Edit in JSFiddle

<div>
  Percentage sized and still centered.
</div>

body {
  background: #900;
}

div {
  position: absolute;
  left: 50%;
  top: 50%;
  transform: translate(-50%, -50%);
  -webkit-transform: translate(-50%, -50%);
  
  
/*  This doesn't work
  margin-left: -25%;
  margin-top: -25%;
  */
  
  width: 40%;
  height: 50%;

  padding: 20px;  
  background: red;
  color: white;
  text-align: center;
  box-shadow: 0 0 30px rgba(0, 0, 0, 0.2);
}