das Fassungsvermögen
capacity
The maximum amount that a container, room, or vehicle can hold; the capacity.
Das Fassungsvermögen des Benzintanks beträgt 60 Liter.
The capacity of the fuel tank is 60 liters.

capacity
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capacity
The maximum amount that a container, room, or vehicle can hold; the capacity.
Das Fassungsvermögen des Benzintanks beträgt 60 Liter.
The capacity of the fuel tank is 60 liters.

This word is composed of 'fassen' (to hold, to contain) and 'Vermögen' (here in the sense of ability). So it literally describes the 'ability to contain' or take in something.
Die Kiste war so voll, ihr Fassungsvermögen war erschöpft.
The box was so full that its capacity was exhausted.
The literal meaning can be recognized from physical units (e.g., liters, cubic meters) or countable things (e.g., people). The figurative, mental meaning is often signaled by adjectives such as 'geistig' (mental), 'emotional' (emotional), or 'intellektuell' (intellectual).
Das Stadion hat ein Fassungsvermögen von 50.000 Zuschauern.
The stadium has a capacity of 50,000 spectators.
When specifying capacity, the structure 'ein Fassungsvermögen von [number] [unit]' (a capacity of [number] [unit]) is almost always used. This pattern is very useful for talking about sizes and volumes.
Der Aufzug hat ein Fassungsvermögen von acht Personen.
The elevator has a capacity of eight people.
In the figurative meaning, it is often expressed that a mental or emotional limit has been reached. A typical verb in this context is 'übersteigen' (to exceed) or 'überschreiten' (to exceed/cross).
Die mathematische Formel überstieg mein Fassungsvermögen.
The mathematical formula exceeded my capacity.
content
'der Inhalt' and 'das Fassungsvermögen' both have to do with the amount in a container. 'Der Inhalt' means what is actually in the container. 'Das Fassungsvermögen', on the other hand, means how much can fit inside at most. Learners may confuse the words because both occur with bottles, boxes, or rooms. A practical tip: Inhalt is the actual contents; Fassungsvermögen is the possible capacity.

Das Fassungsvermögen dieser Wasserflasche beträgt einen Liter.
The capacity of this water bottle is one liter.
Julia schüttet den Inhalt der Tasche auf den Tisch.
Julia pours the contents of the bag onto the table.