Cable Check

What the check does, the formulas behind it, and what it deliberately leaves out.

1. What this check does

For a cable you have already chosen, RokBench computes the load current, compares the design current per set with the cable's allowable ampacity, and estimates the running and motor-starting voltage drop along the cable. It reports what does not hold up and why. It does not select a cable, although it may point to the smallest size in the same cable family that would pass.

2. Inputs used

Load as amperes, kW, HP or kVA; system voltage; single- or three-phase; power factor; efficiency (kW, HP).
Load class: motor, continuous or non-continuous.
Cable family and size, number of parallel sets, length, installation method and ampacity temperature column.
Design ambient temperature (prefilled, editable) and an optional grouping adjustment factor — or a combined correction factor that replaces both.
Optional: system frequency, motor starting method, starting current multiple and starting power factor, voltage drop limits.

3. Formulas and assumptions

Load current

Three-phase

I = \dfrac{P}{\sqrt{3}\,V\,\mathrm{PF}\,\eta} \qquad I = \dfrac{S}{\sqrt{3}\,V}

V line-to-line. η applies to kW and HP inputs.

Single-phase

I = \dfrac{P}{V\,\mathrm{PF}\,\eta} \qquad I = \dfrac{S}{V}

P = \mathrm{HP} \times 745.7\ \mathrm{W}

Blank efficiency uses the DOE minimum for the rating (10 CFR 431.25).

Design current and ampacity

Design current per set

I_d = \dfrac{k\, I}{N}

k = 1.25 for motor and continuous loads, 1.0 otherwise; N = parallel sets.

Allowable ampacity

I_a = I_{\text{table}} \cdot F_t \cdot F_g

Motor

I_d \le I_a

NEC 430.22: 125 % of motor current against the corrected ampacity.

Continuous, non-continuous

I_d \le I_{\text{table, 75 °C}} \quad\text{and}\quad \dfrac{I}{N} \le I_a

NEC 210.19(A)(1), 215.2(A)(1): 125 % before correction at the termination column (110.14(C)), 100 % after correction.

Temperature factor

F_t = \sqrt{\dfrac{T_c - T_a'}{T_c - T_a}}

NEC 310.15(B)(1). Tc conductor rating, Ta′ design ambient, Ta basis ambient; Fg grouping adjustment.

Voltage drop

Drop

\Delta V = \dfrac{c\, I\, L}{1000\,N}\,\bigl(R\cos\varphi + X\sin\varphi\bigr)

c = √3 three-phase, 2 single-phase; R, X in Ω per 1000 ft per conductor; L in ft.

Percent

\Delta V\% = \dfrac{\Delta V}{V} \times 100

Starting drop: same formula with the starting current and starting power factor.

Symbols

$P$	Real power of the load (kW, or HP converted)	kW
$S$	Apparent power	kVA
$V$	System voltage, line-to-line for three-phase	V
$\mathrm{PF},\ \varphi$	Power factor and its angle, PF = cos φ
$\eta$	Motor or equipment efficiency
$I$	Load current	A
$k$	Continuous or motor load multiplier (1.25 or 1.0)
$N$	Number of parallel sets
$I_{\text{table}},\ I_a$	Table ampacity, allowable ampacity after correction	A
$F_t,\ F_g$	Temperature correction factor, grouping adjustment factor
$T_c,\ T_a,\ T_a'$	Conductor rating, table basis ambient, design ambient	°C
$c$	√3 for three-phase, 2 for single-phase
$L$	One-way circuit length	ft
$R,\ X$	Conductor resistance and reactance	Ω per 1000 ft

Phasor diagram with receiving voltage, current at angle phi, and the I·R and I·X drops. — **Figure 1.** Voltage drop as the projection of I·R and I·X on the sending-end voltage.

Cross-section of a three-conductor cable showing conductors, insulation, shield and jacket; beside it two parallel sets. — **Figure 2.** Three-conductor cable cross-section and parallel sets.

Block diagram: table ampacity times temperature factor times grouping factor gives allowable ampacity; load current times 1.25 divided by sets gives design current; the two are compared. — **Figure 3.** From table ampacity to allowable ampacity, compared with design current.

Three small sketches: cables in conduit, cables in an underground duct bank, and a cable in free air. — **Figure 4.** Installation methods: raceway, underground duct, free air.

R, X and ampacity come from the cable library, which is built from manufacturer data sheets. The source is cited with every result. Rows still under source review are flagged.
R is the AC resistance at the temperature stated in the data (typically the conductor rating). No further temperature adjustment is made, which is conservative for lightly loaded cables.
X is scaled in proportion to frequency when the system frequency differs from the data.
HP with efficiency left blank uses the US federal minimum for a 4-pole enclosed motor of that rating (10 CFR 431.25, 2016 levels); the result says so.
The voltage drop formula is the common approximate form, accurate for the small angle between sending and receiving voltages found in feeder and branch circuits.
The ampacity is corrected for ambient temperature by the NEC equation. The design ambient defaults to 40 °C for raceway and free air and 20 °C (earth) for underground duct — RokBench assumptions you should replace with the site value. “Fill from coordinates” takes the site value from NASA POWER climatology (2001–2020): by default the highest temperature recorded in that period, with the hottest month's average daily high offered as an alternative; both are grid averages and can read low for cities. The basis ambient of the rating is taken as 30 °C for raceway (NEC 310.16), 40 °C for free air and 20 °C for underground duct (NEC 311.60). The rooftop adder of NEC 310.15(B)(2) (33 °C for raceways less than 7/8 in above a roof) is not applied automatically — add it to the ambient you enter.
Two ampacity conditions, as the NEC writes them. Motor circuits: 125 % of the motor current must not exceed the corrected ampacity (430.22). Feeders and branch circuits: 125 % of the continuous load (plus the non-continuous load) must not exceed the table value before correction — for low-voltage raceway the 75 °C column, the usual termination rating (110.14(C)) — and the full load must not exceed the corrected ampacity.
Grouping (more than three current-carrying conductors) is not applied unless you enter an adjustment factor. A combined correction factor, if entered, is used as-is instead of the temperature and grouping factors.
If you do not set voltage drop limits, a default limit is applied and shown with the result. Set the limits your project criteria require.

4. What is NOT checked

Upstream voltage drop and source impedance. Starting drop is the cable drop only, not the voltage at the motor terminals.
Harmonics, phase imbalance, neutral current and cable heating from non-sinusoidal loads.
Short-circuit withstand, overcurrent protection and coordination.
Termination temperature limits beyond an informational note.
Conduit fill, tray fill, pulling tension and bending radius.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

NEC 2023 430.6(A)(1), 430.22 — motor full-load current and conductor sizing
NEC 2023 215.2(A)(1), 310.14, 310.15 — feeder sizing, ampacity and correction
NEC 2023 310.10(G) — conductors in parallel
NEC 2023 110.14(C) — termination temperature
NEC 2023 210.19(A) Informational Note No. 4, 215.2(A)(2) Informational Note No. 2 — voltage drop recommendations

6. Validation cases

Hand-calculated cases run on every change. Published textbook cases will be listed on the Validation page.

7. Known issues and changes

See the Engineering Notes. Try the tool: Cable Check.