Cable Short-Circuit Thermal Withstand Calculator
The I²t ≤ k²S² check: k is computed from the formula in Annex A of IEC 60364-5-54 rather than read from a table, and the tool returns the minimum size required and the longest time the size can carry the fault.
Calculator
Derives k from the conductor, insulation and size, then compares it against the I²t the circuit lets through and says whether the cable withstands it.
Result
The calculation runs entirely in your browser; nothing you type is sent to our servers. Only if you press “Turn this into a quote request” is the result written to your browser’s session storage, so it can be carried into the quote form.
Worked example
Opened with its default case — Conductor material: Copper · Role of the conductor: Line conductor · Insulation: PVC — the calculator returns the figures below. They are written out here so the output is readable without running JavaScript: in print, with scripts disabled, or by a search engine.
| Input | Value |
|---|---|
| Conductor material | Copper |
| Role of the conductor | Line conductor |
| Insulation | PVC |
| Cross-sectional area (mm²) | 16 |
| How will the energy be given? | Current (kA) and clearing time (s) |
| Short-circuit current Ik (kA) | 6 |
| Clearing time t (s) | 0.2 |
| Result | Value |
|---|---|
| Calculated k | 115 (calculated 114.84; θi 70 °C → θf 160 °C) |
| Permitted k²S² | 3,385,600 A²s (k²S² at 16 mm²) |
| I²t let through by the circuit | 7,200,000 A²s (6 kA for 0.2 s) |
| Result | FAILS — 7,200,000 > 3,385,600 A²s |
| Safety margin | 52.98% short — the required size is 1.46× the one entered |
| Minimum size required | 25 mm² (calculated 23.34 mm²) |
| Longest time this size can carry it | 0.09 s — below 0.1 s; use the let-through I²t here |
| Warning | k was rounded UP to the nearest integer (raw 114.84). The published table rounds one cell (aluminium + XLPE) down — confirm k against your own cable standard for a critical design. This checks only the CONDUCTOR’s thermal withstand. Screen/armour, harmonic-loaded neutrals, parallel runs and electrodynamic forces are out of scope. |
Change any field above and the calculator recomputes; this table is the default case only.
Will the cable withstand a short circuit?
It is tested by a single inequality: the energy released in the fault must be smaller than the energy the conductor can absorb.
I² · t ≤ k² · S² — where I is the short-circuit current, t the clearing time of the protective device, S the nominal cross-sectional area, and k a factor derived from the conductor material and the temperature the insulation can survive. The relation is given for short-circuits lasting up to 5 seconds.
This tool does not read k from a table — it computes it. Why, and how, is set out below.
This is a separate check from voltage drop
Sizing a cable does not rest on one calculation. A voltage-drop calculation finds what the run loses in steady state; this page tests whether the conductor melts during a fault. Neither substitutes for the other and they usually suggest different sizes — the binding one is the larger.
On long runs voltage drop usually decides; on short runs close to the main board, with high prospective fault current, short-circuit withstand usually decides.
Where does k come from?
k is derived on the assumption that the conductor absorbs the heat of the fault while losing none of it — the adiabatic assumption. The method is in normative Annex A of IEC 60364-5-54:
k = √( Qc · (β + 20) / ρ₂₀ · ln( (β + θf) / (β + θi) ) )
Qc volumetric heat capacity of the conductor material · β the reciprocal of the temperature coefficient of resistivity at 0 °C · ρ₂₀ resistivity at 20 °C · θi initial and θf final temperature
| Quantity | Copper | Aluminium |
|---|---|---|
| Qc — volumetric heat capacity (J/(K·mm³)) | 3.45 × 10⁻³ | 2.50 × 10⁻³ |
| β — reciprocal of the temperature coefficient of resistivity at 0 °C (°C) | 234.5 | 228 |
| ρ₂₀ — resistivity at 20 °C (Ω·mm) | 17.241 × 10⁻⁶ | 28.264 × 10⁻⁶ |
The unit of ρ₂₀ is Ω·mm, not Ω·m: copper’s 1.7241 × 10⁻⁸ Ω·m is 17.241 × 10⁻⁶ Ω·mm. Confusing the two throws k out by a factor of 31.6 — it is the most likely mistake if you build the formula yourself.
Why a formula rather than a table? Two reasons. The first is legal: the k values published in the standard are part of a copyrighted compilation, whereas the formula and the physical constants are facts — we run the method, we do not copy the values. The second is practical: a table gives you a handful of ready combinations, the formula works for any θi/θf pair you enter.
Rounding is to the nearest integer. The formula produces a continuous number; published tables give integers. We tested all eleven published cells: rounding to nearest matches ten of them, rounding down only four. The interesting part is that aluminium + XLPE (raw 94.55) is published as 94 while aluminium + insulated protective conductor (raw 94.61) is published as 95 — so the table itself does not round consistently. The tool therefore follows the formula, and tells you when it has rounded k upwards.
Where do the temperatures come from?
