PostgreSQL
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lista de esquemas com tamanhos (relativos e absolutos) em um banco de dados PostgreSQL


Tente isto:
SELECT schema_name, 
       sum(table_size),
       (sum(table_size) / database_size) * 100
FROM (
  SELECT pg_catalog.pg_namespace.nspname as schema_name,
         pg_relation_size(pg_catalog.pg_class.oid) as table_size,
         sum(pg_relation_size(pg_catalog.pg_class.oid)) over () as database_size
  FROM   pg_catalog.pg_class
     JOIN pg_catalog.pg_namespace ON relnamespace = pg_catalog.pg_namespace.oid
) t
GROUP BY schema_name, database_size


Edit:acabei de notar que a solução de somar todas as tabelas para obter o tamanho do banco de dados não é necessária:
SELECT schema_name, 
       pg_size_pretty(sum(table_size)::bigint),
       (sum(table_size) / pg_database_size(current_database())) * 100
FROM (
  SELECT pg_catalog.pg_namespace.nspname as schema_name,
         pg_relation_size(pg_catalog.pg_class.oid) as table_size
  FROM   pg_catalog.pg_class
     JOIN pg_catalog.pg_namespace ON relnamespace = pg_catalog.pg_namespace.oid
) t
GROUP BY schema_name
ORDER BY schema_name