Grundflächen

Grundfläche (plural Grundflächen) is a German term used in geometry and building planning. It denotes the area of a base plane or the projection of a three-dimensional figure onto a plane. In practice, the Grundfläche defines the footprint of the object when oriented with a vertical axis. The plural Grundflächen may refer to several base areas in different objects or at different sites. The concept is used as a basis for quantitative reasoning about space, volume, and density.

In geometry, the Grundfläche of a solid is the area of its base. For prisms and cylinders, the base is a plane region whose area A is used in volume calculations such as V = A × h. The exact shape of the Grundfläche depends on the cross-section of the solid (for example a rectangle, circle, or polygon).

In architectural and urban planning contexts, Grundfläche refers to the footprint of a building on the ground—the area that the structure occupies when projected onto the site plan. Planning regulations may relate this footprint to land area through the Grundflächenzahl (GRZ). The GRZ expresses the ratio of the Grundfläche to the plot size to control density; related measures, such as the Geschossflächenzahl (GFZ), constrain total usable floor area relative to plot size.

Terminology: The term is common in German-language texts on geometry, architecture, and planning law. It is distinguished from related terms such as Fläche (area in general) and Volumen (volume).