If my parent element is 200px tall and I specify height = 100% with padding = 5px I would expect that I should get a 190px high element with border = 5px on all sides, nicely centered in the parent element.

The obvious answer doesn't work:

#myDiv {
    width: 100%
    height: 100%;
    padding: 5px;
}

display:block is the default display value for a div, but I like to make it explicit.

The container has to be the right type; position attribute is fixed, relative, or absolute.

.stretchedToMargin {
  display: block;
  position:absolute;
  height:auto;
  bottom:0;
  top:0;
  left:0;
  right:0;
  margin-top:20px;
  margin-bottom:20px;
  margin-right:80px;
  margin-left:80px;
  background-color: green;
}

<div class="stretchedToMargin">
  Hello, world
</div>

Can also do percentage:

*.stretchedMargin {
    display: block;
    position:absolute;
    height:auto;
    bottom:0;
    top:0;
    left:0;
    right:0;
    margin-top:1%;
    margin-right:50%;
    margin-left:5%;
    background-color: green;
}