How to Find the Optimal Database Connection Pool Size
A formula which has held up pretty well across a lot of benchmarks for years is that for optimal throughput the number of active connections should be somewhere near ((core_count * 2) + effective_spindle_count). Core count should not include HT threads, even if hyperthreading is enabled. Effective spindle count is zero if the active data set is fully cached, and approaches the actual number of spindles as the cache hit rate falls. Benchmarks of WIP for version 9.2 suggest that this formula will need adjustment on that release. There hasn't been any analysis so far regarding how well the formula works with SSDs.

However you choose a starting point for a connection pool size, you should probably try incremental adjustments with your production system to find the actual "sweet spot" for your hardware and workload.

Remember that this "sweet spot" is for the number of connections that are actively doing work. Ignore mostly-idle connections used for system monitoring and control when working out an appropriate pool size. You should always make max_connections a bit bigger than the number of connections you enable in your connection pool. That way there are always a few slots available for direct connections for system maintenance and monitoring.

https://wiki.postgresql.org/wiki/Number_Of_Database_Connections