Cable correction factors — Ca, Cg, Ci and Cf

The relationship

Iz = It × Ca × Cg × Ci × Cf

I_t is the tabulated current-carrying capacity — a free-air figure quoted at 30 °C for one circuit on its own with no thermal insulation. I_z is what the cable may carry where it is actually installed. When you are selecting rather than checking a cable, the same relationship runs backwards:

It ≥ In ÷ (Ca × Cg × Ci × Cf)

and the whole design has to satisfy Ib ≤ In ≤ Iz, where I_b is the design current and I_n the rating of the protective device.

C_a — ambient air temperature

Ca = √[(θc − θa) ÷ (θc − 30)]

θ_c is the conductor’s permitted operating temperature — 70 °C for thermoplastic insulation, 90 °C for thermosetting — and θ_a is the ambient. The square root follows from the physics: heating goes with I²R, so the current producing a given temperature rise goes with the square root of the temperature headroom remaining.

That single expression reproduces all 26 entries of the published ambient temperature table, both insulation types, to the two decimal places the table is quoted to. The tables below print the computed value to four decimal places beside the published one so the claim can be checked row by row rather than taken on trust. The computed column is generated when this page is built, from the same function the cable capacity calculator calls — nothing here is typed in by hand.

70 °C thermoplastic (PVC)

90 °C thermosetting (XLPE)

Two practical points. Above about 45 °C the choice of insulation stops being a detail and starts being the design: at 55 °C thermoplastic is down to 0.61 while thermosetting still holds 0.76. And 90 °C insulation does not help at the terminations, which are commonly limited to 70 °C — check the equipment before designing to the higher column.

Below 30 °C

The formula returns a factor above 1.00 for cool ambients and the standard permits taking the credit. The calculator on this site holds C_a at 1.00 by default and asks you to opt in, because ambient is the input a designer is least able to guarantee for the life of an installation. A loft at 25 °C in April is not 25 °C in August, and the cable is in the loft for thirty years.

C_g — grouping

Cables bunched together heat one another, and the ones in the middle have nowhere to send that heat. The factor below applies to cables bunched or enclosed — in conduit, trunking or ducting, or bunched and clipped direct to a surface.

Count circuits, not cables and not conductors. A single-phase circuit of line, neutral and cpc is one circuit. A three-phase circuit is one circuit. A protective conductor never counts and neither does a cable carrying no load. Counting conductors is the commonest error here and produces a factor far harsher than the regulation intends.

The table lists those circuit counts and no others. For a count in between — ten circuits, say — read the next row up rather than interpolating: interpolation gives a larger factor and therefore a smaller cable, which is the wrong direction to guess in.

What this page does not give you

The grouping table has further columns for cables laid in a single layer: spaced on a wall or floor, fixed under a ceiling, on perforated tray, on ladder. Those arrangements are kinder, because each cable has air on more sides of it.

Those columns are not published here. BS 7671 is not openly available, and the secondary sources for those columns disagree with one another. This site does not publish a number it cannot verify — the same rule that keeps the reactive component off the conductor resistance table above 16 mm². Read them from Table 4C1 for your reference method; the calculator will take your value and do the rest.

C_i — thermal insulation

Thermal insulation is very good at its job, which is exactly the problem: a cable inside it has no route to shed heat. The halving is the case that matters, and it is usually nobody’s mistake at the time — a cable clipped along a joist was compliant when it was installed, and then the loft was topped up by someone with no reason to think about it.

The length-graded factors are deliberately absent. Two secondary sources give two different sets of values for them — 0.88 / 0.78 / 0.63 / 0.51 against 0.89 / 0.81 / 0.68 / 0.55 — and there is no way to settle which is current without the book. Guessing between them would put a wrong number on a page about conductor sizing.

C_f — protective device

A rewireable fuse has a fusing factor around 2 — it can carry roughly twice its marked rating for a long time before the element gives up — where the general overload rule assumes a device operating at 1.45 times its rating. The cable therefore has to survive a much longer overload, and 0.725 is simply 1 ÷ 1.379, the ratio between the two behaviours.

A worked example

Three circuits in trunking through a roof space that reaches 35 °C, thermoplastic insulation, protected by a 32 A MCB, using a cable tabulated at 27 A.

• C_a = √[(70 − 35) ÷ (70 − 30)] = √0.875 = 0.9354
• C_g = 0.70 (three circuits, bunched)
• C_i = 1.00, C_f = 1.00
• Combined: 0.6548
• I_z = 27 × 0.6548 = 17.7 A

17.7 A against a 32 A device: the cable is not protected. Working forwards instead, the tabulated capacity required is 32 ÷ 0.6548 = 48.9 A — a cable rated 49 A in free air, for a 32 A circuit.

Using this reference

It is free to quote and reproduce with attribution to this page. To have the arithmetic done, including the I_b ≤ I_n ≤ I_z check, use the cable current capacity calculator. Current capacity is only one of the two tests a cable has to pass — the other is voltage drop, and you take whichever gives the larger conductor.

The derivation, the sources and the review process behind these figures are set out in the methodology. This page is reviewed by Salamot Hok, electrician with 10+ years of installation experience. Results are engineering guidance, not a code sign-off — see the disclaimer.

Sources

• IEC 60364-5-52 — Selection and erection of wiring systems: current-carrying capacities — webstore.iec.ch
• IEC 60364-4-43 — Protection against overcurrent — webstore.iec.ch
• BS 7671 — Requirements for Electrical Installations (IET Wiring Regulations) — electrical.theiet.org

ElectroCalculators is not affiliated with BSI, the IET or the IEC. Standard titles, table references and regulation numbers are cited for identification.