Networking Maths

Quick reference for some common and simple equations used in networking, I’ll be adding more as I use/forget them.

Number of hosts or subnets:
Number of “usable” hosts or subnets:

(n being the number of borrowed bits)

Number of links required for a full mesh network: or

(n being the number of nodes in the topology)

Classful networks

Class	Leading Bits	Start		End		   Networks          Addresses
A	     0		0.0.0.0		127.255.255.255	   128 (2^7)         16,777,216 (2^24)
B	     10		128.0.0.0	191.255.255.255	   16,384 (2^14)     65,536 (2^16)
C	     110	192.0.0.0	223.255.255.255	   2,097,152 (2^21)  256 (2^8)
D (mc)	     1110	224.0.0.0	239.255.255.255	   n/a               n/a
E (reserved) 1111	240.0.0.0	255.255.255.255	   n/a               n/a

EIGRP Metric

I doubt this will be used often, but it may be useful when trying to tweak the metric of a particular route by changing the delay (or bandwidth).

The full metic:

However,  the bandwidth and delay values aren’t taken directly from the show commands, rather:

(this gives us the delay in tens of microseconds * 256)

(InterfaceBandwidth and InterfaceDelay refer to the vlaues given from sh interface)

Given the default K values of: K₁ = 1, K₂ = 0, K₃ = 1, K₄=  0, K₅ = 0, the metric becomes much simpler: 

Another interesting fact, taken from the Cisco EIGRP docs:

Cisco routers do not perform floating point math, so at each stage in the calculation, you need to round down to the nearest integer to properly calculate the metrics.