CIDR Subnet Math Explained: /24, /16, /8, and Everything Between

CIDR (Classless Inter-Domain Routing, RFC 4632) is how every modern network is described. An IP address followed by a slash and a number — the prefix length — telling you how many bits at the front of the address name the network.

Old school: class A, B, C. Modern: CIDR. All the sizing is one number.

The Notation

192.168.1.0/24
   ↑ IP    ↑ prefix length

• Prefix length = network bits (leftmost)
• Remaining bits = host bits (rightmost)
• Total is always 32 bits (IPv4) or 128 bits (IPv6)

For IPv4 /24: 24 network bits + 8 host bits = 256 total addresses.

The Formulas

Total addresses  = 2^(32 - prefix)
Usable hosts     = 2^(32 - prefix) - 2   (subtract network + broadcast)

Subtract 2 because:

• All-host-bits-zero is the network address (192.168.1.0 for /24)
• All-host-bits-one is the broadcast address (192.168.1.255 for /24)

Neither can be assigned to a host.

Common Prefixes (IPv4)

Splitting a Subnet

Add bits to the prefix. Each added bit halves the address space.

Example: split 192.168.1.0/24 into four subnets.

• /24 → /26 (add 2 prefix bits = 4 subnets)
• Each /26 has 64 addresses (62 usable)
• Subnet boundaries: .0, .64, .128, .192

192.168.1.0/26     → 192.168.1.0   – 192.168.1.63
192.168.1.64/26    → 192.168.1.64  – 192.168.1.127
192.168.1.128/26   → 192.168.1.128 – 192.168.1.191
192.168.1.192/26   → 192.168.1.192 – 192.168.1.255

Reading a CIDR Block by Hand

To find the network address of 172.16.42.137/20:

1. /20 = 20 network bits = 12 host bits
2. Convert the host portion of the IP to binary
3. Zero out the host bits

Faster method: the network boundary in /20 falls on multiples of 2^(32-20) / 256 = 16 in the third octet. 172.16.42.x — the closest multiple of 16 at or below 42 is 32. So the network is 172.16.32.0/20, covering 172.16.32.0 – 172.16.47.255.

The /31 and /32 Special Cases

• /31 — RFC 3021 lets you use /31 for point-to-point links with 2 usable addresses. No network / broadcast concept. Saves address space vs /30.
• /32 — a single-host “subnet”. Used for loopback interfaces, host routes, and single-IP firewall matches.

IPv6 CIDR

Same notation, different bit widths. Common IPv6 prefixes:

There’s no shortage of IPv6 addresses — you don’t fret about /28 vs /29 the way you do with IPv4.

RFC 1918 Private Ranges

Reserved for internal use, never routed on the internet:

• 10.0.0.0/8 — one giant private range
• 172.16.0.0/12 — 16 /16s (172.16.0.0 to 172.31.255.255)
• 192.168.0.0/16 — 256 /24s

Tools

Use the subnet calculator to:

• Convert between CIDR and dotted netmask
• List all subnets when splitting a block
• Calculate first / last host, network, broadcast
• Compute available host count

Cheaper than doing the math by hand every time.

Related

Check the Port 25 glossary entry, read the What Is a MAC Address? deep dive, and browse DNS record types — CIDR is what routes IP packets that DNS lookups return.