1. Fundamental Formula for Current-Carrying Capacity (IEC 60287) 
 
I_z = √[(Δθ · k² · S²) / (R_th · (1 + λ₁ + λ₂))] 
 

2. Variables & Sub-Formulas 
Δθ (Temperature Rise) 
Δθ = θ_max - θ_amb 
- θ_max: Max conductor temp (e.g., 70°C for PVC). 
- θ_amb: Ambient temp (°C). 

k (Material Constant) 
k = √[1 / (ρ · α)] 
- ρ: Resistivity (Copper: 0.0172 Ω·mm²/m). 
- α: Temp coefficient (Copper: 0.00393 °C⁻¹). 

R_th (Thermal Resistance) 
R_th = R_ins + R_env 
- R_ins: Insulation resistance (PVC: 3.5 K·m/W). 
- R_env: Environmental resistance (soil: 1.0–2.5 K·m/W). 

3. Correction Factors (IEC 60364-5-52) 
Ambient Temp (k₁) 
k₁ = √[(θ_max - θ_amb) / (θ_max - 30)] 

Cable Grouping (k₂) 
- 3 cables: k₂ = 0.85 

Soil Thermal Resistivity (k₃) 
k₃ = √[R_th_ref / R_th_actual] 

4. Voltage Drop Formula (IEC 60364-5-52) 
ΔV = √3 · I · L · [(R·cosφ + X·sinφ) / 1000] 

R (AC Resistance) 
R ≈ 23.7 / S (Ω/km) for copper 

X (Reactance) 
- Typical: 0.08–0.10 Ω/km 

5. Short-Circuit Withstand (IEC 60949) 
S_min = (I_k · √t) / k 
- k: Copper PVC = 115 

6. Key Constants 
 
 

Material	ρ (Ω·mm²/m)	α (°C⁻¹)
Copper	0.0172	0.00393
Aluminum	0.0283	0.00403