Cable Size Formulas: Current and Short-Circuit

Cable sizing formulas for current capacity with correction factors, conductor resistance and temperature, and short-circuit withstand, with worked examples.

The formulas

Ib is the design current, In the rating of the protective device and Iz the current the cable can carry in its installation. Ca and Cg are correction factors for ambient temperature and grouping, taken from the standard you work to. ρ is the resistivity (copper 0.017241 Ω·mm²/m at 20 °C, α = 0.00393 per °C), L the length in metres and A the area in mm². In the last row I is the fault current in amperes, t the clearing time in seconds and k a constant for the conductor and insulation: copper 115 with PVC and 143 with XLPE, aluminium 76 with PVC and 94 with XLPE (IEC 60364-4-43). For PVC conductors above 300 mm² the standard lowers k to 103 for copper and 68 for aluminium, so a large PVC cable needs a larger area than the 115 or 76 figure gives. S is in mm².

Worked example: current capacity

A circuit has a design current of 63 A and a 63 A breaker. The ambient factor is 0.87 and the grouping factor 0.80. These are example factors, so use the ones from your own standard.

1. Ib ≤ In: 63 ≤ 63, so the device is correct
2. It ≥ 63 / (0.87 × 0.80) = 90.52 A, so pick a cable whose tabulated current is at least this value

Worked example: resistance of 100 m of 16 mm² copper

1. R20 = 0.017241 × 100 / 16 = 0.1078 Ω
2. At 70 °C: R = 0.1078 × (1 + 0.00393 × 50) = 0.1289 Ω
3. At 90 °C: R = 0.1078 × (1 + 0.00393 × 70) = 0.1374 Ω

Worked example: short-circuit withstand

A fault of 10 kA is cleared in 0.2 s.

1. Copper with XLPE (k = 143): S ≥ 10000 × √0.2 / 143 = 31.27 mm², so use 35 mm²
2. Copper with PVC (k = 115): S ≥ 10000 × √0.2 / 115 = 38.89 mm², so use 50 mm²

Copper resistance by size

These values come from the resistivity above. Cable data sheets give slightly higher figures because the standard limits for stranded conductors include an allowance, so use the data sheet for the final voltage-drop check.

Frequently asked questions

What decides the final cable size?

The largest of three results: the current capacity after correction, the voltage drop at the load, and the short-circuit withstand at the fault level. Check all three.

Why does grouping reduce the current rating?

Cables run close together heat each other, so each one can carry less current before the insulation reaches its limit.

Why use the resistance at the operating temperature?

Resistance rises with temperature, about 27% for copper at 90 °C compared with 20 °C. A voltage-drop check with the cold value is optimistic.

Where do the standard sizes come from?

They are the preferred sizes of IEC 60228, such as 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240 and 300 mm². Always round up to the next one.

