Usable Hosts in an IPv4 Subnet

An IPv4 prefix of $p$ bits leaves $32-p$ bits for hosts, giving $2^{32-p}$ addresses, of which two are unusable: the all-zeros address names the network itself and the all-ones address is the broadcast. So a /24 has 254 usable hosts, a /26 has 62, and a /30 has 2, which is why point-to-point links were traditionally /30 and wasted half their space.

The minus two is where the money goes when you subnet. Split a /24 into four /26s and you get $4 \times 62 = 248$ usable addresses instead of 254, because each subnet now pays its own network-and-broadcast tax. Split it into sixteen /28s and you are down to $16 \times 14 = 224$. Every additional boundary costs you two addresses, which is invisible on a whiteboard and painfully visible when a /24 will not fit the VLAN plan.

Two exceptions are worth knowing before you trust the formula blindly. RFC 3021 permits a /31 on point-to-point links by dropping the reservation entirely, so a /31 has two usable addresses rather than none, and most modern router platforms support it. A /32 is a single host route, used for loopbacks and for advertising a service address. And the whole thing is an IPv4 story: IPv6 subnets are /64 by convention, which is $1.8 \times 10^{19}$ addresses per LAN, and nobody subtracts two.