The hijab is a very important matter to the extent that the Quran has even directly spoken of it. Allah (swt) says in surah Nur:

“And tell the faithful women to cast down their looks and to guard their private parts, and not to display their charms, except for what is outward, and let them draw their scarfs over their bosoms, and not display their charms except to their husbands, or their fathers, or their husband's fathers, or their sons, or their husband's sons… And let them not thump their feet to make known their hidden ornaments…” [1]

There are numerous hadiths in Usul Kafi about the hijab and its boundaries that have been gathered in the chapter of “That of which belongs to women and can be seen”.

Mus’adah bin Ziyad has narrated Imam Sadiq (as) saying that when he was asked about what the ‘charms’/‘ornaments’ (zinah) women can expose, the imam (as) replied: “The face and the two hands.”

Of course, according to Islam, leaving the face and hands exposed is only permissible if she hasn’t adorned them or if they only bear minor adornment, such as the eyebrows being trimmed and shaped and having facial hair removed (in which aren't considered adornment in some societies and customs). [2]

Since what you are looking for is the fiqhi ruling on this issue, we will present the responses we received regarding your inquiry from the offices of the Grand Ayatullahs:

The office of the Grand Ayatullah Khamenei:

It is obligatory to cover all the hair from non-mahrams.

The office of the Grand Ayatullah Makarem Shirazi:

It is mandatory for all women and girls [who have religiously come of age] to cover their entire bodies from non-mahrams except for the roundness of the face and the hands until the wrists. This can be done using any type of covering as long as it isn't tight and doesn’t stick to the body, although the chador is the best choice for doing this.

The office of the Grand Ayatullah Mahdi Hadavi Tehrani:

If covering the hair is harmful to her, she has to cover it as much as possible from non-mahrams, not any more than that. In this case, when it is harmful to her, she must try not to confront non-mahrams as much as possible (so that they don’t see her hair).

For further information, see:

1- The decree of hijab and the reasons for enforcing it, Question 1174 (website : 1177).

2- The boundaries of hijab, Question 496 (website: 537).

3- The reason for hijab, Question 825 (website: 884).

4- The hijab in Islam, Question 431, (website: 459).

5- Covering the feet for women, Question 5982 (website: 6164) .