die Krümmung
curvature
The state of being bent or curved; a deviation from a straight line or a flat plane.
Die starke Krümmung der Straße erfordert eine langsame Fahrweise.
The strong curvature of the road requires driving slowly.

curvature
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curvature
The state of being bent or curved; a deviation from a straight line or a flat plane.
Die starke Krümmung der Straße erfordert eine langsame Fahrweise.
The strong curvature of the road requires driving slowly.

The noun 'die Krümmung' (curvature) belongs to the word family around the verb 'krümmen' (to bend something) and the adjective 'krumm' (crooked, not straight). The ending '-ung' turns the verb into a feminine noun that describes the process or result of bending.
Der alte Baum krümmt sich im Wind.
The old tree bends in the wind.
To describe what is curved, 'Krümmung' (curvature) is very often combined with a noun in the genitive or with the preposition 'von' + dative.
Die Krümmung des Raumes ist ein zentrales Konzept der Physik.
The curvature of space is a central concept in physics.
The context makes the meaning clear: words like 'Straße' (road) or 'Fluss' (river) point to a geographical bend. In connection with 'Wirbelsäule' (spine) or 'Rücken' (back), a medical meaning is intended. Terms like 'Raumzeit' (spacetime) indicate a scientific context.
Die Krümmung der Banane ist ganz natürlich.
The curvature of the banana is completely natural.
To describe the degree of bending, 'Krümmung' (curvature) is often combined with adjectives such as 'stark' (strong), 'leicht' (slight), 'sanft' (gentle), or 'scharf' (sharp).
Die Straße macht eine scharfe Krümmung nach links.
The road makes a sharp curve to the left.
curve
'die Kurve' and 'die Krümmung' both have to do with something curved. A 'Kurve' is usually the visible curved line or the bend itself, for example on a road or in a graph. 'die Krümmung' describes more the fact that something is curved, or how strongly it is curved. This often sounds more precise or technical. The words can be confused because both describe shapes that are not straight. Put simply: 'die Kurve' is the shape or the path, while 'die Krümmung' is the property of that shape.

Die Ärztin erklärt ihm die Krümmung der Wirbelsäule.
The doctor explains the curvature of his spine to him.
In der engen Kurve musste der Fahrer stark bremsen.
In the tight bend, the driver had to brake hard.