.responsive-video {
    position: relative;
    padding-bottom: 56.25%;
    padding-top: 60px; overflow: hidden;
}

.responsive-video iframe,
.responsive-video object,
.responsive-video embed {
    position: absolute;
    top: 0;
    left: 0;
    width: 100%;
    height: 100%;
}

<div class="responsive-video">
    <iframe ></iframe>
</div>

as seen on https://stackoverflow.com/questions/25228056/responsive-iframe-using-bootstrap