Cable Size and Voltage Drop Calculator

The model follows the steady-state thermal method of IEC 60287-1-1:2023, edition 3.0, equation (2), reduced for an unarmoured low-voltage cable with negligible dielectric, metallic sheath and armour losses. Attached legal preview s3, pages 14–15, gives the heat balance. Thermal resistances are supplied by the user from manufacturer data, measurements or IEC 60287-2-1:2023 calculations.

For area $A$, bulk resistance per length is $r(T)=k_R\rho_{20}[1+\alpha_{20}(T-20)]/A$. Copper data are from NBS Handbook 100 (1966); EC-H19 aluminum data from NBS Handbook 109 (1972), Table 1, attached page 13. The explicit $k_R$ includes construction and AC resistance effects; it must be derived from actual cable data when those effects matter.

The load-circuit calculation retains the complete series-circuit phasor relation, with current and lagging power factor specified at the receiving end. Let $C=k_\varphi I L$, $D=C(r\cos\varphi+x_{load}\sin\varphi)$ and $Q=C(x_{load}\cos\varphi-r\sin\varphi)$; $k_\varphi=2$ for single phase and $\sqrt{3}$ for balanced three phase. With cable-origin voltage magnitude $V_s=U_{nom}(1-d_{up}/100)$, the source equation is $V_s^2=(V_r+D)^2+Q^2$, so $V_r=\sqrt{V_s^2-Q^2}-D$ and cable drop is $V_s-V_r$. The nonnegative quadrature correction is retained at every power factor. ABIT Power System I (2025), PDF page 46, gives the complete source-voltage phasor relation before its optional approximation; the inverse and sizing algebra are derived here. A zero reported load voltage flags an infeasible positive-voltage solution at the entered current. Joule loss remains $nI^2rL$.

With $\Theta=T_1+nG(T_2+T_3+T_4)$ and $\Delta T=T_{lim}-T_a$, the thermal rating is $I_z=\sqrt{\Delta T/[r(T_{lim})\Theta]}$. $G$ is an explicitly supplied thermal-path multiplier, not a tabulated standard grouping factor. Two conductors heat in single phase; three heat in balanced three phase.

For the metallic earth-fault path, $Z_s=\sqrt{[R_e+r_fL(1+1/q)]^2+[X_e+x_{fault,loop}L]^2}$, with $q=A_{PE}/A$. $I_f=c_{min}U_0/Z_s$ is compared with the entered guaranteed trip current $I_a$ at the required time. The IEC screen follows the IEC 60364-4-41:2005+A1:2017, edition 5.1, including 2018 corrigendum, loop-impedance principle. It does not infer a trip time from a generic curve. The independently entered $x_{fault,loop}$ is the complete phase-to-PE loop reactance per one-way route length; it already includes the return path and mutual coupling. It must describe the actual phase/PE geometry and fault configuration. CLC/TR 50480:2011, section 4.3 Note 2, explains why load-circuit reactance and fault-loop reactance can differ.

The NFPA 70 (NEC), 2023 edition, ordinary branch-circuit design screen uses $I_d=I+0.25I_{continuous}$ and conservatively requires $I_d\le I_n\le I_z$. This does not claim code allowable ampacity. Both profiles apply the same physical thermal and loop models.

Area minima follow by solving the heat, full-phasor and fault-loop equations with all non-area quantities held fixed. For the voltage target $V_t=U_{nom}(1-d_{lim}/100)$, the maximum allowable per-conductor resistance is $r_{max}=[\sqrt{V_s^2-(V_t\sin\varphi+Cx_{load})^2}-V_t\cos\varphi]/C$. The implementation evaluates its rationalized positive root for numerical stability; $A_{drop}=k_R\rho(T)/r_{max}$. A nonpositive root means no finite resistance can meet the target. The next metric nominal size or geometrically computed AWG area is selected. A zero area in the minima table marks an infeasible criterion or absence of a listed candidate. The source-impedance and reactance budgets are checked before selection.

