Cable Short-Circuit Withstand Calculator (Adiabatic)

What the calculator does

When a short circuit flows through a cable, the conductor heats faster than it can lose heat, and the only thing that stops the temperature climbing is the protective device opening. The calculator takes the prospective fault current at the fault, the time the device takes to clear it, the conductor material and insulation and the size you have in mind, and checks whether the conductor stays below the temperature its insulation may reach once: 160 °C for PVC, 250 °C for XLPE or EPR. It reports the energy the fault lets through as I²t, the smallest conductor that survives it, the energy your chosen size can absorb, the longest clearing time that size tolerates at that current and the largest current it tolerates for that time.

This is the check in IEC 60364-4-43, clause 434.5.2, and it is the one most often skipped. The current-carrying capacity is checked, the voltage drop is checked, the breaker is chosen, and nobody asks whether a 16 mm² tail from a large transformer can outlast the breaker's tripping time. The same equation sizes the protective (earth) conductor, which carries the fault current back and gets its own k values in IEC 60364-5-54.

Formula

Fault energy I²t = I_sc² × t (A²s, with I in amperes and t in seconds)
Minimum size S_min = √(I²t) ÷ k = I_sc × √t ÷ k (mm²)
Withstand of a size S: (k × S)² (A²s)
Longest clearing time at I: t_max = (k × S ÷ I)²
Largest current for a time t: I_max = k × S ÷ √t

The derivation assumes the fault is over before any heat leaves the conductor, which is what adiabatic means here. All of the I²Rt goes into the heat capacity of the metal, the temperature rise is proportional to I²t ÷ S², and the length cancels out: a long cable and a short one heat by the same amount per metre. Because resistance itself rises with temperature, the integration from the initial temperature θ_i to the final limit θ_f gives a logarithm:

k² = Q_c (β + 20) ÷ ρ₂₀ × ln[(β + θ_f) ÷ (β + θ_i)]

where Q_c is the volumetric heat capacity of the conductor, ρ₂₀ its resistivity at 20 °C and β the temperature at which its resistance would extrapolate to zero (234.5 °C for copper, 228 °C for aluminium). For copper the constant in front works out at 226 A√s/mm², so PVC from 70 to 160 °C gives 226 × √ln(394.5 ÷ 304.5) = 115, and XLPE from 90 to 250 °C gives 143. A line conductor is taken to be at its full-load operating temperature when the fault starts. A separate protective conductor has carried nothing and starts at 30 °C, which is why its k is higher: 143 instead of 115 for PVC copper. The calculator uses the tabulated values of IEC 60364-4-43 Table 43A and IEC 60364-5-54 Table 54.3, listed below.

Worked example

A sub-distribution board fed from a 400 V switchboard, where the fault-level study gives 6 kA at the board. The incoming cable is 16 mm² PVC-insulated copper, and the upstream breaker is a moulded-case unit with its short-time delay set to 0.1 s so that it grades with the outgoing MCBs.

I²t = 6 000² × 0.1 = 3.60 × 10⁶ A²s, and √(I²t) = 1 897 A√s.
Minimum size = 1 897 ÷ 115 = 16.5 mm². The next standard size is 25 mm²: 16 mm² is one size short, by 3.0 %.
What 16 mm² can absorb: (115 × 16)² = 1 840² = 3.39 × 10⁶ A²s, 6 % less than the fault delivers. At 6 kA that is a longest clearing time of (1 840 ÷ 6 000)² = 0.094 s; for a 0.1 s clearing time the current would have to be no more than 1 840 ÷ √0.1 = 5.82 kA.
Verdict: fails. The conductor would reach about 167 °C instead of the 160 °C the PVC is allowed. Either the cable goes up to 25 mm², which absorbs 8.27 × 10⁶ A²s and would reach only about 106 °C, or the device must clear faster.

