Required theoretical section
mm²
Required theoretical section
Electricity · Industrial electricity
Cable size from maximum voltage drop
Determine the conductor cross-section required to stay below a maximum voltage drop, then verify the drop with the selected preferred section.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Selected preferred section
mm²
Selected preferred section
Voltage drop ΔU
Calculated voltage difference along the cable.
Relative voltage drop
%
Voltage drop relative to nominal voltage U.
Load-end voltage U₂
Estimated voltage at the load after the cable voltage drop.
Relation and numerical substitution
S = k · ρ · L · I · cosφ / (ΔUmax − k · L · I · X · sinφ)—
L is the one-way distance from source to load, not the total conductor length. Single-phase uses factor 2 for the outgoing and return path; balanced three-phase uses √3. R = ρ / S. X = const. Only voltage drop is checked: ampacity, protection, short-circuit duty, installation method, grouping and code compliance are not verified. Sstd ∈ {1.5 … 630} mm².
01Formulas and symbols
Formulas used
sinφ
√(1 − cos²φ)sin φΔUmax
U · ΔUmax%ΔUmaxSreq
k · ρ · L · I · cosφ / (ΔUmax − k · L · I · X · sinφ)SreqSstd
min { Sᵢ | Sᵢ ≥ Sreq }SstdΔU
k · L · I · ((ρ / Sstd) cosφ + X sinφ)Voltage drop ΔUU₂
U − ΔULoad-end voltage U₂02Assumptions and limits
Scope of validity
- L is the one-way distance from source to load, not the total conductor length.
- Single-phase uses factor 2 for the outgoing and return path; balanced three-phase uses √3.
- R = ρ / S.
- X = const.
- Only voltage drop is checked: ampacity, protection, short-circuit duty, installation method, grouping and code compliance are not verified.
- Sstd ∈ {1.5 … 630} mm².
03Validation example
Reference numerical case
- U = 400 V ; I = 32 A ; L = 50 m ; cos φ = 0.85 ; ρ = 0.01724 Ω·mm²/m ; X = 0.08 Ω/km ; ΔUmax = 3 %
- Sreq ≈ 3.417 mm²
- Sstd = 4 mm²
- ΔU ≈ 10.269 V ; ΔU% ≈ 2.567 % ; U₂ ≈ 389.731 V
04References
Technical references
- IEC 60364-5-52 — Low-voltage electrical installations: selection and erection of wiring systems.