How to size a cable: current capacity, derating and voltage drop

A cable is sized by three separate questions, and the answer is the largest of the three. Can it carry the load continuously, in the heat and the company it will actually live in, without cooking its insulation? Will the breaker in front of it trip before an overload damages it? And is enough of the supply voltage left at the far end to run the equipment? Most undersized cables in service failed the first question at the design stage, because someone read a current rating off a catalogue and ignored the derating the installation demanded.

Three checks, not one

IEC 60364, and BS 7671 which carries the same tables, set the cable's size by the strictest of these:

• Current-carrying capacity. The conductor must not exceed the temperature its insulation is designed for, 70 °C for PVC and 90 °C for XLPE, when it carries its current for hours. The standard tabulates the current a cable can carry in defined installation conditions, and the designer corrects those values for the real ones. The result is I_z, the cable's effective capacity, and it is matched to the protective device as described next.
• Voltage drop. Resistance times current is voltage lost along the run. It rarely matters on a 10 m circuit and often decides the size on a 100 m one.
• Fault withstand. During a short circuit the conductor heats adiabatically until the breaker clears the fault; it must not reach the temperature at which its insulation is destroyed. This check bites on small conductors on stiff supplies, and on protective conductors.

Below those three sit the minimum sizes the standard allows regardless of current (1.5 mm² copper for fixed power and lighting circuits in IEC 60364-5-52, Table 52.2), the sizing of the neutral where harmonics are present, and the earth-fault loop impedance that decides whether the breaker disconnects fast enough. The cable sizing calculator does the first two checks with the IEC tables; the rest of this guide explains what it is doing and what it is not.

Ib ≤ In ≤ Iz: how the breaker and the cable are matched

Three currents have to line up. I_b is the design current, what the load draws in normal service. I_n is the rated current of the breaker or fuse. I_z is the current the cable can carry continuously in its installed conditions. IEC 60364-4-43 (433.1) requires:

The first inequality says the breaker must not trip on the normal load. The second says the breaker must not let the cable be overloaded: whatever current the breaker will tolerate indefinitely, the cable must tolerate too. This is why a cable is sized from the breaker rating, not from the load. A 25 A pump on a 40 A MCB needs a cable good for 40 A, because nothing stops that circuit from carrying 40 A for as long as it likes.

The third condition deals with the breaker's tolerance. I₂ is the current at which the device is guaranteed to operate within its conventional time (one hour for MCBs up to 63 A). A cable is allowed a small overload of 1.45 times its capacity for that long; an MCB to IEC 60898-1 has I₂ = 1.45 × I_n, so choosing I_n ≤ I_z settles it automatically. A moulded-case breaker to IEC 60947-2 operates at 1.3 × I_n, safer still. A gG fuse only operates for certain at 1.6 × I_n, which is why fused circuits need I_n ≤ 0.9 × I_z.

In practice the designer picks I_n first, as the next standard rating at or above I_b (6, 10, 16, 20, 25, 32, 40, 50, 63, 80, 100, 125, 160, 200, 250 A), then finds the smallest cable whose I_z reaches it. If the cable comes out uncomfortably large, the fix is often a breaker one size closer to the load rather than a fatter conductor.

Reference methods: how a cable is installed decides what it can carry

The same conductor carries different currents depending on how easily its heat escapes. IEC 60364-5-52 reduces the dozens of real installation methods in its Table A.52.3 to a handful of reference methods, each with its own column of ratings in Annex B:

• A1 / A2: insulated conductors (A1) or a multicore cable (A2) in conduit inside a thermally insulated wall. The worst case; heat can only leave through the inner skin of the wall.
• B1 / B2: insulated conductors (B1) or a multicore cable (B2) in conduit, trunking or ducting on a wall or in masonry. The commonest case in Pakistani buildings.
• C: a single-core or multicore cable clipped direct to a wall or ceiling, or embedded in masonry.
• D1 / D2: a cable in a duct in the ground (D1) or buried direct (D2), rated at 20 °C ground temperature and 2.5 K·m/W soil.
• E, F, G: multicore and single-core cables on perforated trays, ladders or in free air, with the best cooling.

