Cable Sizing — Ampacity, Volt Drop, Short-Circuit: Three Checks, and the Biggest Wins

The MCC schedule that nearly got issued

A 75 kW water-injection pump sits 500 m from its 415 V MCC — out at the far edge of the plot, fed along a hot outdoor tray with five other cables touching it. The draughtsman fills in the cable schedule: full-load current 129 A, so a 70 mm² three-core will do, add a margin, call it 95 mm². It goes out for procurement.

Guess first: how far wrong is 95 mm²? One size? Two?

The cable that actually works is 400 mm² — nearly six standard sizes up, and about four times the copper. Nothing in the process data changed. What changed is which check governs.

The misconception, stated plainly

"Size the cable for the running current. The ampacity table gives you the answer; everything else is a sanity check."

This is true often enough to be dangerous. On a short run inside a substation, fed from a modest fault level, the thermal check really does govern and the table really is the answer. So the habit forms. Then it silently produces the wrong cable in exactly the three situations where it matters:

• Long runs → volt drop governs. Drop scales with length; ampacity does not care about length at all. Past a few hundred metres the thermal answer is irrelevant.
• High fault level, slow clearance → short-circuit withstand governs. A 1.5 mm² control cable is thermally fine at 4 A and vaporises in 0.2 s at 31.5 kA.
• Bunched cables on a hot tray → the derated ampacity governs. Six cables touching in 45 °C air have barely two-thirds of their tabulated rating. The table value was never the cable's rating; it was the rating of a cable in a laboratory at 30 °C with nothing next to it.

There are three independent checks, each with its own physics, and the governing one varies from circuit to circuit. The correct size is simply the largest of the three — and on motor circuits there is a fourth, hidden one that beats all of them more often than anyone expects.

S_selected  =  max ( S_ampacity ,  S_voltdrop ,  S_shortcircuit )

Symbol key — every symbol on this sheet

• Ib — design current: the load the circuit actually carries continuously · A
• It — tabulated current: the base rating from the manufacturer/standard table, at reference conditions (typically 30 °C air, one circuit, defined installation method) · A
• Iz — the installed rating: Iz = It × ca × cg × ci × cs. The check is Iz ≥ Ib · A
• ca — ambient temperature derating factor · dimensionless
• cg — grouping derating factor (cables bunched, touching, in layers) · dimensionless
• ci — thermal insulation / enclosure factor · dimensionless
• cs — soil thermal resistivity and burial-depth factor (buried runs only) · dimensionless
• S — conductor cross-sectional area · mm²
• L — route length, one way · m (use km in the volt-drop formula)
• R — a.c. resistance per unit length at the operating temperature · Ω/km
• X — reactance per unit length at 50/60 Hz · Ω/km
• cos φ — power factor; sin φ = √(1 − cos²φ)
• ΔV — volt drop along the cable · V (usually reported as % of nominal)
• Un — nominal system voltage · V
• I_sc — prospective short-circuit current at the cable's supply end · kA
• t — protective device total clearing time for that fault · s
• k — adiabatic material constant (insulation + conductor) · A·s^0.5/mm²
• η — motor efficiency; LRC — locked-rotor current, as a multiple of full-load current

Check 1 — ampacity: the table is not the rating

A cable's thermal limit is the temperature its insulation can sit at forever: 90 °C for XLPE/EPR, 70 °C for PVC. The tabulated current It is whatever current produces that temperature under a specific reference installation. Change the installation and you change the rating:

Iz = It × ca × cg × ci × cs        must satisfy      Iz ≥ Ib
equivalently, required table value:   It ≥ Ib / (ca · cg · ci · cs)

Typical factors (IEC 60364-5-52 family — illustrative values, always use the project's own table):

Two things to notice. The factors multiply, so a hot bunched tray easily lands at 0.6–0.65 — a 35–40 % loss of rating before the cable has carried a single amp. And soil resistivity moves the answer by ±50 %: dry sand around a buried duct bank is a thermal blanket, and the soil thermal resistivity assumed at design stage is one of the least-verified numbers in the whole calculation. Spacing cables apart on the tray, rather than up-sizing them, is very often the cheaper fix — and it is a layout decision, taken early or not at all.

