How to set the margin or padding as percentage of height of parent container?

Solution 1:

The fix is that yes, vertical padding and margin are relative to width, but top and bottom aren't.

So just place a div inside another, and in the inner div, use something like top:50% (remember position matters if it still doesn't work)

Solution 2:

An answer to a slightly different question: You can use vh units to pad elements to the center of the viewport:

.centerme {
    margin-top: 50vh;
    background: red;
}

<div class="centerme">middle</div>