Adiabatic k values
The k factors for S = √(I²t) ÷ k, derived from the material constants and the two temperatures that define each case, with the published values printed alongside.
The equation
S = √(I²t) ÷ k
S is the minimum conductor cross-section in mm² that survives a fault current I for a time t without exceeding its permitted temperature. It is BS 7671 Regulation 543.1.3, and it is valid up to about 5 seconds — past that, enough heat leaves the conductor that treating the process as adiabatic is no longer a safe simplification.
Where k comes from
k = √[ Qc(β + 20) ÷ ρ₂₀ × ln((β + θf) ÷ (β + θi)) ]
Qc is the conductor’s volumetric heat capacity at 20 °C, β the reciprocal of its temperature coefficient of resistivity at 0 °C, ρ₂₀ its electrical resistivity at 20 °C, θi the temperature it is at when the fault begins and θf the highest it may reach.
| Material | β (°C) | Qc (J/°C·mm³) | ρ₂₀ (Ω·mm) | √[Qc(β + 20) ÷ ρ₂₀] |
|---|---|---|---|---|
| Copper | 234.5 | 3.45e-3 | 1.724e-5 | 225.7 |
| Aluminium | 228 | 2.50e-3 | 2.827e-5 | 148.1 |
| Steel (armour) | 202 | 3.80e-3 | 1.380e-4 | 78.2 |
The last column is the part that never changes — it is a property of the metal. Every other difference between k values, across all three tables below, is the logarithm: how hot the conductor already was, and how hot it is allowed to get.
That is why this page derives k rather than transcribing it. A construction the published tables do not list still gets a defensible number, and the derivation can be checked against the ones they do.
How well the derivation agrees
Of the 44 published values checked, 41 land on the same whole number. The largest disagreement anywhere is 0.55 — under 0.6 of a unit, which is inside the rounding of tables quoted as integers. In the tables below the derived value is in bold and the published one in brackets; where the two round differently, the difference is printed rather than hidden.
The agreement column is not decoration. Four steel values for the second table were entered from a secondary source, disagreed by 5–24%, and turned out to be figures from the third table attached to the wrong rows. They were removed rather than accommodated — the calculator still derives a k for those cases, it just does not claim a published figure to check it against.
Line conductors
The conductor is carrying its load when the fault arrives, so it starts at the cable’s rated operating temperature. BS 7671 Table 43.1.
| Construction | θi | θf | Copper | Aluminium |
|---|---|---|---|---|
| 70 °C thermoplastic (PVC), ≤ 300 mm² | 70 °C | 160 °C | 114.8 (115) | 76.1 (76) |
| 70 °C thermoplastic (PVC), > 300 mm² | 70 °C | 140 °C | 102.7 (103) | 68.0 (68) |
| 90 °C thermosetting (XLPE, EPR) | 90 °C | 250 °C | 142.9 (143) | 94.5 (94, +0.55) |
| 85 °C thermosetting rubber | 85 °C | 220 °C | 134.0 (134) | 88.7 (89) |
| 60 °C thermosetting rubber | 60 °C | 200 °C | 140.7 (141) | 93.2 (93) |
| Mineral — covered, or bare and exposed to touch | 70 °C | 160 °C | 114.8 (115) | — |
| Mineral — bare, not exposed to touch | 105 °C | 250 °C | 134.6 (135) | — |
Protective conductor inside a cable, or bunched with one
It carries no load current itself, but it is heated by the conductors around it, so it starts at the same temperature they do. BS 7671 Table 54.3.
| Construction | θi | θf | Copper | Aluminium | Steel |
|---|---|---|---|---|---|
| 70 °C thermoplastic (PVC), ≤ 300 mm² | 70 °C | 160 °C | 114.8 (115) | 76.1 (76) | 41.8 |
| 70 °C thermoplastic (PVC), > 300 mm² | 70 °C | 140 °C | 102.7 (103) | 68.0 (68) | 37.4 |
| 90 °C thermosetting (XLPE) — usual SWA case | 90 °C | 250 °C | 142.9 (143) | 94.5 (94, +0.55) | 51.7 (52) |
| 85 °C thermosetting rubber | 85 °C | 220 °C | 134.0 (134) | 88.7 (89) | 48.5 |
| 60 °C thermosetting rubber | 60 °C | 200 °C | 140.7 (141) | 93.2 (93) | 51.2 |
Protective conductor run separately
It carries nothing and is next to nothing, so it starts at ambient — taken as 30 °C. That extra headroom is the whole reason these values are so much larger. BS 7671 Table 54.2.
| Construction | θi | θf | Copper | Aluminium | Steel |
|---|---|---|---|---|---|
| 70 °C thermoplastic sheathed, ≤ 300 mm² | 30 °C | 160 °C | 142.7 (143) | 94.6 (95) | 52.2 (52) |
| 70 °C thermoplastic sheathed, > 300 mm² | 30 °C | 140 °C | 133.1 (133) | 88.3 (88) | 48.7 (49) |
| 90 °C thermosetting sheathed | 30 °C | 250 °C | 175.6 (176) | 116.3 (116) | 63.9 (64) |
| 60 °C thermosetting rubber sheathed | 30 °C | 200 °C | 159.0 (159) | 105.4 (105) | 58.0 (58) |
| Bare — visible, restricted area | 30 °C | 500 / 300 / 500 °C | 228.1 (228) | 125.3 (125) | 82.3 (82) |
| Bare — normal conditions | 30 °C | 200 °C | 159.0 (159) | 105.4 (105) | 58.0 (58) |
| Bare — fire risk | 30 °C | 150 °C | 138.0 (138) | 91.5 (91, +0.53) | 50.5 (50) |
The three tables are the same conductor
Copper with a 70 °C thermoplastic covering appears in all three, with only θi differing:
- Line conductor, starting at 70 °C — k = 114.8
- Protective conductor in a cable, starting at 70 °C — k = 114.8
- Protective conductor run separately, starting at 30 °C — k = 142.7
That is roughly a 20% difference in the conductor required for an identical fault, in both directions. Reading the separate-conductor row for a cpc that is actually inside the cable undersizes it.
Using this reference
It is free to quote and reproduce with attribution to this page. To have the arithmetic done, including the round-up to a standard size and a pass/fail against the conductor you intend to use, see the adiabatic equation calculator. For the other half of cable selection — the current the cable may carry in normal service — see the correction factors reference and the cable capacity calculator.
Surviving the fault is one requirement. A protective conductor must also give an earth fault loop impedance low enough to disconnect in time, and meet the Table 54.7 minimum where that route is used. Nothing on this page evaluates either.
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 60364-5-54 — Earthing arrangements and protective conductors — 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.