flach
flat
Having little height or depth; level and without significant elevations or depressions.
Die Landschaft hier im Norden ist sehr flach.
The landscape here in the north is very flat.

flat / shallow
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flat
Having little height or depth; level and without significant elevations or depressions.
Die Landschaft hier im Norden ist sehr flach.
The landscape here in the north is very flat.

The adjective 'flach' (flat/shallow) is closely related to the noun 'die Fläche' (surface/area). A 'Fläche' is a level surface. This connection helps you understand the basic meaning of 'flach' as 'level' or 'without height.'
Der Tisch hat eine große, glatte Fläche.
The table has a large, smooth surface.
The literal meaning of 'flach' (flat/shallow) describes physical properties such as a landscape or a plate. The figurative meaning describes abstract things like jokes or conversations that lack depth or sophistication.
Das Ufer des Sees ist hier sehr flach.
The shore of the lake is very shallow here.
In its literal meaning, 'flach' (flat/shallow) can describe both low height, e.g. 'flache Landschaft' (flat landscape), and shallow depth, e.g. 'flaches Wasser' (shallow water). In both cases, it is about a small vertical extent.
Kinder können sicher im flachen Wasser spielen.
Children can play safely in shallow water.
In its figurative meaning, 'flach' (shallow) is very often used for things that are intellectually undemanding. Common combinations are 'ein flacher Witz' (a shallow joke), 'flacher Humor' (shallow humor), or 'eine flache Unterhaltung' (a shallow conversation).
Er macht ständig nur flache Witze, über die niemand lacht.
He constantly makes only shallow jokes that no one laughs at.
In a medical or sports context, 'flach' (shallow) describes breathing that is not deep. People say 'flach atmen' (to breathe shallowly) or 'eine flache Atmung' (shallow breathing).
Nach dem Sprint atmete sie sehr schnell und flach.
After the sprint, she breathed very quickly and shallowly.
The idiom 'sich flach halten' (to keep a low profile) is reflexive and means behaving inconspicuously in order to avoid attention or trouble. You deliberately withdraw.
Nach dem Fehler im Meeting sollte er sich erst einmal flach halten.
After the mistake in the meeting, he should keep a low profile for a while.
just / exactly
'eben' and 'flach' can both describe a surface without major differences in height. In this use, 'eben' mainly means: smooth, level, and without uneven spots. 'flach' emphasizes more that something has little height or depth. A floor can be 'eben' if you can stand or drive on it easily. A plate, a roof, or a lake can be 'flach' if it is not high or not deep. Learners may confuse the words because both can fit landscapes or surfaces. Memory tip: 'eben' is about how level or smooth the surface is; 'flach' is about low height or shallow depth.

Am Ufer ist der See sehr flach, deshalb spielen dort viele Kinder im Wasser.
The lake is very shallow near the shore, so many children play in the water there.
Der Weg durch den Park ist eben und gut für Kinderwagen geeignet.
The path through the park is level and suitable for strollers.