Change the device and the answer moves more than the current ever will. An MCB at 6 kA is on its magnetic element and opens in about 0.01 s: I²t = 3.6 × 10⁵ A²s, √(I²t) = 600, and 600 ÷ 115 = 5.2 mm², so 6 mm² would pass with the same 6 kA. The same current lasting 0.4 s, the disconnection time IEC 60364-4-41 allows a 230 V final circuit, would need 33 mm², so 35 mm². Time enters as a square root, but its range across devices is a factor of fifty, while the fault current on one board rarely varies by more than two or three.

k values and the temperatures behind them

Conductor	Insulation	Initial °C	Final °C	k copper	k aluminium
Line or neutral	PVC 70 °C, up to 300 mm²	70	160	115	76
Line or neutral	PVC 70 °C, above 300 mm²	70	140	103	68
Line or neutral	XLPE or EPR 90 °C	90	250	143	94
Line or neutral	Rubber 60 °C	60	200	141	93
Insulated PE, not part of a cable	PVC 70 °C	30	160	143	95
Insulated PE, not part of a cable	XLPE or EPR 90 °C	30	250	176	116
Insulated PE, not part of a cable	Rubber 60 °C	30	200	159	105

Line-conductor values from IEC 60364-4-43:2008 Table 43A; protective-conductor values from IEC 60364-5-54:2011 Table 54.3, which assumes an initial temperature of 30 °C. The calculator uses the PVC and XLPE rows. A protective conductor that is a core of the same cable starts at the cable's operating temperature and takes the values of Table 54.4, which are the line-conductor values above. Above 300 mm² the final temperature for PVC drops to 140 °C because a thick conductor cannot expand against its insulation as freely. Bare conductors, steel and mineral-insulated cables have their own tables.

I²t withstand of copper conductors, (k × S)²

Size	PVC, k = 115 (A²s)	XLPE or EPR, k = 143 (A²s)	PVC survives 6 kA for
1.5 mm²	29 800	46 000	0.83 ms
2.5 mm²	82 700	128 000	2.3 ms
4 mm²	212 000	327 000	5.9 ms
6 mm²	476 000	736 000	13 ms
10 mm²	1 320 000	2 040 000	37 ms
16 mm²	3 390 000	5 230 000	0.094 s
25 mm²	8 270 000	12 800 000	0.23 s
35 mm²	16 200 000	25 100 000	0.45 s
50 mm²	33 100 000	51 100 000	0.92 s
70 mm²	64 800 000	100 000 000	1.8 s

Line conductors, computed from the k values above. Compare the first two columns directly with the let-through I²t on a breaker or fuse datasheet at the prospective current. The last column is (115 × S ÷ 6 000)²: below about 6 mm² no breaker opens in time at 6 kA, and only a current-limiting device that lets through less than the withstand can protect the conductor.

Assumptions and limitations

Adiabatic means up to about 5 s. The equation is written in IEC 60364-4-43 for clearing times up to 5 s. Beyond that the conductor loses heat to its insulation and surroundings, the check becomes increasingly conservative, and IEC 60949 gives the non-adiabatic method that credits that loss. Within 5 s the error is on the safe side.
The current must be the value at the fault point. The calculator does not compute it. Take it from a fault-level study, from the transformer calculator for the terminals of the transformer, or from the impedance of the cable between the source and the fault for points further out. The largest current is at the near end and is the case for this check; the smallest, at the far end, is what decides whether the device trips in the required disconnection time, which is a different check.
Current-limiting devices let through less than I² × t. An MCB to IEC 60898-1 or a fuse to IEC 60269 opens while the current is still rising and never passes the full prospective current. Their datasheets give the let-through I²t at each prospective current, and that is the figure to compare with (k × S)². Multiplying the prospective current squared by a nominal 0.01 s overstates the energy, so the result here is conservative for those devices and exact for a breaker with a definite time delay.
The result is a minimum, not a size. A conductor that passes this check must still carry its design current with the derating factors of its installation and meet the voltage-drop limit; the cable sizing calculator does both. Usually one of those governs and the withstand check is a formality; the cases where it governs are described in the guide.
Only PVC and XLPE, insulated conductors. Mineral-insulated cables, bare conductors, steel armour or conduit used as a protective conductor, and protective conductors bunched with other cables have their own k values in IEC 60364-5-54 Tables 54.4 to 54.6 and are not covered.
Symmetrical current. The DC offset of an asymmetrical fault adds to the heating in the first cycle or two. It matters for clearing times below about 0.1 s and is one more reason to use the device's measured let-through energy rather than I² × t in that range.

Frequently asked questions

Why does a small cable on a big transformer fail this check?

