Responsive Youtube Video Embeds

Hi, I am using an older template (before the newer responsive templates) which works very well when viewed on a mobile device, with the exception of embedded YouTube videos on my site. Viewed on my iPhone 6s, my Youtube videos do not resize properly in Safari. In Chrome mobile they resize properly only if the iPhone is held horizontally. My understanding is that additional CSS code would be necessary to ensure proper video resizing, but I'm not a coder. I am wondering if updating my site to a newer responsive template would improve how the YouTube videos resize on mobile devices without adding additional CSS code?

Thanks!