The distance between the cooktop and bottom of the hood should be between 30-36”. Lower than that, and it will look and feel cramped, and it won’t be easy to stir tall pots; higher than that and the effluent has more of a chance to escape.

We read that the minimum for what we had was 30" when installing ours so we went with that. We have an electric range and our range hood is hung 30" from the top of the range. We have 8' ceilings so any higher would have looked strange and we needed room to vent out above.

To capture rising and expanding cooking plumes, hoods have to grow as they are raised above the cooktop. There are hoods that specify less than a 30 inch gap, but these are generally short (front-to-back) and do not provide sufficient capture area. With sufficient capture area, sight lines to rear cooking utensils may be blocked. This varies with the cook's height, so side view stick figure drawings may be helpful to see the effect. Also, as the cook bends at the waist, it is best to not require the cook to duck. So the answer 'depends.'