How can I get the page size of a Postgres database?
If you don't have access to pg_controldata ...

There is a simple way:

test=# SELECT current_setting('block_size');
 current_setting
-----------------
 8192


The manual:


  The following “parameters” are read-only, and are determined when
  PostgreSQL is compiled or when it is installed. [...]
  
  block_size (integer)
  
  Reports the size of a disk block. It is determined by the value of BLCKSZ when building the server. The default value is 8192 bytes. The
  meaning of some configuration variables (such as shared_buffers) is
  influenced by block_size. See Section 19.4 for information.


To verify

Create a dummy table with only 1 small row: one data page is allocated. Then check the size of the "main" relation fork with pg_relation_size()

test=# CREATE TEMP TABLE foo AS SELECT 1 AS id;
SELECT 1
test=# SELECT pg_size_pretty(pg_relation_size('pg_temp.foo'));
 pg_size_pretty
----------------
 8192 bytes
(1 row)


So the page size is 8 kB, which is hardly surprising like you mentioned. The manual:


  Every table and index is stored as an array of pages of a fixed size (usually 8 kB, although a different page size can be selected when compiling the server).