Watch the derating happen — add cables to the tray, raise the ambient, and see the conductors heat up towards their 90 °C limit while the spare capacity bar empties: ▶ open the interactive: electrical cable sizing 3d

Check 2 — volt drop: and the reactance floor nobody expects

For a three-phase circuit, with R and X in Ω/km and L in km:

ΔV = √3 · I · L · (R·cos φ + X·sin φ)            three-phase
ΔV = 2 · I · L · (R·cos φ + X·sin φ)             single-phase (out and back)
ΔV % = 100 · ΔV / Un

Typical limits — check the project electrical design basis, they vary:

Running, feeders + final circuit combined :  5 % of Un    (often 3 % for the feeder alone)
Lighting circuits                          :  3 %
Motor terminals during DOL starting        : 15 % (some specs 10 %); contactors drop out
                                              below roughly 80 % of coil voltage

Now the part that makes motor circuits behave differently from everything else. In the bracket, R and X are weighted by cos φ and sin φ:

• Running, a motor sits at cos φ ≈ 0.85–0.88, so sin φ ≈ 0.5. The R term dominates, and R is inversely proportional to conductor area. Double the copper, halve the drop. Up-sizing works.
• Starting, a direct-on-line motor draws 6–7× full-load current at cos φ ≈ 0.25–0.35, so sin φ ≈ 0.95. The X term dominates — and X is set by conductor spacing and geometry, not by conductor area. It sits at 0.078–0.09 Ω/km for practically every size from 25 mm² to 630 mm². Double the copper and X barely moves.

That is the reactance floor: you cannot copper your way out of a starting dip. Past a certain size the drop stops falling and the money stops buying anything. The real fixes are a soft starter or VFD (starting current 2–3× instead of 6–7×), a star-delta starter (≈ 2.2×), a higher distribution voltage, or moving the substation. Cable is the last of those options, not the first.

Slide the length, the starter type and the size, and watch which of the three checks wins — the calculator shows all three answers side by side with the governing one flagged, plus the starting-dip indicator: ▶ open the interactive: electrical cable sizing calc

Check 3 — short-circuit withstand: the adiabatic equation

During a fault the conductor heats so fast that no heat escapes into the insulation. All the I²R energy stays in the copper — adiabatic. Equate the energy let through by the protective device to the energy the conductor can absorb before the insulation is destroyed:

I² · t  ≤  k² · S²                   the withstand condition
S_min   =  I · √t / k                the size it demands

k bundles the conductor's heat capacity, resistivity and the allowed temperature excursion:

Read I·√t as the real driver: halving the clearing time buys the same relief as reducing the fault current by 30 %. Protection settings and cable size are the same conversation. A 0.2 s clearance and a 1.0 s clearance differ by a factor √5 = 2.24 in required area — two or three standard sizes on a large feeder.

k = √[ (Qc(β + 20) / ρ20) · ln( (β + θf) / (β + θi) ) ]

The adiabatic assumption is valid for roughly 0.1 s ≤ t ≤ 5 s. Faster than that, a current-limiting fuse never lets the full prospective current flow and you must use its published let-through I²t instead. Slower than 5 s, heat genuinely does leave the conductor and the adiabatic answer is conservative (but nobody complains about that).

Worked example — the 500 m pump feeder, all four numbers

Motor 75 kW, 415 V, 3-phase, η = 0.94, cos φ = 0.86, DOL (LRC = 6×, cos φ_start = 0.30)
Route 500 m, 3-core XLPE/SWA copper on perforated tray, 6 cables touching, ambient 45 °C
Fault level 31.5 kA at the MCC, breaker total clearing time 0.20 s
Limits: 3 % running volt drop, 15 % starting volt drop at the motor terminals

Full-load current

Ib = P / (√3 · Un · cos φ · η) = 75 000 / (1.732 × 415 × 0.86 × 0.94) = 129.1 A
I_start = 6 × 129.1 = 774 A

Check 1 — ampacity. ca = 0.87 (45 °C), cg = 0.76 (6 touching on tray) → product 0.661.

It required = 129.1 / 0.661 = 195 A    →   50 mm² (187 A) fails, 70 mm² (238 A) passes
S_ampacity = 70 mm²

Check 3 — short-circuit.

S_min = 31 500 × √0.20 / 143 = 31 500 × 0.4472 / 143 = 98.5 mm²   →   S_sc = 120 mm²

Check 2a — running volt drop. R at 90 °C ≈ 23.4/S Ω/km, X ≈ 0.079–0.082 Ω/km, cos φ = 0.86 → sin φ = 0.510. Limit 3 % of 415 V = 12.45 V.

120 mm²:  ΔV = 1.732 × 129.1 × 0.5 × (0.195×0.86 + 0.080×0.510) = 23.3 V = 5.62 %   ✗
240 mm²:  ΔV = 1.732 × 129.1 × 0.5 × (0.097×0.86 + 0.079×0.510) = 13.9 V = 3.34 %   ✗
300 mm²:  ΔV = 1.732 × 129.1 × 0.5 × (0.078×0.86 + 0.079×0.510) = 12.0 V = 2.89 %   ✓
S_voltdrop(run) = 300 mm²

Check 2b — starting volt drop. I = 774 A, cos φ = 0.30 → sin φ = 0.954. Limit 15 % = 62.3 V.

