The headphones that came with your MP3 player probably don't fit into the audio ports on a stereo system or an old mobile phone. Headphones and the devices you connect them to use three standard analog connection sizes: 1/4-inch (6.35mm), 1/8-inch (3.5mm) and 3/32-inch (2.5mm). All three sizes are interchangeable with adapters. The largest is commonly referred to in standard measurements, while the smaller two are referred to in metric. The larger connections have more surface area for establishing better connections and are much less prone to breaking, but there's no noticeable audio quality difference.
The middle sized 3.5mm connector is the one with which you're most likely familiar. Unless specifically designed to work with home stereos or small mobile devices, headphones are going to use 3.5mm. The 3.5mm size is officially considered part of the mini-phone connector family and is most commonly found in personal, portable electronics like iPods, portable DVD players, smartphones and tablets. Also, computers use the 3.5mm connection standard for headphones and speakers.
The 1/4-inch connector implies serious business, but actually it's just the largest available headphone size. It is the official standard connector size for phones, and higher-end headphones designed for home stereo systems usually feature 1/4-inch connectors. Amplifiers and recording equipment often feature the 1/4-inch connection standard as well. The larger jack size is useful since it's sturdier and it's much harder to break loose. Musical instrument amplifiers often feature 1/4-inch audio-out and headphone jacks because, despite how awesome "Rainbow in the Dark" sounds, people don't want to hear you practice it 100 times.
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The 2.5mm connector is the least common of the bunch, mostly found on mobile phones, communication radios and TTY devices. Smartphones and cellular phones have gradually moved towards using the 3.5mm connection over the 2.5mm connection size, making the devices compatible with the common headphone connector. Other than being slightly smaller than the 3.5mm size, 2.5mm looks very similar to the 3.5mm.
Bluetooth and USB
Analog is no longer the only game in town for headphones: you can also connect headphones to a device using Bluetooth or USB. Bluetooth is a wireless connection standard and is commonly found on devices like smartphones and personal media players. USB headphones are usually limited to computer headset devices.
Choosing an Adapter
With the correct adapter, you can scale down a 1/4" headphone set to a 3.5mm or a 2.5mm socket, or scale up 2.5mm and 3.5mm headphones to a 1/4" socket. While the adapter size might be different, the signal's the same regardless of the standard. If you're using an adapter, make sure it's a stereo adapter for headphones, otherwise you'll get sound only out of one speaker. Stereo plugs and adapters have two rings near the tip, whereas the mono counterparts have only one.