1A floor or storey of a building; used as 1階, 2階, etc. to refer to each level counted up from the ground.
オフィスはビルの5階にあります。
The office is on the 5th floor of the building.
このマンションは10階建てだ。
This apartment building has ten floors.
上の階から足音が聞こえる。
I can hear footsteps from the floor above.
2'Stairs' — an archaic/literary use of 階. Modern Japanese normally says 階段, and 階 in this sense is uncommon (cf. the native word きざはし).
神殿の正面には石の階が続いていた。
A flight of stone steps led up to the front of the temple.
3In geology, a chronostratigraphic unit — the body of rock corresponding to an age ('stage'); a technical term.
この化石はジュラ系のある階から産出した。
This fossil came from a particular stage of the Jurassic.
地質年代表では、各階が下位の単位として並んでいる。
In the geological time scale, the stages are arranged as lower-order units.
4A counter for floors of a building. With some numbers the かい becomes voiced (がい) — e.g. 3階 さんがい, 何階 なんがい.
すみません、おもちゃ売り場は何階ですか。
Excuse me, what floor is the toy department on?
エレベーターで7階まで上がってください。
Please take the elevator up to the 7th floor.
受付は3階です。
Reception is on the 3rd floor.