Whilst, as has been pointed out, it is possible to see the current default socket buffer sizes in /proc, it is also possible to check them using sysctl (Note: Whilst the name includes ipv4 these sizes also apply to ipv6 sockets - the ipv6 tcp_v6_init_sock() code just calls the ipv4 tcp_init_sock() function):
sysctl net.ipv4.tcp_rmem
sysctl net.ipv4.tcp_wmem
However, the default socket buffers are just set when the sock is initialised but the kernel then dynamically sizes them (unless set using setsockopt() with SO_SNDBUF). The actual size of the buffers for currently open sockets may be inspected using the ss command (part of the iproute package), which can also provide a bunch more info on sockets like congestion control parameter etc. E.g. To list the currently open TCP (t option) sockets and associated memory (m) information:
ss -tm
Here's some example output:
State Recv-Q Send-Q Local Address:Port Peer Address:Port
ESTAB 0 0 192.168.56.102:ssh 192.168.56.1:56328
skmem:(r0,rb369280,t0,tb87040,f0,w0,o0,bl0,d0)
Here's a brief explanation of skmem (socket memory) - for more info you'll need to look at the kernel sources (e.g. sock.h):
r:sk_rmem_alloc rb:sk_rcvbuf # current receive buffer size t:sk_wmem_alloc tb:sk_sndbuf # current transmit buffer size f:sk_forward_alloc w:sk_wmem_queued # persistent transmit queue size o:sk_omem_alloc bl:sk_backlog d:sk_drops