The default formula use by AWS RDS to calculate the max_connections parameter is: LEAST({DBInstanceClassMemory/9531392},5000)
But It's hard to find the exact value of DBInstanceClassMemory.
So, here are the values I got when I ran the SQL commmand: show max_connections; in some RDS instances:
| Instance type | RAM (GB) | max_connections | 
|---|---|---|
| db.t2.small | 2 | 198 | 
| db.t2.medium | 4 | 413 |