2 Subnet and Host Range Calculations

IPv4 prefixes and masks

An IPv4 address is $32$ bits and is usually written as four decimal octets, such as 192.168.1.77. A CIDR prefix such as $/26$ specifies how many leading bits identify the network; the remaining bits identify addresses within that network. CIDR uses this prefix length instead of the older address classes.

A prefix $/p$ has $p$ network bits and $32-p$ host bits. Its subnet mask consists of $p$ leading $1$ bits followed by $0$ bits.

Address counts and block sizes

The total number of addresses in a prefix is determined by its host-bit count:

For ordinary subnets from $/0$ through $/30$, the number of usable host addresses is typically:

The two excluded addresses are the network address, where all host bits are $0$, and the directed broadcast address, where all host bits are $1$. For example, a $/26$ contains $64$ total addresses and typically $62$ usable host addresses.

To find the block size by hand, locate the first mask octet that is not 255 and subtract its value from $256$. For $/26$, the last mask octet is 192, so the block size is $256-192=64$. The subnet boundaries in that octet are $0$, $64$, $128$, and $192$.

Finding subnet and host ranges

To find a subnet's network address, broadcast address, and usable host range:

1. Find the subnet mask and block size.

2. Locate the block containing the given address. The block's first address is the network address.

3. Identify the block's last address; it is the broadcast address.

4. For an ordinary subnet, the usable host range runs from one address after the network address to one address before the broadcast address.

For 192.168.1.77/26, the mask is 255.255.255.192, and the block size in the last octet is $64$. The blocks are .0–.63, .64–.127, .128–.191, and .192–.255. Since .77 falls in .64–.127, the network address is 192.168.1.64, the broadcast address is 192.168.1.127, and the usable host range is 192.168.1.65–192.168.1.126, containing $62$ addresses.

A prefix can cross an octet boundary. For 172.16.35.123/20, the mask is 255.255.240.0. The block size in the third octet is $256-240=16$; the third-octet blocks include $16–31$, $32–47$, and $48–63$. Because $35$ is in $32–47$, the network address is 172.16.32.0, the broadcast address is 172.16.47.255, and the usable host range is 172.16.32.1–172.16.47.254. This prefix has $2^{12}=4096$ total addresses and typically $4094$ usable hosts.

Subnet size and splitting a block

A longer prefix leaves fewer host bits and therefore creates smaller subnets. Splitting a $/24$ into $/27$ subnets borrows $3$ bits, creating $2^3=8$ subnets. Each $/27$ has $2^5=32$ total addresses and typically $30$ usable host addresses.

Under modern subnetting practice, all definable subnets are usable, including the first and last.

Checking subnet membership

An address belongs to a subnet if applying the subnet mask to it produces that subnet's network address. In bitwise notation:

Another way to check is to see whether the address falls between the subnet's network and broadcast addresses, inclusive. For example, 192.168.1.100 belongs to 192.168.1.64/26 because it falls within .64–.127; 192.168.1.130 does not.

Special prefixes

The usual rule of subtracting $2$ from the total address count has exceptions. A $/31$ is used on point-to-point links, where both addresses are interpreted as host addresses and there is no conventional network/broadcast exclusion. A $/32$ identifies one address and is commonly used as a host route.