Hvis jeg kommer sent til træningscenteret, er der ofte ingen frie håndvægte tilbage.

Hvis means if and introduces a condition.

So Hvis jeg kommer sent ... means If I arrive late ...

You might also hear når in similar sentences, but the nuance is different:

• Hvis jeg kommer sent ... = If I arrive late ...
• Når jeg kommer sent ... = When(ever) I arrive late ...

In this sentence, hvis presents lateness as a condition. Når would make it sound more like a repeated or expected situation.

That is very normal in Danish. Danish often uses the present tense for future meaning when the context already makes the time clear.

So Hvis jeg kommer sent ... literally uses present tense, but it naturally means If I arrive late or If I come late in the future.

English does something similar in many if clauses:

• If I come late, ... not
• If I will come late, ...

So the Danish structure is actually quite close to English here.

Because the sentence begins with a subordinate clause:

Hvis jeg kommer sent til træningscenteret

After that clause, Danish puts a comma before the main clause:

er der ofte ingen frie håndvægte tilbage

So the comma marks the boundary between the if clause and the main statement.

This is because Danish main clauses follow the verb-second rule.

In a simple statement, you would say:

Der er ofte ingen frie håndvægte tilbage.
= There are often no free dumbbells left.

But when the sentence starts with another element, such as the whole hvis clause, that first element takes the first position. Then the finite verb must come second:

Hvis jeg kommer sent til træningscenteret, er der ofte ...

So er comes before der because the sentence has already started with the if clause.

Here, der is the existential there, like in English there is or there are.

So:

• Der er ingen håndvægte = There are no dumbbells

This der does not mean there as a place. It is just a grammatical word used to introduce the existence of something.

In this sentence:

er der ofte ingen frie håndvægte tilbage
= there are often no free dumbbells left

Til is used because the sentence is about arriving to a place:

• komme til træningscenteret = come to / get to the gym

If you were talking about being inside the gym, you would normally use i:

• i træningscenteret = in the gym

The ending -et makes the noun definite:

• et træningscenter = a gym / a training center
• træningscenteret = the gym / the training center

So træningscenteret is the definite singular form.

Yes, sent means late.

• komme sent = arrive late
• komme for sent = arrive too late

For sent is stronger. It suggests that the arrival is later than acceptable, or late enough to cause a problem.

In this sentence, sent is enough because the idea is simply that arriving late often means the dumbbells are gone. If you said for sent, it would sound more like too late specifically.

Ingen is the usual direct way to say no or none before a noun.

So:

• ingen håndvægte = no dumbbells

You can also say ikke nogen håndvægte, and that is grammatical, but ingen is shorter and very natural here.

Compare:

• Der er ingen frie håndvægte tilbage. = There are no free dumbbells left.
• Der er ikke nogen frie håndvægte tilbage. = also possible, often a bit more conversational or emphatic

Here frie means free in the sense of available, not free of charge.

So frie håndvægte means available dumbbells or dumbbells that are not being used.

The -e ending is there because the adjective agrees with a plural noun:

• singular: en fri håndvægt = a free/available dumbbell
• plural: frie håndvægte = free/available dumbbells

The noun itself is:

• en håndvægt = a dumbbell
• håndvægte = dumbbells

Tilbage means left or remaining in this sentence.

So:

ingen frie håndvægte tilbage
means
no free dumbbells left

It is often placed late in the sentence, especially after the noun phrase it relates to. That sounds natural in Danish.

Without tilbage, the sentence would still make sense:

• Der er ofte ingen frie håndvægte.

But tilbage makes the idea clearer: not only are there no free dumbbells, there are none left anymore.