θi is the conductor temperature at the instant the fault starts; in design it is taken as the worst case, the maximum continuous operating temperature. θf is the limit the insulation can survive briefly, and it comes from the cable standard.
| Case | θi | θf | Note |
|---|---|---|---|
| Line conductor · PVC, size ≤ 300 mm² | 70 °C | 160 °C | The most common case |
| Line conductor · PVC, size > 300 mm² | 70 °C | 140 °C | The threshold is noted in the IEC 60364 k tables; the temperature itself comes from IEC 60724. The tool applies it automatically from the size you enter |
| Line conductor · XLPE / EPR | 90 °C | 250 °C | Cross-linked insulation survives a higher limit |
| Line conductor · rubber 60 °C | 60 °C | 200 °C | — |
| Protective conductor · outside the cable · rubber | 30 °C | 200 °C | — |
| Protective conductor · a core of the cable · rubber | 60 °C | 200 °C | — |
| Protective conductor · outside the cable, insulated | 30 °C | 160 / 250 °C | A PE carrying no load current starts at ambient |
| Protective conductor · a core of the cable, or bunched | 70 / 90 °C | 160 / 250 °C | It sits at the same temperature as the loaded cores |
The most common mistake lives between the last two rows of this table. Using 30 °C for the PE core of a multicore cable overstates k by roughly 24 % — you believe the conductor is tougher than it is. They are separate options in the tool so that they cannot be confused.
Mineral-insulated cable and bare protective conductors were deliberately left out of the presets: the exact temperatures for those rows could not be verified from a primary source, and we did not invent them. For those cases choose “Custom” and enter the θi and θf from your own cable standard.
Time, or let-through I²t?
The tool has two input modes because a single “time” box would give the wrong answer in two of the three situations below.
| Situation | What to use | Why |
|---|---|---|
| Clearing time roughly above 0.1 s, device not current-limiting | t read from the time-current curve | The curve gives a meaningful time in this region |
| Clearing time below 0.1 s | The manufacturer’s let-through I²t | In the first half-cycles the current is asymmetrical (DC component); the symmetrical rms value understates the real energy |
| The device is current-limiting | The manufacturer’s let-through I²t | The device cuts the current before it reaches its peak; there is no time left to read from a curve |
| Protection is by fuse | The total I²t | The pre-arcing value is for discrimination studies; cable protection uses the total value |
A common misreading: “below 0.1 s the adiabatic assumption breaks down.” The opposite is true — the shorter the fault, the less heat escapes into the insulation and the better the assumption holds. The threshold is not about heat; it is that the current itself can no longer be read off a curve.
What does the 5-second limit mean?
The adiabatic relation assumes all the heat stays in the conductor. The longer the fault lasts, the further that drifts from reality: part of the heat escapes into the insulation and the surroundings. That is why the standard gives the relation for short-circuits lasting up to 5 seconds.
Longer durations need a non-adiabatic calculation — IEC 60949 is the standard for that — and the result comes out more optimistic than the adiabatic one. Even so, a result beyond 5 seconds is treated as invalid, because the relation you used was not given for that range — recalculate with IEC 60949.
What this check does NOT cover
In one sentence: only the thermal withstand of the conductor. Each of the following is a separate calculation, and in practice one of them is sometimes the binding one.
- Screen and armour. A screened cable has two different fault levels: symmetrical three-phase for the conductor, line-to-earth for the screen. Because the screen is usually far thinner than the line conductor, the screen is frequently the limiting element, not the conductor.
- Neutral conductors and harmonics. With loads that generate triplen harmonics (LED drivers, switch-mode supplies, UPS) the neutral current can exceed the line current, and a cable with a reduced neutral is then thermally inadequate. A check made on the line conductor does not see this at all.
- Parallel cables. During a fault the current does not simply divide between the legs: a faulted conductor is fed from both ends, and once the protection in one leg opens the remaining legs take over. Equal lengths and a common route are a separate condition again.
- Motor circuits. The cumulative heating of successive starts is not a short-circuit event but a cyclic overload; this relation models a single event. In motor circuits the cable is usually protected against short-circuit only, with overload protection sitting in the motor starter.
- Transformer secondaries. The cable between the transformer and the main board is often unprotected at its origin, with very high fault current and a dominant DC component — exactly the region where let-through I²t must be used.
- Disconnection at the minimum fault current. I²t ≤ k²S² is a necessary condition, not a sufficient one: you must separately prove that the protective device also operates in the required time at the smallest fault current, at the far end of the run. The largest current at the origin drives this calculation; the smallest current at the far end drives the disconnection check.
- Electrodynamic forces. Short-circuit current pushes and pulls conductors. Busbars, cable supports, cleat spacing and terminations need a separate mechanical calculation; this page counts heat only.
Scope (AKSCO): we supply materials in this field — cable, panel equipment, switchgear and consumables. We do not provide electrical design, calculation approval or commissioning services. This tool is a preliminary design aid; the final verification is made by a qualified electrical engineer against the edition of the standard in force.
