What is the correct way to say "where are you going?"?

Is it:

> あなたはどこに行きますか

or

> あなたはどこに行くの

Also, can someone please explain that の in "あなたはどこに行くの"?
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grammar syntax
What is the correct way to say: "where are you going?"
Both works, although it'd be better if `あなたは` was elided (unless there is a
need to specifically refer to the person, otherwise it can have either an
accusatory feel or it can have the effect of appearing intimate with the
person). `に` can also be elided.

`の` at the end behaves something like a sentence softener. It tends to have a
feminine undertone. It is related to the sentence ending pattern `~のだ` which
roughly means "It is that ~". The question is derived from `どこ行くのですか` with
`ですか` elided.
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The are both correct. It's just two different expression of politeness.

The first is polite (丁寧語). It is the form that usually ends with ます です.

The latter is less polite and can be used between friends. It uses the form
that usually exists in dictionary to end sentences. (What should be form be
called? In Japanese it may be called くだけた言い方)

You can check this [wiki
article](https://en.wikipedia.org/wiki/Honorific_speech_in_Japanese#Polite_language),
or the [Japanese
version](https://secure.wikimedia.org/wikipedia/ja/wiki/%E6%95%AC%E8%AA%9E#.E4.B8.81.E5.AF.A7.E8.AA.9E).

の here is a final particle (終助詞). It can be used at the end of sentence with a
rising intonation to show question. ([source-
English](http://dictionary.goo.ne.jp/leaf/je2/58754/m1u/%E3%81%AE/) [source-
Japanese](http://dictionary.goo.ne.jp/leaf/jn2/171157/m1u/%E3%81%AE/)):

> （上昇調のイントネーションを伴って）質問または疑問の意を表す。  
>  「君は行かないの」「そんなに悲しいの」「なぜなの」

And there is a note on [the above
page](http://dictionary.goo.ne.jp/leaf/jn2/171157/m1u/%E3%81%AE/):

> [補説]終助詞の「の」は、近世後期以降用いられ、現代語では **うちとけた対話** に用いられることが多い。...

which says that it is usually used in plain text (that does not use ます です).
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Both ways are correct, but there are lots of ways of saying "where are you
going" depending on politeness levels etc. You can also replace the `に`
particle with the `へ` particle in many instances, and in fact you can go
without both `に` and `へ` in many informal situations. Often `あなたは` isn't
necessary as it can be determined by context.

In Japanese there isn't any distinction between "where are you going", "where
are you going to go", "where do you go", "where will you go", "where will you
be going" etc, and it's usually determined by context which is meant.

This is by no means a complete list and the explanations may need to be
corrected, but I hope it will give some idea of the different ways of saying
it:

> どこ行くの more informal, omitting `に`
>
> どこに行くのか／どこに行くの informal  
>  
>
>
> どこに行くのかな informal but "softer", "where are you going I wonder?"
>
> どこに行くのかしら feminine version of the above
>
> どこに行くのだろう not strictly male, but I think it's used more by males similar to
> the above
>
> どこに行くのでしょうか a formal version of `どこに行くのだろう`  
>  
>
>
> どこに行くのですか slightly more polite
>
> どこに行くつもりですか／どこに行く予定ですか polite, "where do you intend to go"
>
> どこ行きますか a polite but colloquial form
>
> どこに行きますか polite form
>
> (...et cetera)
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