This chart shows the max_connections limit, set by AWS, at various MySQL RDS instance sizes.

t2.micro 66
t2.small 150
m3.medium 296
t2.medium 312
M3.large 609
t2.large 648
M4.large 648
M3.xlarge 1237
R3.large 1258
M4.xlarge 1320
M2.xlarge 1412
M3.2xlarge 2492
R3.xlarge 2540

AWS sets the MySQL max_connections system variable according to the size of the RDS instance.  max_connections is the maximum permitted number of simultaneous or concurrent client connections.  A “Too many connections” error message may be displayed if this is reached.

If an application implements long-running queries or creates several concurrent connections from the web or app side, the number of connections is just as important as vCPU cores, memory level or storage IO.

for more info, see the MySQL max_connections sys variable, or AWS’s post regarding DB parameter groups.