Japanese contraction of "no desu". Used at the end of a sentence to indicate the idea of "that's why, that's what it is, because of that...". Unfortunately, this is used much more often than it should be by Japanese speakers, due to the fact that they are generally humble and afraid to speak their mind. Sometimes, they say "n da" for no apparent reason. Anyway, there are actually 4 different variations of this form of the copula, each differing by gender/politeness:

  • no desu- Just as in English, saying the whole thing is the most formal and polite. Tends to be used most often in Japanese writing.
  • n desu- The regular, polite form, used in a conversation where you would speak with the -masu form of verbs, such as with someone you didn't know.
  • no- Used by females who are at least somewhat familiar with the person they are talking to.
  • n da- Used by males in a familiar situation, and increasingly becoming popular among the new "independent woman" types in Japan.
Using "n da" in a sentence:
After an i-adjective or verb, simply say whichever form you want to use at the end of the sentence. You can add ne or yo afterward, if you want. To alter the tense of the sentence, alter the tense of of the verb or adjective, not the "da". For example:

Utsukushii n da yo: Because (she's) beautiful!
Biiru o nonda no: (He/she/someone) drank beer, that's why.

After a na-adjective or a noun, you have to add "na" before using "n da", or any other form of it. Generally, when this is done, the "na" and "n" are simply added together-you say "nan da" instead of "na n da". Examples:

Kare ga suki na no yo: Because I like him!
Gakusei nan desu ne: (He's) a student, that's why.(Or, that's who he is.)
Negatives are also possible:
(o-)kane o motte inakatta n da: I didn't have any money, that's why.
oishikunai n desu: Because it doesn't taste good.

Questions, and other forms of the copula:

By raising one's intonation at the end of a sentence or including "ka", as you would to ask any question in Japanese, "n da" can be also used to ask "why?". Other forms of "da" can be used, such as "daroo", "deshoo", "ja nai", and "ja arimasen". "Daroo" and "deshoo" both mean "probably", hence, "n daroo" means "that's probably why", "that's who he is", etc. However, "n ja nai" doesn't usually mean "that's probably not why". Instead, it's usually used when asking a question to indicate the idea of "shouldn't it be that way" or "right?". More examples:

Doushite zubon o haite inai n desu ka?: Why arent you wearing pants?
Kanojo ga suki nan ja nai?: You like her, right?
Kazoku wa bimbou nan daroo: Probably because the family is poor.

No de:

Another form of "n da" can be used in the middle of a sentence, "no de". Unlike its cousin, "no de" is usually used in its pure form. "No de" is used to indicate the idea of "because of (portion of sentence before no de), (portion after no de)". Another particle, "kara", has pretty much the same meaning, and is somewhat interchangeable. The only difference is that "no de" is a little more formal, and/or is used in emotional sentences more often than the "neutral" kara. Examples of "no de" in action:

Dorama ga daisuki na no de, terebi o katta: Because she really likes dorama(Japanese drama/soap oprea-type shows), she bought a TV.
Furui niku o tabeta no de, byouki ni narimashita: Because he ate old meat, he became sick.

If you don't understand any of this, or don't know how to conjugate japanese verbs, you should probably go check out japanese grammar. I tried to keep the examples simple though :).

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