Maximum load for an existing cable

The reverse calculation uses the selected area, route and thermal installation model, with conductor resistance at $T_{lim}$ even when the forward-mode drop temperature is lower. Let $a=k_\varphi L(r\cos\varphi+x\sin\varphi)$ and $b=(k_\varphi L)^2(r^2+x^2)$. At receiving-voltage target $V_t$, Kirchhoff's phasor equation gives $bI^2+2V_taI+V_t^2-V_s^2=0$. Its positive root is evaluated without subtractive cancellation as

If $V_s\le V_t$, the available drop budget is exhausted and the current is reported as zero.

For total drop budgets of 1%, 3% and 5%, the table reports $I_{drop}$ and $I_{cable}=\min(I_{drop},I_z/k_d)$, where $k_d=1$ in the IEC profile and $1+f_{continuous}/400$ in NEC mode (continuous share entered in percent). Table power uses $P=k_PV_rI\cos\varphi$, with $k_P=1$ for single phase and $\sqrt3$ for three phase, converted to kW. It excludes protection limits. The maximum-load cards additionally impose $I\le I_n/k_d$, $I_n\le I_z$ and $I_f\ge I_a$; otherwise their current and power are zero. Device choice and time-current data remain explicit. Heating-only kW is the nominal-voltage equivalent $k_PU_{nom}(I_z/k_d)\cos\varphi$, before any voltage drop.

Installation thermal paths

The specified-path option preserves the entered $T_2+T_3+T_4$. For one directly buried isolated cable, $T_4=\rho_s\ln(u+\sqrt{u^2-1})/(2\pi)$, $u=2h/D$, with homogeneous soil and an isothermal ground surface. This is the single-isolated-cable boundary geometry of IEC 60287-2-1:2023; Cableizer's open implementation documents the same expression (s9). For air, Newton's surface heat balance gives $T_4=1/(\pi D h_{eff})$. The entered $h_{eff}$ includes convection and radiation at the limiting surface temperature; it is not the IEC empirical coefficient with units involving $K^{5/4}$. These options add the separately entered shared cable-layer resistance $T_2+T_3$ to $T_4$ before applying the common-path multiplier. No installation-method ratings or coefficients are taken from standard tables.

The 127 V single-phase preset is supported by CPFL's supply guide (s10) and Mexico's NOM-001-SEDE-2012, 110-4 (s11). Presets select voltage and phase count, not regional regulatory compliance or frequency-dependent impedance.

• AC, sinusoidal, lagging loads; balanced three phase with an unloaded neutral, or single phase with a full-size return conductor. One cable, no parallel sets.
• Nominal 100% IACS annealed copper or 61% IACS EC-H19 aluminum. PE has the same metal, construction multiplier and temperature as the phase, with an explicit area ratio.
• Default case: 230 V, 32 A, 25 m one way, 6 mm² copper, unity power factor, 70 °C conductor/terminal limit, 30 °C ambient, and 0.08 Ω/km reactance at 50 Hz.
• User-verifiable thermal assumptions: T1 = 0.5 K·m/W, common path = 4 K·m/W, grouping multiplier = 1. These are design inputs, not a certified installation-method ampacity. The 1.05 resistance multiplier is an explicit 5% design allowance, not a standard material constant.
• Thermal paths are constant along the route. Use the thermally worst section. No solar heating, soil drying, dielectric losses or metallic sheath/armour heating.
• Complete phase-to-PE loop reactance defaults to 0.16 Ω/km of one-way route as an explicit close-proximity assumption. It is entered independently of the load-circuit value; obtain both values for the actual geometry, conductor proximity, return path and frequency.
• Receiving-end RMS current and displacement power factor are specified independently of voltage. Upstream drop reduces the cable-origin voltage magnitude; its upstream phase shift and impedance are not reconstructed. The full-phasor inversion is derived here from Kirchhoff's voltage law. Shunt capacitance and leakage are neglected.
• Drop temperature is entered separately from the thermal limit. Fault current uses the hotter of these temperatures to avoid an optimistic cold loop.
• External source resistance and reactance are explicit. Default minimum-voltage factor is 0.95; the separate conventional 0.8 method is not silently added.
• Default protection is a 32 A device with Ia = 160 A entered for 0.4 s. This illustrates the upper magnetic threshold of a typical IEC B32; the actual manufacturer's upper time-current curve governs. Neither device rating nor required time automatically updates Ia.
• Minimum-area calculations assume the same thermal path, grouping, resistance multiplier, load-circuit reactance, complete fault-loop reactance and PE ratio for every candidate. Verify and update these values for the chosen cable.
• Reverse-mode and maximum-load table calculations use the limiting conductor temperature for voltage drop. The entered forward-mode temperature affects only the specified-load calculation.
• Air illustration: 15 mm overall cable diameter, shared internal layers 0.3 K·m/W and effective surface coefficient 8 W/(m²·K). Soil illustration: the same diameter/layers, 0.7 m centre depth and 1.5 K·m/W soil resistivity. These are explicit hypothetical thermal inputs, not ratings for a named cable.
• Buried geometry assumes one fully buried cable, homogeneous non-drying soil and a uniform surface temperature. Air geometry assumes an unobstructed cable with no solar heating and a user-verified effective surface coefficient. Ducts, thermal insulation and complex routes require the specified-path option with studied resistances.
• The 1%, 3% and 5% comparison budgets include upstream drop; a zero current marks an exhausted budget. The comparison table excludes device rating and fault-loop limits. The maximum-load cards include those screens and use the separately entered total target.
• Delivered power is electrical real power at the load, not mechanical shaft output. Heating-only nominal-voltage kW is a before-drop equivalent. Supply presets do not change reactances, source impedance, protection, design profile or local rules.

