Choose IPv4 or IPv6 in "Mode", then enter an IP address and prefix length. The page calculates the network address, host counts, subnet mask and more, and draws a bit diagram.
The prefix length is the "24" in "/24" (the number of network bits). Use 0 to 32 for IPv4 and 0 to 128 for IPv6. With /31 and /32, the number of usable hosts is 0.
Result
Enter an IP address and prefix length on the left and press "Calculate". The network address, host counts and a bit diagram will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formula
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter an IP address and prefix length (for example, 192.168.1.0 /24), and you get the network address, broadcast address and usable host IP range on the spot
- It also calculates the total hosts, usable hosts, subnet mask, wildcard mask, CIDR notation, integer ID and hex ID all at once
- A bit diagram colors the 32 bits of the IP address by network portion and host portion, so you can see how subnetting works
- You can switch between IPv4 and IPv6 modes. In IPv6 mode, it calculates the network, address range and total addresses (\(2^{128-\text{prefix length}}\))
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The IP class (A, B, C and so on) on this page follows the original classful definition based on the first octet (the first number). Classes are an old idea; today's internet mostly uses CIDR, which divides networks freely by prefix length. The "IP type" is "Private" if the address falls in a private IP range and "Public" otherwise, so special addresses such as loopback (127.0.0.1) are classed as "Public". Use a prefix length of 0 to 32 (0 to 128 for IPv6).
What is this calculation used for?
Designing networks for offices and data centers
Large organizations divide one IP network into smaller subnets for each department or location. For example, "to connect up to 60 devices in the sales department, assign a /26, which has 62 usable hosts (\(2^{32-26}-2 = 62\))". You choose the prefix length from the number of devices you need.
Subnet calculation is a basic design skill that network administrators and infrastructure engineers use almost every day.
Setting up a home or office router (Wi-Fi)
"192.168.1.0/24" and "subnet mask 255.255.255.0", which you often see in a home router's settings, are exactly this calculation. A /24 has 254 usable hosts, so you can connect up to 254 devices in total, such as phones, computers and TVs.
It also helps when a device will not connect: you can check whether its IP address is in the right range (network).
Building networks in the cloud (AWS, Azure and others)
When you create your own private network in the cloud (such as an AWS VPC), you give its address range in CIDR notation, for example "this VPC is 10.0.0.0/16, and a subnet inside it is 10.0.1.0/24". Overlapping ranges cannot talk to each other, so you need to work out the network addresses and host counts correctly.
For cloud engineers, subnet calculation is a must-have skill and the starting point for building an environment.
A standard topic in networking certifications
Certifications such as Cisco's CCNA and CompTIA Network+ repeatedly ask questions like "Given this IP address and subnet mask, find the network address, the broadcast address and the number of usable hosts".
Binary AND and OR and powers of 2 - the four formulas on this page - are exactly what earns those points. With the steps and the bit diagram, you can practice by working through problems yourself.
Setting address ranges in firewalls and access control
In firewall rules and access control lists (ACLs), such as "allow traffic only from this subnet", you specify the addresses to allow or deny together in CIDR notation (for example, 192.168.10.0/24). If you get the network address and range wrong, you may block traffic by mistake or open a hole by accident.
In security work, this calculation is the basis for specifying ranges that are exactly right, no wider and no narrower.
Formula
Network address (IP AND subnet mask)
Standard notation
(the usual math form)
\(N\)
\(=\)
\(\mathrm{IP}\)
\(\mathbin{\text{AND}}\)
\(\mathrm{mask}\)
In words
(symbols replaced with words)
④
network address \(N\)
\(=\)
①
IP address
③
\(\mathbin{\text{AND}}\)
②
subnet mask
The formula in words
①
Compare each bit of
the IP address
with each bit of
②
the subnet mask
,
③
keep a 1 only where both bits are 1 (the AND operation),
④
and you get the
network address \(N\)
(the address with all host bits set to 0)
Quick example
For 192.168.10.130 with /24 (subnet mask 255.255.255.0), only the last octet changes
network address
\(=\)
192.168.10.130 (IP)
\(\mathbin{\text{AND}}\)
255.255.255.0 (mask)
\(130 = 10000010_{2}, \quad 0 = 00000000_{2}\)
\(10000010 \mathbin{\text{AND}} 00000000 = 00000000 = 0\)
\(\Rightarrow 192.168.10.0\)
Key idea
AND (logical conjunction) is the operation that gives 1 only where both bits are 1. A subnet mask has 1s in the high bits (the network portion) and 0s in the low bits (the host portion), so ANDing it with an IP address keeps the network portion as it is and turns every host bit into 0. This gives the first address of that network, the network address.