The spread is large. A 10 mm² PVC copper cable carrying single-phase current is rated 46 A in A1, 57 A in B1, 63 A in C and 60 A in D1. The tables also distinguish two loaded conductors (single-phase and DC) from three (three-phase), because three heat sources in one conduit run hotter than two: the same 10 mm² in B1 is 57 A single-phase but 50 A three-phase. The neutral of a balanced three-phase circuit carries little current and is not counted, unless harmonic-rich loads fill it with third-harmonic current, in which case Annex E of the standard derates the whole cable.

Choose the reference method honestly. A cable that runs clipped along a beam and then dives into a conduit in an insulated ceiling is rated for the conduit in the insulated ceiling; the worst section of the route governs.

Derating for heat and neighbours

The tabulated values assume 30 °C air, or 20 °C ground, and one circuit on its own. Two correction factors bring them to the real installation, and they multiply:

Ambient temperature, C_a (Table B.52.14 for air, B.52.15 for the ground). A conductor at 70 °C in 30 °C air has 40 °C of temperature rise to work with; in 45 °C air it has only 25 °C, so it can dissipate less and carry less. For PVC the factor is 0.87 at 40 °C, 0.79 at 45 °C and 0.71 at 50 °C; XLPE, with its 90 °C ceiling, is hit less: 0.91, 0.87 and 0.82. The temperature to use is that of the air around the cable, not the weather report. In Lahore, Multan or Karachi in June a closed ceiling void, a conduit on a sun-facing wall or a switchroom without ventilation can be well above 40 °C for hours a day, and a design done at 30 °C is a design for another country.

Grouping, C_g (Table B.52.17). Cables loaded together in one conduit, trunking or bunch heat each other. For circuits bunched or enclosed, the factor is 0.80 for two circuits, 0.70 for three, 0.57 for six and 0.50 for nine; single layers on walls or trays are treated a little more kindly, and buried ducts have their own table. The factor applies to every circuit in the group, so a trunking with nine circuits has halved the capacity of each of them.

The two compound. At 45 °C with three circuits in the conduit, C_a × C_g = 0.79 × 0.70 = 0.553, and a 40 A breaker needs a cable tabulated at 40 ÷ 0.553 = 72.3 A: 16 mm² in method B1, where the same circuit alone at 30 °C would have been fine on 6 mm² (41 A). That is not conservatism; it is the difference between a cable that lasts thirty years and one whose PVC hardens, cracks and eventually faults.

Voltage drop: the long-cable check

Once a size passes the thermal check, the voltage lost along the run is:

with L the one-way length and r the conductor resistance per metre at its operating temperature, about 20 % above the 20 °C value for a PVC cable at 70 °C and 28 % above for XLPE at 90 °C. IEC 60364-5-52 Annex G recommends keeping the drop from the origin of the installation to the load within 3 % for lighting and 5 % for other uses when the supply is a public low-voltage network (6 % and 8 % from a private transformer), and equipment can be stricter: a motor at 90 % voltage draws more current, runs hotter and may not start under load.

Voltage drop grows with length while the thermal check does not, so there is always a distance beyond which it takes over. For a 40 A single-phase circuit on 10 mm² the drop is 2.6 % at 40 m and 5 % at about 77 m; past that the cable goes up a size for reasons that have nothing to do with heat. How voltage drop works covers the physics and the effects on equipment; the voltage drop calculator gives the numbers for any size and temperature.

Fault current and the adiabatic check

A short circuit at the far end of a cable can push thousands of amperes through it for the few milliseconds to few hundred milliseconds it takes the breaker to clear. The conductor has no time to lose heat, so its temperature rise depends only on the energy let through, I²t, and IEC 60364-4-43 (434.5.2) requires the conductor to be at least:

where S is the cross-section in mm², I the fault current, t the clearing time and k a constant that carries the conductor from its working temperature to the limit its insulation survives once (160 °C for PVC, 250 °C for XLPE). Turned around, a 1.5 mm² PVC copper conductor can absorb (115 × 1.5)² = 29 800 A²s: a 545 A fault for 0.1 s, or 1 725 A for 0.01 s. Whether that is enough depends on the prospective fault current at the point of the fault and on how quickly the device operates at that current, which is read from its let-through energy or time–current curve. Modern MCBs limit let-through energy so well that the check is usually satisfied for the sizes their ratings imply, but it must be done where the fault level is high, the breaker is slow, or the conductor is small, and it is the check that sizes the protective (earth) conductor. The calculator does not do it.

