In MySQL, you can query the information_schema.tables
table to return information about the tables in a database. This table includes information about the data length, index length, as well as other details such as collation, creation time, etc. You can use the information in this table to find the size of a given database or all databases on the server.
You can also use the MySQL Workbench GUI to find details about the database (including its size).
This article provides a quick overview of both methods.