Most users are interested in how much sound leakage there is with open back headphones, which will bother people surrounding them. The amount of sound leakage varies wildly between different models, but it's usually measured in dB(A). A rule of thumb is to expect around 1dB(A) of sound leakage for every 1 foot of distance. So an open back headphone with a measured 30dB(A) of sound leakage would probably leak about 30dB at a length of 1 foot, and thus around 12dB at 2 feet (which is the generally accepted minimum for what is minimally acceptable)
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Open-back headphones are mainly used either in a private setting or in situations where you aren't bothered by the sound leakage. For instance, they're great at home when you don't want to disturb anyone around you but also want to listen to your music without wearing overly isolating closed back headphones. They're also great when gaming or watching movies in a room by yourself because they deliver an experience similar to speakers.
For even more private listening, check out supra-aural closed-back headphones like the popular AKG K 240 (which many people use at home).
On the whole, open back headphones tend to be less isolating than closed-back models. This is because they don't form a complete seal around your ears, which would block out more sound. As an example, the popular Sennheiser HD 598 are rated at 30dB of sound leakage. Some noise-cancelling headphones have an isolation rating of around 20dB - 30dB, so the HD 598 are less isolating than that.
Open back headphones have several benefits over closed-back models, especially for specific uses. One of the most obvious is soundstage open-back headphones deliver an open and spacious experience thanks to their design, which lets air in and out of the ear cups. This can be great for gaming and movies/TV shows because it gives you a more realistic and immersive experience. They're also more comfortable for most people since they don't exert as much pressure on the ear as closed-back models of similar weight.
Closed-back headphones are generally ideal for city commuting since they better block out noise (both from your music leaking and the noises around you). On the whole, open-back headphones are better at delivering an open experience with a great soundstage. They're also usually more comfortable to most people than closed-back headphones. If you're mainly going to be using your headphones indoors, open back models are generally the way to go.
Sound leakage is relatively common with open-back headphones since they don't block out any noise around you by forming a seal over the ear. It's hard to avoid entirely, but you can do a few things to reduce the amount of sound leakage you have. The most obvious is to turn the volume down so it doesn't leak as much.
Another option is to consider purchasing an open back headphone that uses memory foam or other comfort-enhancing material in the ear cups - although this will also reduce noise isolation by a small amount. If you want to retain as much sound isolation as possible, consider checking out supra-aural closed back headphones like the AKG K 240.
Closed-back headphones are better for commuting, travel and use in public spaces since they don't leak sound into your ears or out to the world around you. Open back models are best suited for people who listen mostly at home, where they have the opportunity to blast the volume up a bit more without bothering anyone else.