Die Raumkapazität bestimmt die Teilnehmerzahl.

Because both Raumkapazität and Teilnehmerzahl are feminine nouns in German.

• die Raumkapazität = the room capacity
• die Teilnehmerzahl = the number of participants

In this sentence, one die is for the subject and the other is for the direct object. Since feminine nouns use die in both the nominative and accusative singular, the article does not change here.

So:

• die Raumkapazität = nominative feminine singular
• die Teilnehmerzahl = accusative feminine singular

That is why both look the same.

The subject is die Raumkapazität, and the object is die Teilnehmerzahl.

A good clue is the verb bestimmt = determines. In real-world meaning, room capacity determines the number of participants, not the other way around.

Word order also helps:

• Die Raumkapazität = first position, so it is most naturally understood as the subject
• bestimmt = verb
• die Teilnehmerzahl = object

So the basic structure is:

Subject + verb + object

= Die Raumkapazität bestimmt die Teilnehmerzahl.

Here, bestimmt means determines, sets, or governs.

The verb is bestimmen.

Common meanings of bestimmen include:

• to determine
• to define
• to decide
• to specify

In this sentence, it means that the room capacity sets the limit for how many participants there can be.

Grammar-wise:

• infinitive: bestimmen
• 3rd person singular present: bestimmt

Because the subject die Raumkapazität is singular, the verb is singular too.

Because the subject is third person singular:

• die Raumkapazität = it

So the verb bestimmen is conjugated in the present tense:

• ich bestimme
• du bestimmst
• er/sie/es bestimmt
• wir bestimmen
• ihr bestimmt
• sie/Sie bestimmen

Since die Raumkapazität is singular, German uses bestimmt.

Yes, both are compound nouns, which is very common in German.

1. Raumkapazität

This is made of:

• Raum = room, space
• Kapazität = capacity

Together: room capacity

2. Teilnehmerzahl

This is made of:

• Teilnehmer = participant(s)
• Zahl = number

Together: number of participants

A helpful rule with German compounds: The last part usually determines the grammatical gender.

• die Kapazität → die Raumkapazität
• die Zahl → die Teilnehmerzahl

So both compounds are feminine because their final element is feminine.

German often expresses this idea with a compound noun instead of a phrase with von.

English says:

• the number of participants

German very naturally says:

• die Teilnehmerzahl

This is more compact and idiomatic in formal or administrative language.

You could sometimes rephrase with die Zahl der Teilnehmer, which literally means the number of the participants. That is also correct and common.

So these are both possible:

• die Teilnehmerzahl
• die Zahl der Teilnehmer

The compound form is especially neat and typical German.

Grammatically, yes, because both noun phrases have the same form: die .... But the meaning would change to:

The number of participants determines the room capacity.

That could make sense in a different context, but it is not the same idea as the original sentence.

Because nominative and accusative feminine singular look identical, German readers often rely on meaning and context to understand which noun is doing the action.

So the original sentence means:

• The room capacity determines the number of participants.

The reversed version would mean:

• The number of participants determines the room capacity.

Yes, but the verb must stay in the second position in a main clause.

Original:

• Die Raumkapazität bestimmt die Teilnehmerzahl.

You could also say:

• Die Teilnehmerzahl bestimmt die Raumkapazität.
  This changes the meaning.
• Bestimmt die Raumkapazität die Teilnehmerzahl?
  This makes it a yes/no question.
• Durch die Raumkapazität wird die Teilnehmerzahl bestimmt.
  This is a passive version: The number of participants is determined by the room capacity.

If you move elements around, be careful: in this sentence, case markings do not clearly distinguish subject and object because both nouns are feminine with die. So word order and context become especially important.

Yes, it sounds fairly formal, neutral, and administrative.

Words like:

• Raumkapazität
• Teilnehmerzahl

are common in contexts such as:

• event planning
• regulations
• safety limits
• registration forms
• official notices

In everyday speech, people might use a simpler phrasing, for example:

• Wie viele Leute teilnehmen können, hängt von der Raumgröße ab.
• Die Größe des Raums bestimmt, wie viele Teilnehmer es geben kann.

But the original sentence is perfectly natural in formal written German.

A rough English-friendly guide:

• Raumkapazität ≈ rowm-kah-pah-tsee-TAIT
• Teilnehmerzahl ≈ TYLE-nay-mer-tsahl

A few pronunciation notes:

• Raum rhymes roughly with English nowm
• z in German is pronounced ts
• ä in Kapazität sounds like a vowel similar to eh/ay, depending on accent
• zahl has a long a sound, roughly like tsahl

The main stress is usually:

• RaumkapaziTÄT
• TeilNEHmerzahl

Yes. A word-for-word translation helps, but it can sound a little stiff in English.

Word for word:

• Die = the
• Raumkapazität = room capacity
• bestimmt = determines
• die Teilnehmerzahl = the participant number / the number of participants

Natural English would usually be:

• The room capacity determines the number of participants.

The main tricky point is Teilnehmerzahl. English usually prefers a phrase like the number of participants rather than a compact compound noun.

So German is more compact here than English.