Broadcast address (network OR wildcard mask)
Standard notation
(the usual math form)
\(B\)
\(=\)
\(N\)
\(\mathbin{\text{OR}}\)
\(W\)
In words
(symbols replaced with words)
③
broadcast address \(B\)
\(=\)
①
network address \(N\)
②
\(\mathbin{\text{OR}}\)
②
wildcard mask \(W\)
The formula in words
①
Compare each bit of
the network address \(N\)
with each bit of
②
the wildcard mask \(W\) (the subnet mask with its 0s and 1s swapped)
, and set a 1 wherever either bit is 1 (the OR operation),
③
and you get the
broadcast address \(B\)
(the address with all host bits set to 1)
Quick example
From the network 192.168.10.0 and the wildcard mask 0.0.0.255, only the last octet changes
broadcast address
\(=\)
192.168.10.0 (network)
\(\mathbin{\text{OR}}\)
0.0.0.255 (wildcard)
\(0 = 00000000_{2}, \quad 255 = 11111111_{2}\)
\(00000000 \mathbin{\text{OR}} 11111111 = 11111111 = 255\)
\(\Rightarrow 192.168.10.255\)
Key idea
OR (logical disjunction) is the operation that gives 1 wherever either bit is 1. A wildcard mask is the subnet mask with its 0s and 1s swapped, so its host bits are all 1. ORing it with the network address fills every host bit with 1, which gives the last address of that network, the broadcast address. The broadcast address is a special address for sending to every device on the network at once.
Total hosts (a power of \(2\))
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(H\)
\(=\)
\(2\)
\(32-p\)
③
total hosts \(H\)
\(=\)
①
2 (on or off)
②
host bits \(32-p\)
The formula in words
①
Multiply
2 (the two states of one bit, on or off)
by itself
②
as many times as the number of host bits \(32-p\) (32 bits minus the \(p\) network bits)
,
③
and you get the
total number of hosts \(H\)
Quick example
For /24, the host portion has \(32-24=8\) bits, so
total hosts
\(=\)
2
8 (host bits)
\(2^{32-24} = 2^{8} = 256\)
Key idea
Each host bit can be 0 or 1, two choices. With \(32-p\) host bits, there are \(2^{32-p}\) combinations, and that is the total number of addresses in the network (the total number of hosts). Each time the prefix length \(p\) goes up by 1 (one more network bit), the number of hosts is cut exactly in half.
Usable hosts (total − 2)
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(U\)
\(=\)
\(H\)
\(-\)
\(2\)
③
usable hosts \(U\)
\(=\)
①
total hosts \(H\)
\(-\)
②
2 (network and broadcast)
The formula in words
①
From
the total number of hosts \(H\)
,
②
subtract
2 (the network address at the start and the broadcast address at the end)
,
③
and you get the
number of usable hosts \(U\)
(the number of addresses you can give to devices)
Quick example
For /24, the total number of hosts is 256, so
usable hosts
\(=\)
256 (total hosts)
\(-\)
2
\(256 - 2 = 254\)
Key idea
In each network, the first address (the network address) and the last address (the broadcast address) are reserved for special uses and cannot be given to devices. So the number of addresses you can actually use is the total minus 2. The exceptions are /31 (2 addresses) and /32 (1 address): subtracting 2 leaves nothing, so the number of usable hosts is treated as 0 (/31 has a special use for point-to-point links).
Subnet calculations rest on four formulas - network address = IP AND subnet mask, broadcast address = network OR wildcard mask, total hosts = \(2^{32-p}\), and usable hosts = total − 2. Each time the prefix length \(p\) goes up by 1, the network splits in two and the number of hosts is cut in half. IPv6 works the same way, and the total number of addresses is \(2^{128-p}\).
