Found a good solution here: http://codepen.io/shshaw/pen/OVGWLG
So your CSS would be:
.video-container {
position: absolute;
top: 0;
bottom: 0;
width: 100%;
height: 100%;
overflow: hidden;
}
.video-container video {
/* Make video to at least 100% wide and tall */
min-width: 100%;
min-height: 100%;
/* Setting width & height to auto prevents the browser from stretching or squishing the video */
width: auto;
height: auto;
/* Center the video */
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%,-50%);
}
HTML:
<div class="video-container">
<video>
<source src="https://stackoverflow.com/questions/36949747/~/Videos/myvideo.mp4" type="video/mp4" />
</video>
</div>