Because the withstand grows with the square of the size and the fault energy with the square of the current, and a 630 kVA transformer at 4 % impedance delivers about 22.7 kA at its terminals. A 2.5 mm² PVC copper conductor absorbs 82 700 A²s, which at 22.7 kA is used up in 0.16 ms. No breaker opens in that time. The only devices that can protect such a conductor there are current-limiting ones, an MCB or a fuse, whose let-through at 22.7 kA is below 82 700 A²s, and the datasheet has to confirm that. Otherwise the tail must be bigger than its load needs, which is why control-supply tails on large boards are often 6 or 10 mm² for a few amperes.

What does the let-through energy on an MCB datasheet mean?

It is the I²t the breaker actually passes before the arc is extinguished, plotted against the prospective current. Because a current-limiting MCB opens within a few milliseconds and chops the current before its peak, this is much less than the prospective current squared times any clearing time you might assume. IEC 60898-1 groups breakers into energy-limiting classes; class 3 is the tightest, and for a type B breaker of 16 A or less it limits the let-through at 6 kA to 35 000 A²s. Compare that with the 29 800 A²s a 1.5 mm² PVC conductor can absorb: on the class limit alone 1.5 mm² is marginal at a 6 kA fault level, and it is the manufacturer's own curve, normally below the class limit, that decides. At 2.5 mm² (82 700 A²s) there is room.

Can I rely on the upstream breaker to protect the cable?

Only with its actual operating time at this current. An upstream moulded-case or air circuit-breaker set to grade with the devices below it has a short-time delay of 0.1 to 0.5 s, and at 6 kA that delay turns 6 mm² of adequate cable into a need for 25 or 35 mm². If the upstream device is the only protection for a cable, the cable must be sized for the upstream device's clearing time, or a device with a shorter time must be put at the cable's origin. IEC 60364-4-43 allows the short-circuit protection to be placed up to 3 m downstream of the point where the cable's capacity reduces, provided the risk of fault in that length is minimised and the conductors are not near combustible material; it does not allow the check to be skipped.

Why does the protective conductor get a higher k?

Because it starts cooler. A line conductor is assumed to be at its full-load operating temperature, 70 °C for PVC, when the fault begins, so it has 90 °C of rise available to 160 °C. A separate protective conductor carries no current in normal service; IEC 60364-5-54 takes it to start at 30 °C, giving 130 °C of rise, and the logarithm in the derivation turns that into k = 143 instead of 115. A protective conductor that is a core of the same cable does not get the benefit, because it sits against the hot line conductors, and Table 54.4 gives it the line-conductor values.

What about the 5 s rule?

Two different things are called that. IEC 60364-4-43 writes the adiabatic equation for durations up to 5 s; for longer faults the conductor loses enough heat that IEC 60949 should be used instead, and in practice a low-voltage fault that lasts more than 5 s is a protection problem, not a cable one. Separately, IEC 60364-4-41 allows up to 5 s for automatic disconnection of distribution circuits and of final circuits above 32 A on a 230 V TN system (0.4 s for final circuits up to 32 A). Those are maximum disconnection times for shock protection, and if the minimum fault current at the far end of a circuit only trips the device in 5 s, then 5 s at that current is what the cable, and especially the protective conductor, must survive.

References

IEC 60364-4-43:2008, Low-voltage electrical installations — Part 4-43: Protection for safety — Protection against overcurrent — 434.5.2 the adiabatic equation and its 5 s limit; Table 43A k values for line conductors; 434.2.1 position of short-circuit protective devices
IEC 60364-5-54:2011, Low-voltage electrical installations — Part 5-54: Selection and erection of electrical equipment — Earthing arrangements and protective conductors — 543.1 sizing of protective conductors; Table 54.2 ratios; Table 54.3 k for insulated protective conductors not incorporated in cables; Annex A derivation of k
IEC 60364-4-41:2005+AMD1:2017, Part 4-41: Protection for safety — Protection against electric shock — Table 41.1 maximum disconnection times; 5 s for distribution circuits
IEC 60949:1988, Calculation of thermally permissible short-circuit currents, taking into account non-adiabatic heating effects — the method for durations beyond the adiabatic range
IEC 60898-1:2015, Circuit-breakers for overcurrent protection for household and similar installations — Part 1: Circuit-breakers for a.c. operation — energy-limiting classes and let-through I²t limits (Annex ZA of the EN edition)
IEC 60947-2:2016, Low-voltage switchgear and controlgear — Part 2: Circuit-breakers — short-time withstand Icw and the let-through characteristics of moulded-case and air circuit-breakers

Last reviewed 2026-09-20.

Cable short-circuit withstand calculator

Short-circuit withstand