This query lists the sizes of all tables in MySQL:

SELECT 
  TABLE_SCHEMA, 
  TABLE_NAME, 
  CONCAT(ROUND(data_length / ( 1024 * 1024 ), 2), 'MB') DATA, 
  CONCAT(ROUND(data_free  / ( 1024 * 1024 ), 2), 'MB') FREE 
from information_schema.TABLES 
where TABLE_SCHEMA NOT IN ('information_schema','mysql', 'performance_schema');

This query lists the database sizes:

SELECT 
  TABLE_SCHEMA, 
  TABLE_NAME, 
  CONCAT(ROUND(sum(data_length) / ( 1024 * 1024 ), 2), 'MB') DATA 
from information_schema.TABLES 
where TABLE_SCHEMA NOT IN ('information_schema','mysql', 'performance_schema') 
group by TABLE_SCHEMA;