Flach vs. eben
The German words flach and eben both translate to "flat" in English, but they describe different physical characteristics. While flach refers to a lack of height, depth, or elevation, eben describes a surface that is smooth, level, and free of bumps or irregularities.
Flach
The word flach describes something that lacks height, depth, or steepness. It is used to express that an object is low to the ground, a body of water is shallow, or a landscape has no mountains or hills.
Das Wasser im See ist hier sehr flach.
(The water in the lake is very shallow here.)
Wir wohnen in einem Haus mit einem flachen Dach.
(We live in a house with a flat roof.)
Holland ist ein sehr flaches Land.
(Holland is a very flat country.)
Sie trägt lieber flache Schuhe als hochhackige.
(She prefers wearing flat shoes over high-heeled ones.)
Der Patient hatte eine sehr flache Atmung.
(The patient had very shallow breathing.)
Der Teller ist zu flach für eine Suppe.
(The plate is too flat for a soup.)
Er warf einen flachen Stein über das Wasser.
(He threw a flat stone across the water.)
Eben
The word eben describes a surface that is perfectly level, smooth, and uniform. It emphasizes the absence of bumps, holes, slopes, or uneven textures on a surface or piece of land.
Wir brauchen einen ebenen Untergrund für das Zelt.
(We need a level surface for the tent.)
Der Tischler hobelt das Holz bis es völlig eben ist.
(The carpenter planes the wood until it is completely smooth.)
Die Straße ist hier sehr eben und gut asphaltiert.
(The road here is very even and well-paved.)
Ein Billardtisch muss absolut eben sein.
(A pool table must be absolutely level.)
Das Flugzeug landete auf einer weiten ebenen Wiese.
(The airplane landed on a vast level meadow.)
Der Teig muss zu einer ebenen Fläche ausgerollt werden.
(The dough must be rolled out into an even surface.)
Nach dem Walzen war der Rasen schön eben.
(After rolling the soil the lawn was beautifully even.)
Summary
In short, use flach when contrasting something with being high, deep, or steep, such as shallow water or a country without mountains. Use eben when you want to emphasize that a surface is smooth, horizontal, and without bumps or holes, such as a well-paved road or a level floor.