Possible Fix for Maintaining Background Image/Video Aspect Ratio

Had a hard time finding any answers on how to maintain a specific, responsive aspect ratio for Brine Family index sections with background videos. My client has a full width background video that needs to avoid cropping, and this was the best solution I could figure out.

Does anyone know how to calculate the padding for other aspect ratios, like 3:4? 

I will post a link to the site when it is live.

section#your-section-url { 
position: relative; 
width: 100%; 
padding-top: 56.25%; /* 16:9 Aspect Ratio */ }