I wrote this mixin to fix an element to an absolute aspect ratio. It resizes the element relative to the viewport, or ``vw`` and ``vh``.

GameFrame.css

#frame {
    top: 0rem;
    left: 0rem;
    right: 0rem;
    bottom: 0rem;
    margin: auto;
    position: fixed;
    overflow: hidden;
}

@media(min-aspect-ratio: 640 / 360) {
    #frame {
        font-size: 0.27778vh;
        width: 177.77778vh;
        height: 100vh;
    }
}

@media(max-aspect-ratio: 640 / 360) {
    #frame {
        font-size: 0.15625vw;
        height: 56.25vw;
        width: 100vw;
    }
}

GameFrame.scss

@mixin aspect-ratio($width, $height) {
    top: 0rem;
    left: 0rem;
    right: 0rem;
    bottom: 0rem;
    margin: auto;
    position: fixed;
    overflow: hidden;

    @media(min-aspect-ratio: #{$width + "/" + $height}) {
        font-size: (($width/$height)*100vh)/$width;
        width: ($width/$height)*100vh;
        height: 100vh;
    }
    @media(max-aspect-ratio: #{$width + "/" + $height}) {
        font-size: (($height/$width)*100vw)/$height;
        height: ($height/$width)*100vw;
        width: 100vw;
    }
}

#game-frame {
    @include aspect-ratio(640, 360);
}

Any children can be positioned in units of em instead of px, since the font-size is likewise relative to the viewport.