
die Ausdehnung
expansion
The increase in the space that something takes up, for example through heat or growth.
Die Ausdehnung von Wasser zu Eis kann Rohre sprengen.
The expansion of water into ice can burst pipes.
expansion / extent
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expansion
The increase in the space that something takes up, for example through heat or growth.
Die Ausdehnung von Wasser zu Eis kann Rohre sprengen.
The expansion of water into ice can burst pipes.

extent
The spatial extent or size of an area or region.
Die riesige Ausdehnung der Wüste ist beeindruckend.
The vast extent of the desert is impressive.
'Ausdehnung' (expansion/extent) is a noun derived from the separable verb 'sich ausdehnen' (to expand). The ending '-ung' turns the verb into a feminine noun.
Das Universum dehnt sich ständig aus, und diese Ausdehnung wird von Astronomen gemessen.
The universe is constantly expanding, and this expansion is measured by astronomers.
The meaning depends strongly on the context. If it is about a process or a physical change (e.g., through heat), it refers to expansion. If it is about geography or a static description, it refers to spatial extent.
Die Ausdehnung des Metalls bei Hitze ist ein physikalisches Phänomen.
The expansion of metal in heat is a physical phenomenon.
In this meaning, 'Ausdehnung' (expansion) is often found in scientific contexts. Typical combinations are 'thermische Ausdehnung' (thermal expansion), 'die Ausdehnung von Gasen' (the expansion of gases), or 'die Ausdehnung eines Materials' (the expansion of a material).
Beim Bau von Brücken muss die thermische Ausdehnung des Stahls berücksichtigt werden.
When building bridges, the thermal expansion of the steel must be taken into account.
When referring to spatial extent, the word is often combined with geographical or abstract terms. For example: 'die räumliche Ausdehnung' (spatial extent), 'die geografische Ausdehnung' (geographical extent), or 'die Ausdehnung eines Reiches' (the extent of an empire).
Die volle Ausdehnung des alten Römischen Reiches war gewaltig.
The full extent of the ancient Roman Empire was enormous.
length
„Länge“ and „Ausdehnung“ both describe spatial size. „Länge“ refers to a specific distance from one end to the other, while „Ausdehnung“ emphasizes the spatial extent of an area or region. Use „Länge“ for a single dimension and „Ausdehnung“ for a larger area or region.

Die Ausdehnung des Naturschutzgebiets umfasst die gesamte Fläche hinter dem Strand.
The nature reserve extends across the entire area behind the beach.
Die Länge des Strandes beträgt von einem Ende zum anderen fast fünf Kilometer.
The beach is almost five kilometers long from one end to the other.