眠い (nemui) means “sleepy” | MotiTan Japanese Dictionary

More examples

もう眠いです。mō nemu i de su

I am already sleepy.

昨夜遅くまで勉強したので、今日は眠いです。saku ya oso ku ma de ben kyō shi ta no de kyō wa nemu i de su

I studied until late last night, so I am sleepy today.

Describes the bodily state in which sleep is beginning to feel necessary.

眠たいnemutai: An informal way to describe a feeling of needing sleep.

眠気を感じ、眠りたくなる状態である。nemu ke o kan ji nemu ri ta ku na ru jō tai de a ru

眠い (nemui) is a native Japanese adjective historically related to 眠る (nemuru, "to sleep"), describing the state that leads toward sleep.

In everyday Japanese, 眠いです (nemui desu) is a common polite way to say that the speaker feels sleepy, while 眠い (nemui) alone is casual.