min-height

value: <length> | <percentage> | none | inherit
initial value: none
inherited: no
percentages: calculated with respect to the height of the generated box's containing block
applicable to: all elements (except some table elements)

The property min-height determines the minimum height that the box for the element can obtain. The height for the element's box can be larger than this value, but it can not go smaller. There is no default value for min-height. The min-height value set for a parent or ancestor element is not inherited by the children elements. 

Take Note: If an element has a "min-height" and a "height" set for it, the element's box cannot reduce to a size smaller than the value set with "min-height"

Example:

div.quotebox {min-height: 200px;}

Keep in mind that the outer dimensions of an element will be affected by its padding but not by its margins. The value set for padding will be added to the height of the element to calculate its overall size in most cases.