PostgreSQL database connection time how to check how much time PostgreSQL database takes for making connection?
Try with this query does the trick:

select *
from pg_stat_activity
where datname = 'mydatabasename';


Info:

See this closely related answer.

pg_stat_activity is a view in the pg_catalog schema.

You can query it by SELECTing from it like any other table, eg SELECT * FROM pg_stat_activity. The manual page you linked to explains its columns.

You'll sometimes find yourself wanting to join on other tables like pg_class (tables), pg_namespace (schemas), etc.

pg_stat_activity does not expose information about back-end memory use. You need to use operating-system level facilities for that. It does tell you the process ID, active user, currently running query, activity status, time the last query started, etc. It's good for identifying long-running idle in transaction sessions, very long running queries, etc.

Frankly, PostgreSQL's built-in monitoring is rather rudimentary. It's one of the areas that's not that exciting to work on, and commercial clients aren't often willing to fund it. Most people couple tools like check_postgres with Icinga and Munin, or use Zabbix or other external monitoring agents.

In your case it sounds like you really want pg_stat_statements, and/or PgBadger log analysis with suitable logging settings and possibly the auto_explain module.

Credits to: Craig Ringer