How to Calculate the cable size and protective device rating 

Electrical Installation Design
This is an older video. New video coming soon to clear this up
The term 'Iz' has been incorrectly used when it should be 'It''
The calculation method is still correct, however.
'It' is the value we find in BS7671 appendix 4 after we carry out out correction factor calculation.
The calculated value I have since discovered, has no name.
From BS76712
This method is used in items 5.1 and 5.2 and produces a value of current
and that value (or the next larger value) can be readily located in the
appropriate table of current-carrying capacity and the corresponding
cross-sectional area of conductor can be identified directly.
It should be noted that the value of It appearing against the chosen
cross-sectional area is not Iz. It is not necessary to know Iz where the
size of conductor is chosen by this method.
All rating factors affecting Iz (i.e. for factors for ambient temperature,
grouping and thermal insulation) can, if desired, be applied to the
values of It as multipliers. This involves a process of trial and error until
a cross-sectional area is reached so that Iz is not less than Ib and not
less than In of any protective device it is intended to select. I
n any event, if a rating factor for protection by a semi-enclosed
fuse is necessary, this has to be applied to In as a divisor.
It is therefore more convenient to apply all the rating factors to In as divisors.
This method is used in items 5.1 and 5.2 and produces a value of current
and that value (or the next larger value) can be readily located in the
appropriate table of current-carrying capacity and the corresponding
cross-sectional area of conductor can be identified directly.
It should be noted that the value of It appearing against the chosen
cross-sectional area is not Iz. It is not necessary to know Iz where the
size of conductor is chosen by this method.
How to carry out cable calculations to correctly size your electrical conductors
Design Current
Protective devices
Current carrying capacity
Volt drop
Sizing of the MCB/Fuse
and more...
At 21.29 you might spot I used the In instead of Ib in the volt drop calculation. So 16A instead of 13.04 A
Volt drop is actually 13.23v not 16.24v
Still unsuitable cable though
22.16 Maths error Ib x L