[ \textDuct Diameter = 2 \times \sqrt\frac\textMinimum Duct Area\pi ]
[ \textMin duct area = \frac\textTotal cable area\textSpace factor ]
When you use a calculator, it is performing the following logic:
Correct sizing provides room for additional circuits later without replacing the entire containment system. The UK "40% Fill Rule"
Advanced calculators incorporate a pulling tension check based on cable mass, coefficient of friction (0.3 – 0.5 typical for PVC duct), and bend radius.
[ \textTotal Cable Area = \sum_i=1^n \pi \times \left(\fracd_i2\right)^2 ]