Related

Cable Size CalculatorCable Derating CalculatorVoltage Drop FormulasWire Gauge ConverterThree-Phase Power FormulasPower Factor and the Power TriangleAC Circuit Formulas: Reactance and ImpedanceTransformer Formulas: Current and Fault LevelInduction Motor FormulasLighting Formulas: Lux, Lumens and CandelaBattery Formulas: Capacity and RuntimeSolar PV Formulas: Array Size and StringsCapacitor Formulas: Energy and RC Time ConstantEarthing Formulas: Earth Rod and Fault LoopEnergy and Cost Formulas: kWh and PaybackGenerator Formulas: kVA, Current and FuelUPS Formulas: kVA, DC Current and BatteryHarmonics Formulas: THD and True Power FactorShort-Circuit Formulas: Fault Level by MVAUnbalance Formulas: Voltage and Neutral CurrentResistor Formulas: Series, Parallel, DividerMotor Starting Formulas: DOL, Star-DeltaCircuit Breaker Formulas: Rating and TripCooling Formulas: Airflow and Heat LoadHeating Formulas: Energy and Heater PowerPer-Unit Formulas: Base Values and ImpedanceLED Formulas: Resistor Value and PowerConduit Fill Formulas: Percent Fill and SizeLightning Protection Formulas: Rolling SphereTransformer Efficiency and Regulation FormulasPump Formulas: Hydraulic, Shaft and Motor PowerFan Formulas: Air Power and Affinity LawsInductor Formulas: Energy and L/R Time ConstantRMS, Peak and Average Value FormulasResonance Formulas: Frequency, Q, BandwidthMotor Efficiency Formulas: Input and SavingsDemand, Load and Diversity Factor FormulasCable Tray Fill Formulas: Area and Cable CountConductor Resistance Formulas and TemperatureTransmission Line Formulas: Drop and LossesStar-Delta Conversion Formulas for Resistors4-20 mA Loop Formulas: Scaling and ResistorCable Loss Formulas: Power and Annual CostOp-Amp Formulas: Inverting and Non-Inverting555 Timer Formulas: Frequency and Duty CycleThévenin and Norton FormulasWheatstone Bridge Formulas: Balance and OutputConductor Force Formulas: Short-Circuit ForcesCT Burden Formulas: Lead Resistance and VAGear and Belt Drive Formulas: Speed and TorqueSkin Effect Formulas: Skin DepthRC Filter Formulas: Cutoff Frequency and GainRectifier Ripple Formulas: Capacitor FilterBuck and Boost Converter Formulas: Duty CycleHeat Sink Formulas: Junction TemperatureBattery Pack Formulas: Series and ParallelMotor Acceleration Time FormulasZener Regulator Formulas: Series ResistorBJT Bias Formulas: Voltage Divider BiasPt100 RTD Formulas: Resistance and TemperatureNTC Thermistor Formulas: Beta EquationFusing Current Formulas: Wire Fuse EstimateFlywheel Formulas: Stored EnergyLinear Regulator Formulas: Power and EfficiencyMOSFET Loss Formulas: Conduction and SwitchingRelay Coil Formulas: Current and ResistorTransformer Inrush Current FormulasBattery Charge Time FormulasWind Turbine Power Formulas: Betz LimitDetuning Reactor Formulas: Capacitor BanksTransformer Tap Changer FormulasCable Pulling Tension FormulasInsulation Resistance Formulas: PI and DARPower Transfer and Power Angle FormulasSolar Panel Temperature Derating FormulasVoltage Change and Flicker FormulasSoft Starter and VFD Sizing FormulasEarth Fault Loop and RCD FormulasBattery Internal Resistance FormulasBusbar Size and Short-Circuit FormulasADC Resolution and Sampling FormulasCapacitor Switching Inrush FormulasCable Charging Current FormulasSolar DC to AC Ratio FormulasMeasurement Uncertainty FormulasParallel Transformer Load Sharing FormulasPeukert Law and Battery Runtime FormulasCapacitor Discharge Time FormulasHydraulic Power and Cylinder Force FormulasThermocouple Voltage FormulasTransformer Vector Group FormulasPower Supply Hold-Up Time FormulasHoist and Lift Power FormulasCompressor Power FormulasRectifier Bridge Sizing FormulasPCB Trace Width and Current FormulasHeat Pump COP FormulasSound Level and dB Addition FormulasDuty Cycle and RMS Load FormulasSupercapacitor Energy FormulasStep and Touch Voltage FormulasContactor Sizing FormulasInverter-Fed Motor Cable FormulasPneumatic Cylinder Force and Air UseBusbar Temperature Rise FormulasMotor Temperature Rise FormulasBattery Storage Round-Trip EfficiencyThermal Time Constant FormulasSolar Charge Controller Sizing FormulasPoint Illuminance FormulasGenerator Droop and Load Sharing FormulasTwo-Wattmeter Method FormulasVFD Braking Resistor FormulasLoad Bank Test FormulasTransformer Cooling Class Rating FormulasEnergy Meter Multiplier FormulasOvercurrent Relay Curve FormulasSingle-Tuned Harmonic Filter FormulasCable Sheath Circulating Current FormulasDifferential Protection Slope FormulasEarth Electrode Spacing FormulasSolar Array Row Spacing FormulasDC Lighting Voltage Drop FormulasTransformer Loss of Life FormulasMotor Start Voltage Dip in the Cable FormulasNeutral Earthing Resistor FormulasCable I²t Withstand Check FormulasMotor Locked-Rotor Code Letter FormulasSynchronous Speed and Pole FormulasBattery C-Rate and Cycle Life FormulasEV Charging Time FormulasConveyor Belt Power FormulasParallel Plate Capacitor FormulasSolenoid and Coil Inductance FormulasPower Factor Correction Payback FormulasTransformer Through-Fault Current FormulasTransformer EMF Equation FormulasDelta-Star Resistor Conversion FormulasCurrent Shunt Resistor FormulasSolar Energy Yield and Degradation FormulasElectrolysis and Faraday’s Law FormulasAGL Series Circuit Load and CCR Sizing FormulasAGL Maximum Fittings on a CCR FormulasAGL Isolating Transformer FormulasAGL CCR Input Power and Energy FormulasAGL Brightness Step FormulasAGL Lamp Life FormulasComplex Number Formulas: Polar and RectangularPhasor Addition Formulas: Sum and DifferencePercentage Error Formulas for MeasurementsTrigonometry Formulas for Electrical EngineersMean and Standard Deviation FormulasQuadratic, Logarithm and Power FormulasPercentage, Ratio and Rounding FormulasProbability, Combinations and Binomial FormulasConversion Centre