Symbols and terms
Symbols
| \(N\) | N | The network address, the first address of the network (all host bits 0). It is used as the name of the network itself. |
| \(B\) | B | The broadcast address, the last address of the network (all host bits 1). It is used to send to every device on the network at once. |
| \(W\) | W | The wildcard mask, the subnet mask with its 0s and 1s swapped. Its host bits are all 1, and it is used to find the broadcast address and in access control lists. |
| \(p\) | p | The prefix length, the "24" in "/24". It tells how many bits the network portion has. (From "prefix".) |
| \(H\) | H | The total number of hosts, the total number of addresses in the network, \(H = 2^{32-p}\). (From "host".) |
| \(U\) | U | The number of usable hosts, the number of addresses you can actually give to devices. It is the total minus 2 (the network address and the broadcast address). |
| \(\land\) | AND | Logical AND (conjunction). The result is 1 only when both bits are 1. It is used to find the network address. |
| \(\lor\) | OR | Logical OR (disjunction). The result is 1 when either bit is 1. It is used to find the broadcast address. |
Terms
| subnet | Each of the smaller networks that a large IP network is divided into. Splitting a network by department or location (subnetting) makes it easier to manage and more secure. |
| subnet mask | A 32-bit value that shows where the network portion of an IP address ends and the host portion begins. It has 1s for the network bits and 0s for the host bits (for example, 255.255.255.0). |
| prefix length | The number of network bits. It is written like "/24" and carries the same information as the subnet mask in a shorter form. |
| CIDR | Classless Inter-Domain Routing, usually pronounced "cider". A method that divides networks freely by prefix length instead of by class, written with a slash, as in "192.168.1.0/24". It is the standard on today's internet. |
| network address | The first address of the network (all host bits 0). It is not given to any device and is used as the name of the network itself. |
| broadcast address | The last address of the network (all host bits 1). It is a special address for sending to every device on the network at the same time. |
| wildcard mask | The subnet mask with its bits flipped. The host bits are all 1. It is used to calculate the broadcast address and in router access control lists (ACLs). |
| octet | One of the four parts of an IPv4 address separated by periods (8 bits, 0 to 255). In 192.168.1.0, "192", "168", "1" and "0" are each one octet. |
| private IP address | An IP address reserved for use only inside a home or organization (10.0.0.0 to 10.255.255.255, 172.16.0.0 to 172.31.255.255 and 192.168.0.0 to 192.168.255.255, defined in RFC 1918). It cannot be used on the internet as is. An address that works across the whole internet is called a public IP address. |
| IP class (classful addressing) | An older system, used before CIDR became common, that set the size of a network by its first number (the first octet) as Class A, B, C and so on. It is no longer used for routing, but the terms are still around, so this page shows the class too. |
| IPv4 | The 32-bit addressing system (about 4.3 billion addresses), the most widely used one. It is the main focus of this page. |
| IPv6 | The newer 128-bit addressing system, with a practically unlimited number of addresses. It was created to solve the shortage of IPv4 addresses. |
| bit | The smallest unit of information, either 0 or 1. An IPv4 address is made of 32 bits and an IPv6 address of 128 bits. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Binary and decimal (high school computer science) |
|
| Powers and exponents (Grades 6–8) |
|
| Logical AND and OR (high school computer science) |
|
| Bits and bytes (high school computer science) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table for total hosts and usable hosts
| Prefix length p | 24 |
| Host bits (32−p) | =32-B1 |
| Total hosts | =2^B2 |
| Usable hosts | =MAX(B3-2,0) |
Table for the subnet mask
| Prefix length p | 24 |
| Subnet mask as an integer | =(2^32)-(2^(32-B1)) |
| First octet | =INT(B2/16777216) |
| Second octet | =INT(MOD(B2,16777216)/65536) |
| Third octet | =INT(MOD(B2,65536)/256) |
| Fourth octet | =MOD(B2,256) |
In the first table, enter a prefix length in B1, and the host bits, total hosts and usable hosts are calculated automatically. "^" is the power symbol, so "=2^B2" is "2 multiplied by itself B2 times". For /24, you get 256 total hosts and 254 usable hosts. MAX(…,0) keeps the result from going below 0 for /31 and /32.
