smooth-scroll.html

<input id="top" type="button" value="Scroll down (1sec)" onclick="smoothScrollTo(document.getElementById('bottom').offsetTop)">

<p>Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.</p>

<input id="bottom" type="button" value="Scroll up (500ms)" onclick="smoothScrollTo(0, 500)">
<script>
window.smoothScrollTo = (function () {
  var timer, start, factor;
  
  return function (target, duration) {
    var offset = window.pageYOffset,
        delta  = target - window.pageYOffset; // Y-offset difference
    duration = duration || 1000;              // default 1 sec animation
    start = Date.now();                       // get start time
    factor = 0;
    
    if( timer ) {
      clearInterval(timer); // stop any running animations
    }
    
    function step() {
      var y;
      factor = (Date.now() - start) / duration; // get interpolation factor
      if( factor >= 1 ) {
        clearInterval(timer); // stop animation
        factor = 1;           // clip to max 1.0
      } 
      y = factor * delta + offset;
      window.scrollBy(0, y - window.pageYOffset);
    }
    
    timer = setInterval(step, 10);
    return timer;
  };
}());
  </scrpt>