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Cable voltage drop

Calculate the voltage drop of a feeder from the conductor resistance and reactance, corrected for temperature, the maximum length for the allowed drop and whether the conductor size withstands the short circuit.

IEC 60364-5-52annex G, voltage dropIEC 60228class 2 conductor resistanceNECchapter 9, table 8, AWG and kcmil conductorsIEC 60364-4-43adiabatic equation, table 43A

Example cases
Cable voltage drop
E1Circuit and load
V
m
%

In three-phase, the voltage is line to line.

E2Conductor
°C
Ω/km

0.08 if unknown (IEC 60364-5-52).

Ω/km

Optional, at operating temperature.

E3Short circuit
kA
s

Use a decimal point. The calculation runs in your browser and updates as you type.

Percent drop

— %

Voltage drop

— V

Line current

— A

Length for the allowed drop

— m

Size for short circuit

— mm²

Operating R

— Ω/km

Drop versus length
  • Drop with this load
  • Allowed drop
  • Maximum length
The drop grows in proportion to length. The magenta dot is your cable; the gray line marks the length at which the allowed drop is reached.
Short-circuit withstand
  • tmax = (k · S / I)²
  • Your fault
Logarithmic scales. Below the curve the cable withstands the fault; the dot is your current and clearing time. Valid for faults up to about 5 s.

Step-by-step calculation

What it means for your installation

    What it is for

    For a quick check of whether a plant feeder or a substation station service feeder delivers the voltage the equipment needs at the end of the cable, and whether its size withstands the fault current for the time the protection takes to clear. It is useful when adding load, replacing a motor or checking a cable that runs hot.

    How it is calculated

    IEC 60364-5-52annex G

    u = b · (ρ1 · L / S · cos φ + λ · L · sin φ) · IB

    It is the annex G expression, with b = 1 in three-phase (line-to-neutral drop, divided by U0) and b = 2 in single phase. Here the equivalent form with the line-to-line voltage is used, which gives the same percentage: ΔV = b · I · L · (R · cos φ + X · sin φ), with b = √3 in three-phase and b = 2 in single phase, out and back. L is the one-way length, and R and X are per unit length and divided by the number of parallel conductors. The percentage is 100 · ΔV / V.

    Exact drop, for comparison

    Vr = √(Vs² − (I X cos φ − I R sin φ)²) − I (R cos φ + X sin φ)

    The annex G formula is an approximation that holds when the drop is small. The detail also shows the exact phasor drop with a fixed source voltage; both agree within a few tenths of a point while the drop is a few percent.

    Current

    Three-phase: I = P / (√3 · V · cos φ) or S / (√3 · V) · Single-phase: I = P / (V · cos φ) or S / V

    IEC 60228table 2 and annex BNECchapter 9, table 8

    Conductor resistance

    Rθ = R20 · (1 + α20 · (θ − 20))

    For metric sizes, the maximum DC resistance of IEC 60228 class 2 stranded conductors is used. For AWG and kcmil, the values of NEC chapter 9, table 8 for uncoated stranded conductors are used, given at 75 °C and referred to 20 °C with the same coefficient. α20 = 0.00393 /°C for copper and 0.00403 /°C for aluminum (IEC 60228, annex B); they match the coefficients in the table 8 note at 75 °C.

    IEC 60364-4-43434.5.2 and table 43A

    Short circuit

    I² · t ≤ k² · S² → S ≥ I · √t / k

    It is the same adiabatic equation as IEC 60949. k values from table 43A: copper with PVC 115 up to 300 mm² and 103 above, copper with XLPE or EPR 143; aluminum with PVC 76 and 68, aluminum with XLPE or EPR 94. The tool picks the PVC column by size. With parallel conductors, each is assumed to carry an equal share of the current.

    Limits of the calculation

    • It is an estimate, not a study. It assumes a balanced load concentrated at the end of the cable.
    • It does not include skin or proximity effect, which raise the AC resistance of large sizes. If you have the manufacturer's AC resistance, enter it.
    • The actual reactance depends on the cable arrangement: use the manufacturer's values for your installation.
    • The adiabatic equation only holds for faults up to about 5 s. It does not replace the check of the metallic shield of medium-voltage cables.
    • It does not calculate ampacity, which depends on the installation method, grouping and ambient temperature.

    Frequently asked questions

    How is the voltage drop in a three-phase cable calculated?

    With ΔV = √3 · I · L · (R · cos φ + X · sin φ), where I is the line current, L the one-way length, R and X the conductor resistance and reactance per unit length and φ the power factor angle. In single phase the √3 factor becomes 2, because the current flows out and back. The percentage is obtained by dividing by the nominal voltage.

    What is the maximum allowed voltage drop in a cable?

    It depends on the standard, the local code and the contract. IEC 60364-5-52, annex G, recommends values around 3 % for lighting and 5 % for other uses when the installation is supplied from the public low-voltage network, and higher values when it has its own substation. The NEC recommends in an informational note 3 % on the branch circuit and 5 % in total. Large motors usually also need a limit during starting.

    How is a cable checked for short circuit?

    With the adiabatic equation I² · t ≤ k² · S², where S is the cross-section in mm² and k a factor that depends on the conductor and insulation materials (IEC 60364-4-43). For example, k = 115 for copper with PVC and 143 for copper with XLPE or EPR. If the fault energy exceeds what the cable withstands, the insulation is damaged before the protection clears.

    We design your feeders

    We size cables for ampacity, voltage drop and short circuit, and coordinate them with the protection of the plant or substation. The engineering is done remotely, with no travel to your site.

    See design and studiesSee primary engineering

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