Ratio function: helps find corresponding width or height. http://sassmeister.com/gist/7590739

SassMeister-input-HTML.html

<div class="box box1"></div>
<div class="box box2"></div>

SassMeister-input.scss

// ----
// Sass (v3.3.0.rc.1)
// Compass (v0.13.alpha.10)
// ----

@import "compass";

// Strip unit type.
@function strip-unit($num) {
  @return $num / ($num * 0 + 1);
}

// Return numeric value of corresponding ratio.
@function ratio($type, $value, $horizvalue, $vertvalue) {
  $output: '';
  @if $type == "height" {
    $output: strip-unit(round($value * $vertvalue / $horizvalue));
  } @else if $type == "width" {
    $output: strip-unit(round($value * $horizvalue / $vertvalue));
  }
  @return $output;
}

$value1: 160px;
$value2: 400px;
.box {
  background: #ccc;
  margin: 1em;
}
.box1 {
  height: #{ratio(height, $value1, 16, 9)}px;
  width: $value1;
}
.box2 {
  height: $value2;
  width: #{ratio(width, $value2, 3, 4)}px;
}

SassMeister-output.css

.box {
  background: #ccc;
  margin: 1em;
}

.box1 {
  height: 90px;
  width: 160px;
}

.box2 {
  height: 400px;
  width: 300px;
}

SassMeister-rendered.html

<div class="box box1"></div>
<div class="box box2"></div>