Praise be to Allah.
Vomiting refers to when food etc is expelled from the stomach outside the body.
With regard to whether this breaks the fast or not, the ruling depends on whether it was done deliberately or not. If a person vomits deliberately, this breaks the fast and he has to make up that day. If he cannot help vomiting and vomits involuntarily, then his fast is still valid and he does not have to do anything else. We have already discussed this in question no. 38023.
If a person needs to vomit because he is sick and vomiting will help him to recover, then it is permissible for him to do that, but he has to make up that day after Ramadaan, because Allaah says (interpretation of the meaning):
“and whoever is ill or on a journey, the same number [of days which one did not observe Sawm (fasts) must be made up] from other days”
According to the correct scholarly view, it makes no difference whether the amount of vomit is great or small. If a person vomits deliberately and only a small amount comes out, the fast is broken. It says in al-Furoo’: If a person makes himself vomit and vomits anything, then his fast is broken, because of the report of Abu Hurayrah: “Whoever cannot help vomiting does not have to do anything but whoever makes himself vomit deliberately has to make up that day.” Al-Furoo’, 3/49. This hadeeth was narrated by Abu Dawood, 2380; al-Tirmidhi, 720 – he said the scholars follow this. It was classed as saheeh by al-Albaani.
But there is a difference between spitting and vomiting. Spitting and hawking etc do not come from the stomach, so there is nothing wrong with expelling that matter. But vomiting comes from the stomach as explained above.
And Allaah knows best.