too many connection error mysql: how to calculate max_connections how to calculate this values to get the best results to resolve this error "too many connection error mysql" and make my API faster 
       in mysql

   wait_timeout = ??
   max_connections = ??
   max_user_connections = ??
   key_buffer = ??
   query_cache_size = ??
   query_cache_limit = ??
   tmp_table_size = ??
   table_cache = ??
   max_concurrent_transactions ?? 
   max_concurrent_queries ??


and in apache 2

   ServerLimit ??
   StartServers ??
   MaxClients ??
   MinSpareThreads ??
   MaxSpareThreads ??
   ThreadsPerChild ??


what values should i set to this variable to get the best performance

system specification

amazon RDS 100GB DB STORAGE db.t1.micro

1 amazon LBS having two node attached to it each with

   amazon EC2 m1.small 1.7 GB RAM and 8 GB MAGNETIC HARD DISK 
   DEBAIN 7.1 WHEZZY O.S
Before deciding on value for max_connections I suggest that you look at WHY it reached the max_connection condition. A bunch of sleeping/idle connection due to loose coding is very common cause. Check if you have proper value for wait_timeout and adjust if this is your symptom.

Besides that, I would check for INSERT/UPDATE query that holds table locks for too long, as well as slow queries that get piled up once in a while.