CIDR Notation and Subnet Math

In one line

CIDR writes the mask as a prefix length (/24); a /n network has 2^(32−n) addresses, and splitting or combining networks is just moving that number.

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Key ideas

01
CIDR (Classless Inter-Domain Routing) writes 192.168.1.0/24: the /24 means the first 24 bits are the network. It replaced the old fixed Class A/B/C scheme, which wasted huge address blocks.
02
Size rule: a /n block has 2^(32 − n) addresses. /32 = 1 address (one host), /30 = 4, /28 = 16, /24 = 256, /20 = 4,096, /16 = 65,536, /8 = 16.7 million. Each step of 1 in the prefix halves or doubles the size.
03
Splitting: a /24 contains two /25s, four /26s, eight /27s, and so on. 10.0.0.0/24 = 10.0.0.0/25 + 10.0.0.128/25. Aggregating works the other way: adjacent, aligned blocks combine into a larger one (route SUMMARISATION).
04
Mask conversions worth memorising: /24 = 255.255.255.0, /16 = 255.255.0.0, /20 = 255.255.240.0, /26 = 255.255.255.192, /28 = 255.255.255.240.
05
Is an address inside a range? Compare the first n bits. 10.0.5.9 is inside 10.0.0.0/16 (the first 16 bits are 10.0) and also inside 10.0.4.0/23, which covers 10.0.4.0–10.0.5.255, but not inside 10.0.6.0/23. Ranges that don't end on an octet boundary are where mistakes happen, so check with ipcalc or Python's ipaddress module rather than guessing.
06
Practical planning (the same rule as the AWS and Terraform courses): give every environment a non-overlapping block, size subnets generously for container workloads, and leave room to grow. Overlapping ranges make peering and VPNs impossible later.

Code & diagrams

subnet-math.pypython

Python's standard library does subnet math reliably, which makes it handy in scripts and reviews.

import ipaddress

net = ipaddress.ip_network("10.20.0.0/16")
print(net.num_addresses)                       # 65536
print(list(net.subnets(new_prefix=20))[:3])    # first three /20s
print(ipaddress.ip_address("10.20.33.7") in ipaddress.ip_network("10.20.32.0/20"))  # True

# Do two ranges overlap?
a, b = ipaddress.ip_network("10.20.0.0/16"), ipaddress.ip_network("10.20.128.0/17")
print(a.overlaps(b))                           # True

SplitA24diagram

Rendering diagram…

Explain it without notes

Why does increasing the prefix length by one halve the number of addresses?

Practice

Split 172.16.0.0/22 into four equal subnets. Write them in CIDR.

Does 192.168.10.200 belong to 192.168.10.128/26?

Trade-offs

↔
Large subnets are simple and leave room for growth but waste address space; small ones conserve space but run out, and resizing a subnet in the cloud usually means recreating it.

Done when you can

I can compute the size of any /n block.
I can split a block into smaller subnets and write them in CIDR.
I can check whether an address is in a range (and use a tool to confirm).