300 mm²:  ΔV = 1.732 × 774 × 0.5 × (0.078×0.30 + 0.079×0.954) = 66.2 V = 15.96 %   ✗
400 mm²:  ΔV = 1.732 × 774 × 0.5 × (0.058×0.30 + 0.078×0.954) = 61.7 V = 14.86 %   ✓
S_start = 400 mm²   ←  GOVERNS

Answer: 400 mm². And look at what the last step bought: +33 % copper for 1.1 percentage points of starting dip, because at cos φ = 0.30 the reactance term is 81 % of the bracket and refuses to shrink. That is the signal to stop sizing and start re-engineering. Fit a star-delta starter (2.2× → 284 A) and the starting drop at 300 mm² falls to 5.9 %: one size smaller, 1.3 tonnes less copper over 500 m (100 mm² × 3 cores × 500 m × 8 960 kg/m³), and a better answer for the switchgear too.

Final comparison — the four numbers from one circuit:

Common pitfalls

• Sizing on running current alone — the headline error, and it under-sizes precisely on the long, remote, expensive circuits where a re-pull costs the most.
• Using the tabulated It as though it were Iz. Ambient and grouping are not "margin"; they are part of the rating. Applying an extra "design margin" on top while also forgetting ca and cg is the classic double error that cancels to roughly the right answer — until it does not.
• Grouping factors applied to the whole tray. The factor depends on the number of loaded circuits and on spacing; a tray of mostly-idle spares is not nine loaded cables.
• Ignoring volt drop from the transformer and busbar. The 15 % at the motor terminals is the total dip, and the source impedance contributes. Cable-only analysis flatters the result.
• Up-sizing to fix a starting dip past the point where reactance dominates. Check the split between R·cos φ and X·sin φ before buying more copper.
• Using the fault level at the MCC to size the far end of a long cable. The cable's own impedance reduces the fault current along the run, so the adiabatic check at the remote end is less onerous — but the check must be done at the supply end, where the current is highest.
• Forgetting the earth/armour conductor has its own adiabatic check with a much lower k (≈ 50 for steel wire armour). Armour that is adequate as a screen can be inadequate as a protective conductor.
• Buried runs: the soil thermal resistivity is assumed, not measured. And a duct bank changes it again. This single number can move the answer two sizes.
• Parallel cables: the fault current and load share between them, but a single-phase-to-earth fault on one cable does not — and circulating currents need the phases transposed or the cables trefoiled consistently.

Outcome

• Three independent checks — derated ampacity (Iz ≥ Ib), volt drop (ΔV = √3·I·L·(R cos φ + X sin φ)) and short-circuit withstand (I²t ≤ k²S²) — and the answer is the largest of the three. Which one governs changes circuit by circuit.
• Ampacity is a thermal answer that depends on the installation: ca × cg × ci × cs routinely reaches 0.6–0.65 on a hot bunched tray, and soil resistivity moves buried runs by ±50 %.
• Volt drop is the long-run governor; on motors the starting dip is the usual hidden governor because at cos φ ≈ 0.3 the X term dominates and X is nearly independent of conductor size. Reactance floor: past a point, more copper buys almost nothing — change the starter instead.
• Short-circuit demands S ≥ I√t/k; clearing time enters as √t, so protection settings and cable size are one decision. k = 143 Cu/XLPE, 115 Cu/PVC, 94 Al/XLPE, ≈ 50 steel armour.
• Worked case: a 75 kW motor at 500 m needed 70 / 120 / 300 / 400 mm² from the four checks — the running-current habit under-sized it by nearly six standard sizes.
• Interactive: ▶ open the interactive: electrical cable sizing calc — all three checks live, governing check flagged, volt-drop bar and starting-dip indicator.
• 3D: ▶ open the interactive: electrical cable sizing 3d — bunched tray with the derating shown as heat, a section through the cable, and the volt-drop gradient along the run.

Open items

• Add the fourth check most specs also require: earth-fault loop impedance / disconnection time, and the resulting minimum size for the protective conductor.
• Add HV (6.6 / 11 kV) sizing: charging current, screen bonding (single-point vs both-ends) and the sheath voltage limit.
• Add a real IEC 60287 steady-state thermal calculation for a duct bank, to replace the table factors with first principles.
• Cross-link to rotating equipment: motor starting torque falls as V², so a 15 % dip is a 28 % torque loss — the pump may not break away even if the contactor holds.

Educational teaching material — simplified and illustrative. Not for engineering design use.
© EPiC Circle · provided by PipeAxis