7-Zip is free software with open source. The most of the code is under the GNU LGPL license. Some parts of the code are under the BSD 3-clause License. Also there is unRAR license restriction for some parts of the code. Read 7-Zip License information.
You can use 7-Zip on any computer, including a computer in a commercial organization. You don't need to register or pay for 7-Zip.