Rules and source review date: 2026-10-25. Check against the standard in force. This tool provides engineering design screens, not installation approval or a certificate of IEC/NEC compliance. Installation work belongs to a qualified electrician (Elektrofachkraft).

For low-voltage circuits up to 1000 V AC, with the supplied cable thermal model and impedance valid at operating frequency. The material temperature model is used over −20 to 120 °C; permitted cable and terminal temperatures can be lower. At 60 Hz, update both load and fault-loop reactances and the AC resistance multiplier. The 3% default is a selected target; NEC 3% branch / 5% combined guidance is generally informational, while local rules and equipment requirements may differ.

The fault-loop screen applies only to bonded metallic return paths. Its separate complete loop-reactance input must be verified for the actual phase-to-PE path, conductor proximity, mutual coupling and fault configuration; balanced three-phase load reactance is not a substitute. Separate or remote PE routing can substantially alter the loop reactance. It does not verify TT earth-electrode/RCD operation, IT systems, touch voltages, bonding continuity, protective conductor minimum size, disconnection-time rules, prospective maximum fault current, breaking capacity, selectivity or short-circuit thermal withstand. A matching Ia only supports disconnection if the entered device curve and required time are correct. NEC mode uses this loop calculation as an engineering screen, not as a substitute for NEC equipment grounding rules.

NEC listed cable allowable ampacity, adjustment/correction procedures, 110.14(C) terminations, small-conductor protection and special equipment articles remain separate checks. No ampacity tables from VDE 0298-4, IEC 60364-5-52 or NEC are copied. Voltage drop uses the full series-circuit phasor relation even below 10% projected drop. It assumes prescribed receiving current and power factor; constant-power or voltage-dependent loads need a coupled load solution. If no positive receiving voltage exists, the displayed zero voltage is an infeasibility marker and cannot pass the drop screen. Leading power factor, harmonics, unequal single-phase conductors, motor starting, cable joints, transient/cyclic heating and loaded three-phase neutrals are outside scope.

Reference cases use NBS wire resistance data and Schneider's published motor example. Schneider's rounded 5 V result uses conservative resistivity 0.0237 Ω·mm²/m; the full-phasor physical copper model at 90 °C gives about 4.78 V, explicitly allowed in that case's tolerance. This difference is documented rather than fitted away.

Maximum-load mode is a steady-state, prescribed power-factor capacity screen. Its cable-only comparison table must not be used as a protective-device rating. A zero protected load result can mean unsuitable entered protection even while the cable has nonzero physical capacity. The maximum-load calculation does not select or certify a breaker. For air and buried scenarios, confirm actual thermal coefficients, cable geometry and the thermally worst route section; do not substitute their hypothetical defaults for manufacturer data. The analytic ground boundary does not model layered soil, ducts, drying or interacting cable groups.