There are any number of ways to watch things on your TV, from old-school antennas to modern fiber-optic connections or even hooking it up to your computer for streaming content. Many modern TVs even let you skip the requirement for a computer and directly connect an external hard drive to watch movies on your TV. It's a good option, especially in situations – cough, "unsupervised kids," cough – where streaming is problematic and you'd like to keep tighter control of what's on the screen.
First Things First
Before you connect your hard drive to the TV, and especially before you spend hours loading it up with content, you'll need to make sure that it will work with your television. Check your user manual, or the manufacturer's website, to see what minimum specs you'll need to meet and then compare those to the hard drive you want to use. Many TVs will only support a hard drive of up to 2 TB, for example, so if you had a 4 TB drive you'd have to partition it into a pair of 2 TB spaces. Hard drives can also structure their data in a number of ways, so you'll need to know which file-systems your TV can support. Most TVs are fine with NTFS, which is how Windows 10 formats a disk by default. If you have a Mac or Linux computer you'll need to deliberately format your drive in NTFS, rather than the Mac's APFS or Ext4 on Linux. Your operating system's documentation can tell you how to do that.
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Connect Your Hard Disk to the TV
Take a look at your USB connectors on the TV. Some TVs may have more than one, and if so one of them might be labeled as USB/HDD. That's the one you want to use for your hard drive. If there's only one, or if none of them are labeled specifically for the hard drive, don't worry about it. Just use what you've got. When you plug the hard drive into the USB port, you should feel a slight vibration as it's recognized and read by the TV. Depending on the case it's in, you may also be able to see a light flickering on and off. Use your remote to choose the USB drive as your input device, and you should be able to see your content using the TV's built in file browser. Just choose the file you want to watch, and select it with the remote. It should begin playing.
Choosing Compatible Files
It's important to remember that your TV probably won't be able to recognize as many types of media files as your computer. Your user manual should tell you which file types your TV can recognize, or if you've lost your manual you can check the manufacturer's website. If all else fails, you can always try a clip and see if it works. If not, you'll have to convert the file into something your TV can recognize. If you have the free VLC Media Player on your computer, you can use that to convert between most audio and video file types. Bear in mind that if the file is protected by some form of digital rights management, or DRM, it's against U.S. law to break it for the sake of making a copy.
A Couple of Cautions
An external hard drive can usually draw all the power it needs from the USB port itself, but most manufacturers recommend that you use a drive with its own power supply. There's a perfectly good reason for that: If you accidentally shut off your TV it can turn off the drive, and if there's a file being used at that moment it could become corrupted. If the drive has its own power, that can't happen. This is also why it's a prudent idea to have a backup of any file you put on that drive. If it's your only copy of that once-in-a-lifetime vacation video, you'll really regret losing it.
Limitations of Older TVs
Most new HDTVs and "smart" TVs are really good about using external devices, but older televisions might have a few limitations. For example, they might require your drive to be formatted in FAT32 format. If that's the case it'll only recognize a drive of up to 32 GB, and you might just as well use a USB thumb drive instead. In some cases, older TVs might not recognize your USB device at all. Some of the earliest TVs to incorporate a USB connector intended it only as a diagnostic port, for their service technicians. If you have one of those older TVs, or if you have one with HDMI inputs but no USB port, you'll have to be a bit more creative to connect your hard drive to the TV.
Connecting Through a Separate Device
If your TV doesn't have a working USB connection, or if its built in file browser is so limited it's just frustrating to use, you might have to use some kind of hard drive to TV adapter. Your most straightforward option is to use a separate device, such as a Roku or PVR. These usually have a USB connection for your hard drive and an HDMI output to connect up to your TV, and they'll have a built-in file browser that's usually pretty good. If taking your computer into the living room isn't a viable option whenever you want to watch a movie or video clip, this is probably going to be your best bet.