The second table splits the subnet mask into its four octets (0 to 255). B2 calculates the whole mask as one integer, and B3 to B6 take out each octet using quotients and remainders of division by powers of 256. For /24, the result is 255.255.255.0.
The second table splits the subnet mask into its four octets (0 to 255). B2 calculates the whole mask as one integer, and B3 to B6 take out each octet using quotients and remainders of division by powers of 256. For /24, the result is 255.255.255.0.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table for total hosts and usable hosts
| Prefix length p | 24 |
| Host bits (32−p) | =32-B1 |
| Total hosts | =2^B2 |
| Usable hosts | =MAX(B3-2,0) |
Table for the subnet mask
| Prefix length p | 24 |
| Subnet mask as an integer | =(2^32)-(2^(32-B1)) |
| First octet | =INT(B2/16777216) |
| Second octet | =INT(MOD(B2,16777216)/65536) |
| Third octet | =INT(MOD(B2,65536)/256) |
| Fourth octet | =MOD(B2,256) |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace B1 with your own prefix length. Taking out each octet with INT (quotient) and MOD (remainder) works the same way too.
How to calculate it in Python
import ipaddress
ip = "192.168.10.130" # IP address
prefix = 24 # prefix length (the 24 in /24)
net = ipaddress.ip_network(f"{ip}/{prefix}", strict=False)
total = net.num_addresses # total hosts = 2 ** (32 - prefix)
usable = max(total - 2, 0) # usable hosts (0 for /31 and /32)
print(f"Network address: {net.network_address}")
print(f"Broadcast address: {net.broadcast_address}")
print(f"Subnet mask: {net.netmask}")
print(f"Wildcard mask: {net.hostmask}")
print(f"Total hosts: {total}")
print(f"Usable hosts: {usable}")
The standard library's ipaddress module is all you need. strict=False in ip_network lets you pass an IP whose host bits are not 0 (such as 192.168.10.130) and treats it as its network instead of raising an error. Change the IP address and prefix length at the top and run it.
How to write it in LaTeX and other math languages (copy and paste)
Network address (IP AND subnet mask)
N = IP ∧ mask
N = \mathrm{IP} \land \mathrm{mask}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>N</mi>
<mo>=</mo>
<mi>IP</mi>
<mo>∧</mo>
<mi>mask</mi>
</mrow>
</math>
N = IP ^^ mask
BitAnd[ip, mask]
N := Bits:-And(ip, mask);
N = bitand(ip, mask);
N = IP ∧ mask
Broadcast address (network OR wildcard mask)
B = N ∨ W
B = N \lor W
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>B</mi>
<mo>=</mo>
<mi>N</mi>
<mo>∨</mo>
<mi>W</mi>
</mrow>
</math>
B = N vv W
BitOr[network, wildcard]
B := Bits:-Or(network, wildcard);
B = bitor(network, wildcard);
B = N ∨ W
Total hosts (a power of \(2\))
H = 2^(32 − p)
H = 2^{32 - p}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>H</mi>
<mo>=</mo>
<msup>
<mn>2</mn>
<mrow><mn>32</mn><mo>−</mo><mi>p</mi></mrow>
</msup>
</mrow>
</math>
H = 2^(32 - p)
2^(32 - p)
H := 2^(32 - p);
H = 2^(32 - p);
H = 2^(32-p)
Usable hosts (total − 2)
U = H − 2
U = H - 2
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>U</mi>
<mo>=</mo>
<mi>H</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</math>
U = H - 2
H - 2
U := H - 2;
U = H - 2;
U = H - 2
How to have ChatGPT do the calculation
You are a network calculation assistant. Do the following calculation by actually running Python (the standard library's ipaddress module), and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). For the IPv4 address 192.168.10.130 with a prefix length of /24, find: 1. The network address 2. The broadcast address 3. The subnet mask and the wildcard mask 4. The total number of hosts and the number of usable hosts Show the code you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Related Features
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Converts between binary and decimal, the two forms of an IP address. The foundation for subnet bit calculations
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Scientific Notation Converter (b×10ⁿ, E Notation, Engineering Notation)
Writes very large numbers, such as the number of IPv6 addresses, in a short form with powers of 10
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