der Sturz
fall
The sudden and usually unintended falling down of a person or object.
Bei dem Sturz von der Leiter hat er sich den Arm gebrochen.
He broke his arm in the fall from the ladder.

fall / overthrow / lintel
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fall
The sudden and usually unintended falling down of a person or object.
Bei dem Sturz von der Leiter hat er sich den Arm gebrochen.
He broke his arm in the fall from the ladder.

'Der Sturz' (the fall) is the noun form of the verb 'stürzen' (to fall / to topple / to plunge). All meanings of the noun—falling down, overthrowing, dropping—are also found in the verb.
Die alte Vase ist vom Regal gestürzt und zerbrochen.
The old vase fell from the shelf and broke.
The context makes the meaning clear: with people, it is about falling down; in politics, about loss of power; in business, about prices; and in construction, about a structural element above an opening.
Der Sturz der Königin führte zu politischer Instabilität.
The overthrow of the queen led to political instability.
To describe the reason for or place of a fall, the prepositions 'von' (from, origin) and 'auf' (onto, destination) are often used. The phrase 'zu Sturz kommen' means 'to fall down'.
Der Sturz vom Fahrrad war schmerzhaft.
The fall from the bicycle was painful.
In a political context, people often speak of the 'Sturz einer Regierung' (overthrow of a government) or 'Sturz eines Regimes' (overthrow of a regime). A person or event can also 'zu Sturz bringen' someone, meaning bring them down.
Der Skandal brachte den Minister zu Sturz.
The scandal brought down the minister.
To describe the intensity of the drop, 'Sturz' (fall/drop) is often combined with adjectives such as 'plötzlich' (sudden), 'dramatisch' (dramatic), or 'rapide' (rapid).
Wir erlebten einen rapiden Sturz der Temperaturen.
We experienced a rapid drop in temperatures.
case / fall
'der Fall' and 'der Sturz' can both refer to a downward movement. When a person or object falls down, 'der Sturz' is usually more natural in everyday language. In this meaning, 'der Fall' often sounds more general or somewhat more factual and describes the downward movement itself. In many situations involving injury or an accident, people therefore say 'Sturz'. The words can be confused because they can describe the same event here. Important: 'der Fall' also has many other meanings; 'der Sturz' is usually clearer for people and objects.

Nach dem Sturz vom Fahrrad tat Max der Arm weh.
After the fall from his bike, Max's arm hurt.
Beim Fall aus dem Fenster wurde die Vase völlig zerstört.
The vase was completely destroyed in the fall from the window.