Subnet Calculator

An IPv4 address is a 32-bit unsigned integer, written as four 8-bit octets in decimal. Every subnetting question is a question about those 32 bits, so the first move is always to convert to binary using the octet place values $128, 64, 32, 16, 8, 4, 2, 1$:

So 192.168.10.130 is 11000000.10101000.00001010.10000010.

A prefix length $/n$ means the mask is $n$ consecutive 1 bits followed by $32-n$ zero bits. The 1 bits mark the network portion, the 0 bits the host portion:

• /24 → 11111111.11111111.11111111.00000000 = 255.255.255.0
• /26 → 11111111.11111111.11111111.11000000 = 255.255.255.192

Going the other way, convert each mask octet to binary and count the ones: $255$ is eight ones and $254$ is 11111110, seven ones, so 255.255.254.0 is /23.

The condition people forget: a valid mask is contiguous ones followed by zeros. 255.255.255.192 is legal because $192 =$ 11000000. 255.255.255.160 is not, because $160 =$ 10100000 — its ones are separated by a zero.

Network address

AND the address with the mask, bit by bit ($1 \wedge 1 = 1$, everything else $0$). Octets masked by 255 pass through unchanged, so only the boundary octet does real work. For 192.168.10.130/26:

130  = 1 0 0 0 0 0 1 0
192  = 1 1 0 0 0 0 0 0   (mask)
AND  = 1 0 0 0 0 0 0 0  = 128

Network = 192.168.10.128.

Broadcast address

Keep the network bits, set every host bit to 1: 10000000 → 10111111 $= 128 + 63 = 191$, so the broadcast is 192.168.10.191.

Host count

With $h = 32 - n$ host bits:

$\text{addresses} = 2^{h}, \qquad \text{usable hosts} = 2^{h} - 2$

The $-2$ removes the network address (all host bits 0) and the broadcast (all host bits 1). A /26 has $h = 6$: $2^6 = 64$ addresses, $62$ usable.

Block size shortcut

$256 - 192 = 64$, so /26 subnets start every 64 addresses: .0, .64, .128, .192. To size a subnet instead, find the smallest $h$ with $2^{h} - 2 \ge H$ and take $n = 32 - h$.

• Assuming the given address is the network address. 192.168.10.130/26 is a host inside 192.168.10.128/26. Always AND first.
• Subtracting 2 where it does not apply. A /31 point-to-point link (RFC 3021) gives 2 usable addresses, and a /32 is a single host route.
• Off-by-one on the broadcast. Broadcast $=$ network $+$ block size $-1$, not network $+$ block size.
• Reading the prefix backwards. A larger $n$ means a smaller network: /26 holds a quarter of what /24 holds.
• Non-contiguous masks. Only masks of the form ones-then-zeros are valid, which is why the mask octet is always one of 0, 128, 192, 224, 240, 248, 252, 254, 255.
• Carrying IPv4 habits into IPv6. IPv6 has no broadcast address and no $-2$ rule; a /64 simply holds $2^{64}$ addresses.