Efficient data storage and transmission have become of utmost importance in today's digital era. File compression processes are crucial to addressing this issue. The purpose of this study is to examine and compare the use of the Arithmetic Coding Method and the LZW Method in file compression. Both of these methods are known for their excellent compression capabilities, but there has been limited research comparing them in the context of real-world use. This research employed a range of files, including text, photos, and recordings, to test both approaches. Results indicate that the arithmetic coding method typically offers a slightly better compression ratio compared to the LZW method. However, LZW provides faster compression and decompression speeds, making it more suitable for real-time applications or where response time is critical. Nonetheless, the choice between these two methods largely depends on the specific needs of a given application. For purposes requiring the highest compression ratio, the arithmetic coding method might be more appropriate. however, the LZW method might be more suitable for purposes demanding quick compression and decompression. In summary, both the arithmetic coding and LZW methods have their own strengths and weaknesses. A thorough understanding of the features and requirements of the file to be compressed is vital for choosing the most fitting method. the LZW method might be more suitable for purposes demanding quick compression and decompression. In summary, both the arithmetic coding and LZW methods have their own strengths and weaknesses. A thorough understanding of the features and requirements of the file to be compressed is vital for choosing the most fitting method. the LZW method might be more suitable for purposes demanding quick compression and decompression. In summary, both the arithmetic coding and LZW methods have their own strengths and weaknesses. A thorough understanding of the features and requirements of the file to be compressed is vital for choosing the most fitting method.