.

Including at makes the structure clearer.

Sometimes, yes, but not always.

Depending on context, Jeg gætter på, at ... can sound like:

• I guess that ...
• I suppose that ...
• I’m guessing that ...

In some situations, English I bet ... is close:

• Jeg gætter på, at hun kommer for sent.
• I bet she’ll be late.

But I bet can sound more confident or more idiomatic than jeg gætter på. So I guess is often the safest match.

Yes, absolutely. It sounds natural and conversational.

A speaker might also use slightly shorter spoken versions, such as:

• Jeg gætter på, hun kommer for sent til mødet.
• Hun kommer vist for sent til mødet.
• Jeg tror, hun kommer for sent til mødet.

But your original sentence is completely normal and usable in everyday Danish.

You would change jeg to vi and keep the rest basically the same:

• Vi gætter på, at hun kommer for sent til mødet.

That means We guess / We think she’ll be late for the meeting.

The verb changes too:

• jeg gætter
• vi gætter

In the present tense, many Danish verbs have the same form for all persons, so gætter stays gætter.