Kreis

Kreis is a German noun with several related meanings. In geometry, a Kreis is the set of all points in a plane at a fixed distance, the radius, from a given point called the center. The figure is commonly known as a circle in English. The circumference is 2πr and the area is πr^2. The term derives from Old High German kreis and is related to Latin circulus, meaning “little circle.”

In administrative geography, Kreis denotes a territorial unit or district. In German-speaking countries it refers to an intermediate level between municipalities (Gemeinden) and higher-level states (Länder). In Germany, the concept appears in forms such as Landkreis (rural district) and Kreisfreie Stadt (a city that is itself a district). The exact status and naming vary by state; some use Landkreis as the official term, while others commonly use Kreis for the same level. Urban districts that are administratively independent of surrounding rural districts are called Kreisfreie Städte in several states.

Historically, Kreis also designated subdivision within larger territories in the Holy Roman Empire, Prussia, and the Austrian Empire, functioning as an administrative circle or jurisdiction. In modern Austria and Switzerland, the term has been used in certain cantons or historical contexts, but current structures often employ Bezirke, Amtsbezirke, or similar terms instead of Kreis.

Overall, Kreis reflects a dual tradition in German-speaking regions: as a mathematical concept describing a circle and as a term for a mid-level administrative district, with usage shaped by regional constitutional history.