IEC 60364-5-54 gives the following formula for the calculation of the factor k:
k= Q c ( β+20 ) ρ 20 ln( β+ θ f β+ θ i )
where Qc = volumetric heat capacity of conductor at 20°C, J.K-1.mm-3 ß = reciprocal of temperature coefficient of resistivity at 0 °C ρ20 = electrical resistivity of conductor material at 20 °C, Ω.mm ϴi = initial temperature of conductor, °C ϴf = final temperature of conductor, °C
Note: strictly speaking ß is specfied at 0 °C. Within myCableEngineering calcuations, ß is determined by taking the reciprocal of the 20 °C temperature coefficient. This introduces a small, but negligible error.
For manual calculations, the following will give realistic results:
Substituting the above values and rearranging the IEC equation slightly, gives:
k=226 ln( 1+ θ f − θ i 234.5+ θ i ) - copper conductors
k=148 ln( 1+ θ f − θ i 228+ θ i ) - aluminium conductors
k=78 ln( 1+ θ f − θ i 202+ θ i ) - steel