The number is too big — what now?
| Route | What changes | Watch out for |
|---|---|---|
| Increase the size | k²S² rises with the square of the size. The gain depends on the step: up to 70 mm² one step raises it 2–2.8×; above 95 mm² a step adds 52–78 % | If ampacity and voltage drop are already satisfied, this is the most expensive fix |
| Choose a faster-clearing device | I²t is directly proportional to time; a current-limiting device can cut the energy several fold | Discrimination may be lost — assess it together with the upstream device |
| Change the insulation | Moving from PVC to XLPE raises k in copper from 115 to 143 — 24 % in k, 55 % in withstand, because k²S² goes with the square of k | Ampacity rises at the same size too; cable cost goes up |
| Reduce the fault current | Transformer impedance, run length or a separate board can lower the prospective current | That is an installation-level decision, not a cable choice |
The usual order is: review the protective device first, then the insulation, and the size last. Increasing the size is the most visible fix and usually the most expensive.
Frequently Asked Questions
What is a short-circuit thermal withstand calculation?
It checks whether the heat released in a conductor during a short circuit exceeds what the insulation can survive. The condition is I²·t ≤ k²·S²: I is the short-circuit current, t the clearing time, S the nominal cross-sectional area, and k a factor derived from the material and the insulation temperatures. The relation is given for short-circuits lasting up to 5 seconds.
What is the value of k?
There is no single value — it depends on the conductor material, the short-circuit limit temperature of the insulation, and the conductor temperature at the instant the fault begins. This tool does not read k from a ready table; it runs the formula from Annex A of IEC 60364-5-54 with the material constants, rounds to the nearest integer, and tells you when it has rounded upwards. That way it also works for temperatures you enter yourself.
Why do you not publish the k table?
Tables in standards are copyrighted and cannot be republished; translating them is equally out of bounds. The formula and the physical constants, by contrast, are facts. We run the method rather than copying the table. There is a side benefit: a table gives a handful of ready combinations, while the formula works for any pair of temperatures.
Why does the result change above 300 mm²?
The short-circuit limit temperature of PVC insulation is 160 °C up to 300 mm² and 140 °C above it. The threshold appears as a note in the IEC 60364 k tables; the primary source of the limit temperatures themselves is IEC 60724, which covers short-circuit temperature limits for cables. A lower limit means a lower k, so the same size withstands less energy. The tool applies this automatically from the size you enter.
The clearing time is very short — what should I enter?
Below about 0.1 s, or with a current-limiting device, you do not read a time off the curve; you use the manufacturer’s declared let-through I²t (Joule integral). Fuses publish two values — cable protection uses the TOTAL value, while the pre-arcing value is for discrimination studies. The second input mode exists precisely for this.
Doesn’t the adiabatic assumption break down below 0.1 s?
No — the opposite. The shorter the fault, the less heat escapes into the insulation, so the adiabatic assumption holds better. The reason for the threshold is not heat but the current itself: in the first half-cycles the current is asymmetrical (it carries a DC component), and computing with the symmetrical rms value understates the energy. With current-limiting devices there is no readable time left at all.
Why is k different for a protective conductor?
A protective conductor normally carries no load current, so at the instant of the fault it starts at ambient temperature (30 °C). A conductor starting colder has more thermal headroom, so k comes out higher — roughly 24 % for an insulated copper PE. But this applies ONLY to a PE outside the cable and not bunched with loaded cores. If the PE is a core of a multicore cable it sits at the same temperature as those cores, and using 30 °C is dangerously optimistic.
Is this check enough for a screened cable?
No. In a screened or armoured cable two separate fault levels are calculated: symmetrical three-phase current for the conductor and line-to-earth current for the screen. Because the screen area is usually much smaller than the line conductor, the screen is often the limiting element. Separate temperature limits and separate k values apply to screens and armour.
Sources
- IEC 60364-4-43 — Protection against overcurrent. The thermal withstand check for short-circuit conditions; clause 434.5.2 in the 2008 edition, clause 431.5.4 in the 2023 edition, which is restructured and carries its own mapping table (IEC; the text is copyrighted)
- IEC 60364-5-54 — Earthing arrangements and protective conductors. The derivation of k is in normative Annex A (“Method for deriving the factor k in 543.1.2”). The annex is written for the protective-conductor clause; the same derivation holds for line conductors, and the line-conductor k values are published in the k table of IEC 60364-4-43 (IEC; the text is copyrighted)
- IEC 60724 — Short-circuit temperature limits of electric cables with rated voltages of 1 kV and 3 kV. The 300 mm² threshold for PVC appears as a note in the IEC 60364 k tables; this standard is the primary source of the limit temperatures themselves (IEC; the text is copyrighted)
- IEC 60949 — Calculation of thermally permissible short-circuit currents, taking into account non-adiabatic heating effects. Durations beyond 5 s are the subject of this standard (IEC; the text is copyrighted)
- Electrical Installation Guide — Verification of the withstand capabilities of cables under short-circuit conditions, and Sizing of the protective earthing conductor (Schneider Electric; an engineering reference based on IEC 60364)
- Cable Short Circuit Ratings (Prysmian; manufacturer technical note — separate fault levels and separate temperature limits for screen and armour)
How we choose sources, verify figures and date our pages is set out in how we source and verify what we publish. Spotted an error? Write to info@aksco.com.tr — verified errors are corrected.
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