Cable size calculator: mm² and AWG by current, copper or aluminium

What this calculator does

It returns the minimum conductor cross-section for a given current and, if asked, checks that the voltage drop along the circuit stays within the limit. It does so in the two sizing systems that coexist on the market — the metric cross-sections of IEC 60228 and the American AWG and kcmil sizes — and for copper and aluminium conductors with thermoplastic (PVC, 70 °C) or thermosetting (XLPE or EPR, 90 °C) insulation.

The output is two numbers that have to be read together: the size demanded by heating (current-carrying capacity) and the size demanded by voltage drop. The larger of the two is the one to install.

First condition: current-carrying capacity

A cable heats up by Joule effect, and its insulation has a maximum temperature it must not exceed in continuous service: 70 °C for PVC and 90 °C for cross-linked polymers. The current that brings it exactly to that temperature is its current-carrying capacity Iz, and it depends on how the cable sheds heat: a cable in free air is not the same as one buried in an insulating wall, nor is a single cable the same as one in a bundle of twelve.

IEC 60364-5-52 tabulates Iz for every size, material and insulation as a function of the reference installation method, identified by a letter:

• A1 and A2: insulated conductors or a multicore cable in conduit in a thermally insulated wall. The worst case.
• B1 and B2: the same, with the conduit on the wall or in trunking.
• C: multicore cable clipped direct to the wall or on an unperforated tray.
• D1 and D2: cable in a buried duct or buried direct. The reference temperature here is that of the ground, 20 °C.
• E: multicore cable in free air or on a perforated tray, with air circulating around it.

The table values are given at 30 °C ambient (20 °C buried) and for a single circuit. When reality differs, correction factors apply: for temperature (Tables B.52.14 and B.52.15, from 1.22 at 10 °C down to 0.50 at 60 °C for PVC) and for grouping (Table B.52.17: 0.80 with two circuits together, 0.70 with three, 0.50 with nine). The calculator uses the row for cables bunched in air or embedded, which is the most conservative; if your layout is a single layer on a tray the factors are somewhat kinder, and the difference can be entered in the “other correction factor” box.

The condition checked is Ib ≤ Iz × kT × kG: the design current may not exceed the corrected capacity.

NEC 310.16 does the same with American sizes and three temperature columns (60, 75 and 90 °C) according to the insulation type (TW; THW/THWN/XHHW; THHN/XHHW-2). Ambient temperature correction uses the formula of 310.15(B)(1) and the adjustment for more than three current-carrying conductors in the same raceway uses Table 310.15(C)(1). One rule the calculator flags when relevant: for 14, 12 and 10 AWG the overcurrent protection is capped at 15, 20 and 30 A even if the table allows more (240.4(D)).

Second condition: voltage drop

A long conductor can run cool and still deliver less voltage to the load than it needs. The drop is computed from the conductor impedance at its operating temperature:

ΔU = k × Ib × L × (R·cos φ + X·sin φ)

with k = 2 for single-phase and DC and k = √3 for three-phase; R is the resistance per metre (material resistivity at 70 °C or 90 °C divided by the cross-section) and X the reactance, which in low-voltage cables is around 0.08 Ω/km and only matters for large sizes at low power factor. The calculator finds the smallest size that keeps ΔU below the permitted percentage of the nominal voltage.

Metric versus AWG

The two systems are not interchangeable one for one. In IEC 60228 the nominal cross-sections follow a progression from 1.5 to 300 mm² (and up to 1000 mm² for large conductors). The American Wire Gauge defines diameters in a geometric progression in which the area doubles every three sizes: 10 AWG is 5.26 mm², so 7 AWG would be 10.5 mm². Above 4/0 AWG (107 mm²) the size is expressed in kcmil, thousands of circular mils, where 1 kcmil = 0.5067 mm².

What matters in practice: the calculator solves the two tables separately and, next to each result, shows the equivalent in the other system. That a metric size “equals” an AWG size only means its area is equal or greater; the current-carrying capacity remains the one in the relevant table.

Worked example

Three-phase motor at 400 V with a design current of 63 A and cos φ = 0.85. Copper cable with XLPE insulation, clipped direct to the wall (method C), 30 °C, no other circuits nearby. Length 120 m, maximum permitted drop 3%.

• By current-carrying capacity: Table B.52.3 gives 71 A for 10 mm² with three loaded conductors, and 71 ≥ 63. Minimum size 10 mm². In the NEC 90 °C column, 6 AWG carries 75 A.
• By voltage drop: at 90 °C the resistivity of copper is 0.02198 Ω·mm²/m. With 10 mm², ΔU = √3 × 63 × 120 × (0.002198 × 0.85 + 0.00008 × 0.527) = 25.0 V, or 6.3%: far too much. With 16 mm² it falls to 3.96%; with 25 mm², to 2.58% (10.3 V).
• Recommended size: 25 mm² copper XLPE, equivalent to 3 AWG. Voltage drop governs, not heating, as is usual on circuits longer than 50 or 60 m.

Were the same circuit in aluminium, heating would call for 16 mm² (Table B.52.5, method C: 76 A) and voltage drop for 50 mm²: 35 mm² lands at 3.02%, just over the limit.

What this calculator does not do

It does not select the overload protection or verify the condition I2 ≤ 1.45 × Iz; it does not compute short-circuit current or check the minimum size for thermal withstand (k²S² ≥ I²t); it does not size the neutral or the protective conductor, nor does it account for the harmonics that load the neutral in installations with a lot of electronics. It also does not cover sizes above 300 mm² or methods F and G for spaced single-core conductors. The table values correspond to the 2009 edition of IEC 60364-5-52 and to NEC Table 310.16; national rules (in the UK, BS 7671; in Spain, the REBT and UNE-HD 60364-5-52) may impose additional conditions.

What checks it

The actual current in a circuit in service is measured by power and power-quality analysers, which also log the power factor and harmonics the calculator takes for granted. Loop impedance and conductor continuity of the installed cable are verified with multifunction installation testers, and a conductor running above its temperature gives itself away on a thermal imaging camera long before the insulation fails.