Sizing a power cable is not one calculation but three, applied to the same conductor and resolved by whichever is tightest. The cable must carry the design current continuously without exceeding the insulation temperature, it must deliver the voltage the load needs at the far end of the run, and it must survive the prospective short-circuit current for as long as the protection takes to clear it. A cable that passes two of the three checks is not sized. This calculator applies all three to the values you supply and reports which one binds.
One design decision is worth stating up front. The calculator holds no ampacity table of its own. The base current-carrying capacity is an input, taken from the table that matches your installation method in the standard that governs your project, and so are the derating factors and the adiabatic constant. That is deliberate: tabulated ratings depend on the reference method, the conductor arrangement, the ambient or soil reference temperature and the number of loaded conductors, and a number lifted out of context is worse than no number at all. The drop-down of indicative values is a convenience for exploring the arithmetic, not a rating.
Cable Sizing Calculator
Ampacity derating, voltage drop and short-circuit withstand, and which one binds
Check one: derated ampacity
Every published current-carrying capacity is quoted for one specific set of conditions: a stated installation method, a stated ambient or soil temperature, a stated soil thermal resistivity for buried runs, and a single circuit on its own. Real installations depart from all of those, so the tabulated value is multiplied by correction factors before it is compared with the design current \(I_b\):
\[ I_z = I_{base}\,k_{amb}\,k_{grp}\,k_{soil} \;\ge\; I_b \]
The grouping factor is usually the one that does the damage. A cable that is comfortable on its own can lose a third of its rating once it shares a tray or a duct bank with several other loaded circuits, because each cable is heating the others. Ambient temperature acts in the same direction in hot plant rooms and hot climates, and for buried cables the soil thermal resistivity and burial depth together determine how easily the heat escapes. The calculator takes each factor as a direct input, with typical ranges shown as hints, because the correct value depends on details of the arrangement that no calculator can infer.
The utilisation figure reported by the tool is \(I_b/I_z\) expressed as a percentage. Anything above 100% means the conductor would run hotter than its insulation allows in steady state.
Check two: voltage drop
Voltage drop is a load-current problem, not a fault problem, and it is the check that most often decides the size on long runs. Resolving the drop along the load current gives the familiar working expression:
\[ \Delta V_{3\phi} = \sqrt{3}\; I_b\, L \left(R\cos\varphi + X\sin\varphi\right), \qquad \Delta V_{1\phi} = 2\; I_b\, L \left(R\cos\varphi + X\sin\varphi\right) \]
Here \(L\) is the one-way route length in kilometres and \(R\) and \(X\) are the per-kilometre resistance and reactance of one conductor at the operating temperature. The factor 2 in the single-phase case accounts for the go and return conductors; the factor \(\sqrt{3}\) in the three-phase case converts the per-phase drop into a line-to-line drop. The percentage is then referred to the nominal system voltage:
\[ \Delta V\% = \frac{\Delta V}{U_n}\times 100 \]
The convention used here is that \(U_n\) is the voltage you enter, which for the three-phase case is the line-to-line voltage. That pairs correctly with the \(\sqrt{3}\) factor above, since both sides of the ratio are line-to-line quantities. Mixing a line-to-line drop with a phase voltage denominator is a common error and inflates the percentage by \(\sqrt{3}\).
Two details matter in practice. First, \(R\) must be the resistance at the operating temperature, not at 20 °C: a copper conductor at 90 °C has roughly 27% more resistance than the same conductor at 20 °C, and using the cold value understates the drop. The calculator estimates \(R\) from the cross-section, material and insulation temperature by default and lets you override it with the manufacturer figure. Second, reactance is not negligible. At small cross-sections \(R\) dominates and \(X\) can almost be ignored, but above roughly 95 mm² the two are comparable, which is why going up a size stops buying much drop reduction and parallel cables become the better answer.
Check three: short-circuit thermal withstand
During a short circuit the fault current is far above the continuous rating, but it lasts only until the protection operates. Over that interval essentially no heat leaves the conductor, so the temperature rise is set by the energy let through, \(I^2t\), divided by the thermal capacity of the metal. Equating the let-through energy to the energy that takes the conductor from its initial temperature to the maximum the insulation tolerates gives the adiabatic equation:
\[ S \;\ge\; \frac{I\sqrt{t}}{k} \]
with \(I\) the RMS fault current in amperes, \(t\) the clearing time in seconds, and \(S\) the cross-section in mm². The constant \(k\) depends on the conductor material and on the initial and final temperatures, which in turn depend on the insulation:
\[ k=\sqrt{\frac{Q_c\left(B+20\right)}{\rho_{20}}\,\ln\!\left(\frac{B+\theta_f}{B+\theta_i}\right)} \]
where \(Q_c\) is the volumetric heat capacity of the conductor, \(\rho_{20}\) its resistivity at 20 °C, \(B\) the reciprocal of the temperature coefficient of resistance at 0 °C, and \(\theta_i\) and \(\theta_f\) the initial and final conductor temperatures. In routine work nobody evaluates this expression: \(k\) is read from a table in the applicable standard. The calculator offers indicative defaults for the four common material and insulation pairings and lets you type your own, which is what you should do once you have the governing table in front of you.
Note the square-root dependence on time. Halving the clearing time reduces the required cross-section by only about 29%, but it is still usually cheaper than more metal, which is why current-limiting protection and lower time settings are the first thing to look at when this check is the one that binds.
The adiabatic assumption is conservative and is normally accepted for clearing times up to a few seconds. For very short times a current-limiting device may cut the let-through energy well below \(I^2t\) computed from the prospective current, and for very long times heat conduction into the surroundings makes the result pessimistic. Neither correction is applied here.
