Calculating a subnet step by step

What we are looking for

For a given address with its prefix, for example 192.168.10.77/27, we want six pieces of information:

1. The block-size method (the fastest)

You can do it in your head, in five steps. Example: 192.168.10.77/27.

Step 1: find the interesting octet. It is the mask octet that is neither 255 nor 0 (or the last 255 if the prefix is a multiple of 8). A /27 gives 255.255.255.224: it is the 4th octet, worth 224.

Step 2: compute the block size. Block size = 256 − 224 = 32.

Step 3: list the multiples of the block size in that octet: 0, 32, 64, 96, 128…

Step 4: bracket the address. The 4th octet of the address is 77. It lies between 64 and 96. So the network starts at 64, and the next network at 96.

Step 5: work out the rest.

2. The binary method (to understand and check)

This is what the machine actually does. We only look at the interesting octet, here the 4th.

Network address: a bitwise logical AND between the address and the mask. A bit stays at 1 only if it is 1 on both sides.

Address   77    0100 1101
Mask     224    1110 0000
                ---------
AND             0100 0000   = 64   → network 192.168.10.64

Broadcast address: keep the network bits, and set every host bit (the 0s of the mask) to 1.

Mask       224    111 00000   (3 network bits, 5 host bits)
Network     64    010 00000
Broadcast   95    010 11111   → broadcast 192.168.10.95

Both methods give the same result: the block size is just a shortcut for the binary calculation.

3. Example 2: the block size on the 3rd octet

Address: 172.16.45.200/20.

1. Mask of a /20: 255.255.240.0. The interesting octet is the 3rd (240).
2. Block size = 256 − 240 = 16.
3. Multiples of 16: 0, 16, 32, 48, 64…
4. The 3rd octet of the address is 45: it lies between 32 and 48.
5. Apply the rule from the tip: the 4th octet is 0 for the network and 255 for the broadcast.

4. Example 3: the block size on the 2nd octet

Address: 10.5.130.9/12.

1. Mask of a /12: 255.240.0.0. The interesting octet is the 2nd (240).
2. Block size = 16.
3. Multiples of 16: 0, 16, 32…
4. The 2nd octet is 5: it lies between 0 and 16.
5. The 3rd and 4th octets are 0 for the network and 255 for the broadcast.

5. Two questions people often ask

Are these two machines on the same network?

192.168.10.77/27 and 192.168.10.100/27? With a block size of 32, the first is in the network starting at 64 (64 to 95), the second in the one starting at 96 (96 to 127). Answer: no. They cannot talk directly: they need to go through a router.

Which prefix for N hosts?

Look for the smallest network whose number of hosts is at least N. Example for 50 hosts:

Leave some headroom: the gateway and network devices take addresses too, and networks only ever grow.

What about /31 and /32?

The "− 2" formula does not apply to them. A /32 means a single address (a specific machine, in a firewall rule or a route). A /31 holds two addresses, both usable, with no network or broadcast address: it is used for point-to-point links between two routers (RFC 3021).

6. Check with a tool

Once you have done the calculation by hand, a tool can confirm it.

ipcalc (Linux, macOS with Homebrew)

sudo apt install ipcalc
ipcalc 192.168.10.77/27

Excerpt of the output:

Network:   192.168.10.64/27
HostMin:   192.168.10.65
HostMax:   192.168.10.94
Broadcast: 192.168.10.95
Hosts/Net: 30

On macOS, install it with brew install ipcalc.

Python (all systems)

Python ships with a module dedicated to IP addresses. This line works on Linux, macOS and Windows (replace python3 with py on Windows):

python3 -c "import ipaddress; n=ipaddress.ip_interface('192.168.10.77/27').network; print(n, n.broadcast_address, n.num_addresses-2)"

Result:

192.168.10.64/27 192.168.10.95 30

7. Practice

Key takeaways

• Block size = 256 − the value of the interesting octet in the mask.
• The network starts on the multiple of the block size just below the address; the broadcast is just before the next multiple.
• Octets after the interesting octet are 0 (network) and 255 (broadcast).
• First host = network + 1, last host = broadcast − 1.
• Check with ipcalc or Python's ipaddress module.