Direct answer
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Yes, in almost every practical setup a VoIP service needs a working internet connection, because it carries your voice as digital data across an IP network instead of over a dedicated phone wire.[3] The narrow exception is internal calling: two IP phones on the same local network can reach each other over that network alone, with no path to the public internet.[5] Anything that reaches the outside world, meaning other people, mobile numbers, or the traditional phone network, depends on broadband, and US rules build that into the definition of 'interconnected VoIP,' which requires a broadband connection from the user's location.[1] That connection does not have to be a wired line, since home or office broadband, Wi-Fi, and cellular data all carry VoIP as long as there is enough bandwidth and the link stays up.[6][9]