Which check binds, and what to do about it
The three checks are independent, and each responds to a different remedy. The bar chart in the calculator expresses each one as the fraction of its own limit that the chosen cable uses, which puts them on a common scale so the longest bar is the binding constraint. The pattern is worth internalising, because it tells you what to change:
- Ampacity binds on short, heavily loaded, densely grouped runs. The remedies are a larger section, parallel cables, or a better installation method with more spacing and a cooler route. Improving the grouping factor often recovers more capacity than one size step.
- Voltage drop binds on long runs, especially at low voltage and low power factor. The remedies are a larger section, a shorter route, a supply point closer to the load, or power factor correction at the load.
- Short-circuit withstand binds close to the source, where the prospective fault current is high, and where protection is slow. The remedies are a larger section, faster or current-limiting protection, or a lower fault level at that point.
Worked example
Take the default case: a three-phase 400 V circuit carrying a design current of 100 A over a 100 m run at a power factor of 0.9, wired in 35 mm² copper with XLPE insulation. The base ampacity entered is 138 A, with an ambient factor of 0.96, a grouping factor of 0.80 and a soil factor of 1.00. The prospective fault current is 10 kA cleared in 0.2 s, and \(k\) is taken as 143.
Ampacity: \(I_z = 138 \times 0.96 \times 0.80 \times 1.00 = 105.98\) A, so the 100 A design current uses 94% of the thermal limit.
Voltage drop: 35 mm² copper at 90 °C has a resistance of about 0.628 Ω/km, and taking 0.08 Ω/km for reactance, the resolved impedance is \(0.628 \times 0.9 + 0.08 \times 0.436 = 0.600\) Ω/km. Over 0.1 km at 100 A the three-phase drop is \(\sqrt{3}\times 100 \times 0.1 \times 0.600 = 10.39\) V, which is 2.60% of 400 V. Against a 3% limit that is 87% utilisation.
Withstand: \(S_{min} = 10000\sqrt{0.2}/143 = 31.3\) mm², so the 35 mm² conductor uses 89% of its withstand capability.
All three land in the high eighties and low nineties, and ampacity is the tightest at 94%. The cable passes, but with no allowance for load growth and no room for an extra grouped circuit. Increase the design current to 106 A, or add one more circuit to the group, and the ampacity check fails first. As a contrast, stretch the run to 400 m at 60 A and voltage drop takes over as the binding constraint; raise the fault current to 20 kA with a 0.3 s clearing time and the withstand check fails on its own, needing about 63 mm².
How to read the classification
- Passes: all three checks clear with margin, the tightest of them using no more than about 90% of its limit. The size is defensible against the inputs given.
- Marginal: at least one check is within roughly 10% of its limit. Nothing is violated, but there is no allowance for load growth, for an extra circuit added to the group later, or for an input that turns out to be slightly optimistic. Treat this as a prompt to go up a size or to firm up the assumptions.
- Fails: at least one check is exceeded. The note names which one and what to change.
Working in per-unit as well as amperes?
The free Per-Unit System Cheat Sheet covers base conversions and change of base on one printable page, which is what you need when the fault current for this calculation comes out of a per-unit study.
Frequently asked questions
Why does the calculator not include an ampacity table?
Because a current-carrying capacity is meaningless without its installation method, reference temperature and conductor arrangement, and those details are exactly what a drop-down hides. Entering the base ampacity yourself forces you to open the table that governs your project, which is where the number has to come from anyway. The indicative values offered in the tool are there so the arithmetic can be explored, and they must be replaced by the tabulated figure before any result is used.
Should the voltage drop percentage use line-to-line or phase voltage?
Use whichever is consistent with the drop in the numerator. This calculator computes a line-to-line drop for the three-phase case, using the \(\sqrt{3}\) factor, and divides it by the line-to-line voltage you enter. Dividing a line-to-line drop by a phase voltage overstates the percentage by a factor of \(\sqrt{3}\), which is a frequent source of oversized cables.
What clearing time should I use for the withstand check?
The operating time of the protective device at the prospective fault current at that point, read from its time-current characteristic, including any intentional time delay used for grading. Using the maximum time delay setting rather than the instantaneous time is the conservative choice, and it is the relevant one where upstream grading forces a delay.
Does the adiabatic check size the protective earth conductor too?
The same equation is used for protective conductors, but with the earth-fault current and the earth-fault clearing time in place of the phase values, and with a value of \(k\) appropriate to the protective conductor’s own insulation and installation. The calculator applies the equation to the phase conductor only. Size the protective conductor separately.
Why does going up a size help voltage drop less than expected?
Resistance falls roughly in proportion to cross-section, but reactance is almost independent of it. Once the reactive term \(X\sin\varphi\) is comparable with the resistive term \(R\cos\varphi\), further increases in section leave most of the drop untouched. At that point running two cables in parallel, correcting the power factor, or shortening the route does more than one more size step.
Related reading
- All EE Power School calculators: the full set of interactive power system tools.
- Two-Bus Load Flow Calculator: the same voltage drop physics taken further, into voltage stability and the PV nose curve.
- Symmetrical Components Calculator: resolve the unbalanced fault currents that feed the withstand check.
- SCR Calculator: screen system strength, which sets the fault level at a point of connection.
References
- IEC 60364-5-52, Low-voltage electrical installations. Selection and erection of electrical equipment. Wiring systems. Current-carrying capacities, correction factors and voltage drop for LV installations.
- IEC 60364-5-54, Low-voltage electrical installations. Earthing arrangements and protective conductors. The adiabatic equation and the constant k.
- IEC 60502, Power cables with extruded insulation and their accessories for rated voltages from 1 kV up to 30 kV.
- IEC 60287, Electric cables. Calculation of the current rating. The thermal model behind published ampacity tables.
- NFPA 70 (National Electrical Code), Article 310, for installations following the NEC rather than IEC practice.