In order to create a database, the PostgreSQL server must be up and running (see Section 17.3).
Databases are created with the SQL command CREATE DATABASE:
CREATE DATABASE name;
where name follows the usual rules for SQL identifiers. The current role automatically becomes the owner of the new database. It is the privilege of the owner of a database to remove it later on (which also removes all the objects in it, even if they have a different owner).
The creation of databases is a restricted operation. See Section 20.2 for how to grant permission.
Since you need to be connected to the database server in order to execute the CREATE DATABASE command, the question remains how the first database at any given site can be created. The first database is always created by the initdb command when the data storage area is initialized. (See Section 17.2.) This database is called postgres. So to create the first "ordinary" database you can connect to postgres.
A second database, template1, is also created by initdb. Whenever a new database is created within the cluster, template1 is essentially cloned. This means that any changes you make in template1 are propagated to all subsequently created databases. Therefore it is unwise to use template1 for real work, but when used judiciously this feature can be convenient. More details appear in Section 21.3.
createdb does no magic. It connects to the postgres database and issues the CREATE DATABASE command, exactly as described above. The createdb reference page contains the invocation details. Note that createdb without any arguments will create a database with the current user name, which might or might not be what you want.
Note: Chapter 19 contains information about how to restrict who can connect to a given database.
Sometimes you want to create a database for someone else. That role should become the owner of the new database, so he can configure and manage it himself. To achieve that, use one of the following commands:
CREATE DATABASE dbname OWNER rolename;
from the SQL environment, or:
createdb -O rolename dbname
from the shell. You must be a superuser to be allowed to create a database for someone else (that is, for a role you are not a member of).