OSI 7 Layer Communications Model:

Sockets are a session library, which means that sockets reside in Layer
5.

The data is broken into packets via TCP in the Transport Layer (Layer
4) or via IP in the Network Layer (Layer 3), which are hidden from you
by sockets.

In other words, if I'm not mistaken, Java by itself can't give you this
information ... you would probably have to retrieve it from a log or a
tool somewhere.

"streams" are conceptually not "packets", which exist at a lower layer
in the protocol stack.

At any rate Java doesn't provide any way to determine this.

However you can make a rough guess if you know the MTU for the network
(usually 1500 bytes for ethernet, but ifconfig can tell you for sure).

Determine the lower bound by counting the total bytes sent, and
dividing by the MTU. This assumes that every IP datagram is completely
filled.

Determine the upper bound by doing the same calculation individually
for every call to OutputStream.write(n bytes), rounding *up* whenever
n is not an exact multiple of MTU, since the extra bytes will require
an additional packet.

Depending on sender timing and other issues, the real answer will lie
somewhere between the two bounds, but likely closer to the upper
bound.

/gordon