The example in numbers

A 40 A single-phase load at 230 V, 40 m from the board, PVC single-core conductors in conduit on a wall (B1), 40 °C in the ceiling void, one circuit, a 40 A MCB, power factor 0.85, 5 % limit:

1. C_a = 0.87, C_g = 1.00. Table value needed: 40 ÷ 0.87 = 46.0 A.
2. B1, two loaded conductors: 6 mm² is 41 A, too small; 10 mm² is 57 A. I_z = 57 × 0.87 = 49.6 A; 40 ≤ 40 ≤ 49.6 holds.
3. Voltage drop on 10 mm² at 70 °C: r = 0.00219 Ω/m, ΔV = 2 × 40 × 40 × 0.00219 × 0.85 = 5.96 V, 2.59 %, within 5 %.
4. Result: 10 mm² copper, decided by current-carrying capacity; voltage drop alone would have allowed 6 mm².

Add two more circuits to the conduit and the table value needed climbs to 65.7 A, so 16 mm². Bury the run in a duct instead (D1, ground at 30 °C, C_a = 0.89): the table value needed is 44.9 A and 6 mm² (46 A) passes the thermal check, but at 40 m its drop of 4.36 % is close to the limit and at 46 m it fails, so the buried route ends up on 6 mm² or 10 mm² depending on its exact length.

Common mistakes

• Sizing from the load when the breaker is bigger. A 20 A load on a 32 A MCB gets a cable for 20 A. When a second machine is plugged in, or a motor stalls, the circuit runs at 30 A for hours with nothing to stop it, and the cable was never rated for that. Size for I_n.
• Using the 30 °C rating in a Pakistani summer. A roof-space conduit at 45 °C removes 21 % of a PVC cable's capacity. If the design was done at 30 °C, every circuit in that space is undersized for two months of the year.
• Bunching in a trunking. Nine circuits in one trunking halve the capacity of each. Either count the group and derate, or split the run into several trunkings or conduits so that the factor stays near 1.
• 4 mm² for a 32 A geyser or shower circuit in conduit in an insulated wall. In method A1 a 4 mm² PVC cable is rated 26 A at 30 °C and 22.6 A at 40 °C; 6 mm² gives 29.6 A at 40 °C, still short of 32 A. That circuit needs 10 mm² (46 × 0.87 = 40.0 A), or a route that is not inside the insulation.
• Taking the XLPE rating with 70 °C terminals. A 90 °C conductor landed on a breaker or busbar rated for 70 °C connections overheats the terminal (BS 7671 Regulation 512.1.5 makes this explicit). Use the 70 °C column, or equipment rated for 90 °C.
• Reading the wrong column. Clipped-direct ratings for a cable that is in conduit; two-loaded-conductor ratings for a three-phase circuit; copper ratings for aluminium. The tables are unforgiving of this and the mistakes all go the same way.
• Forgetting the far end. A tube well, a gate motor or a workshop 120 m from the board is usually sized by voltage drop, not current. Check both.

Cable sizing is arithmetic, but the arithmetic has to be done with the real installation in front of it. Ahmedonics designs distribution and control installations as part of its custom engineering and system integration work; the calculator is the same method, in the open, for the circuits you size yourself.

References

• IEC 60364-5-52:2009, Low-voltage electrical installations — Part 5-52: Selection and erection of electrical equipment — Wiring systems — Table 52.2 minimum sizes; Annex A installation methods; Annex B current-carrying capacities and correction factors; Annex E harmonics; Annex G voltage drop
• IEC 60364-4-43:2008, Part 4-43: Protection for safety — Protection against overcurrent — 433.1 overload coordination; 434.5.2 short-circuit withstand and the k values
• IEC 60898-1:2015, Circuit-breakers for overcurrent protection for household and similar installations — Part 1: Circuit-breakers for a.c. operation — conventional non-tripping and tripping currents 1.13 In and 1.45 In
• IEC 60228:2004, Conductors of insulated cables — conductor resistance for the voltage drop
• BS 7671:2018+A2:2022, Requirements for Electrical Installations, Appendix 4 — the same current-carrying capacity tables and a worked procedure for applying the rating factors