Electrical cable sizing: ampacity, correction factors and voltage drop per NBR 5410

What cable sizing is

Sizing a cable is not picking a size from the load’s rated current: it is finding the smallest commercial cross-section that satisfies two independent criteria at once — current-carrying capacity (ampacity) and voltage drop — within the circuit’s real installation method. The cable must carry the current without the insulation exceeding its allowable temperature and, at the same time, deliver to the load a voltage within a narrow band. The final size is the larger of the two requirements.

The most common field mistake is to size by the raw rated current, skip the correction factors, and later find cables overheating in a crowded conduit or motors starting poorly from undervoltage. The cause is almost always the same: the tabulated ampacity was treated as if it held in the real installation, when it holds in a far more favorable reference condition.

The design current

It all starts with the design current Ib, the current the load actually draws. For a three-phase load defined by active power:

Ib = P·1000 / (√3·V·PF·η)

where P is the power [kW], V the line voltage [V], PF the power factor and η the efficiency. For single-phase, the √3 leaves the denominator and V/√3 is used. When the load is defined by apparent power (kVA) — the typical case for transformers — S enters directly, without PF·η, because the efficiency is already embedded: Ib = S·1000/(√3·V).

The corrected current: why the table ampacity is not enough

The tabulated current-carrying capacity (Iz) applies to a reference condition: 30 °C ambient in air and a single circuit. In the real installation, two things degrade that capacity:

• Ambient temperature above the reference reduces the insulation’s thermal margin — factor Ft.
• Grouping of several circuits in the same conduit, raceway or tray makes the cables heat each other — factor Fa.

In addition, some loads require the conductor to be oversized: a motor at 125% of the full-load current (Imult = 1.25), a capacitor at 135% (IEC 60831). Putting it together, the required ampacity is:

Ibc = (Ib · Imult) / (Ft · Fa)

Since Ft and Fa are below 1, the division raises the requirement. It is this corrected current — not the bare Ib — that must be compared against the ampacity table.

Selecting the section by ampacity

With Ibc in hand, the section is the smallest commercial size whose tabulated ampacity, in the chosen installation method, exceeds the corrected current per circuit (Ibc divided by the number of parallel cables per phase):

S = smallest section with Iz_table(S, method) ≥ Ibc / n_cables

The ampacity table depends on the NBR 5410 reference method (Table 33): A1 and A2 (conduit in a thermally insulating wall, the most severe), B1 and B2 (surface conduit), C (on a wall or unperforated tray), D (buried in ducts), E and F (tray or perforated raceway, the most favorable). The same 70 mm² copper cable carries 149 A in conduit (B2) and 216 A on a perforated tray (F) — about 45% more — because the tray in air dissipates heat far better than the conduit. Getting the method wrong is getting the size wrong.

Material and insulation change the table

The base tables are for copper, EPR/XLPE 90 °C insulation. Two physical adjustments are applied:

• Aluminum: resistivity ≈ 1.649 times that of copper → higher resistance (×1.649) and lower ampacity (×1/√1.649 ≈ 0.779). Aluminum always needs a larger size and produces more voltage drop.
• PVC 70 °C: smaller thermal margin → ampacity derated by √[(70−30)/(90−30)] ≈ 0.816 relative to EPR 90 °C; the table resistance drops slightly (×0.938).

Treating aluminum as copper, or PVC as EPR, is a direct undersize.

The voltage-drop check

Ampacity guarantees the cable does not overheat; voltage drop guarantees the load receives enough voltage. For three-phase:

ΔV% = 100·√3·Ib·L·(R·cosφ + X·sinφ) / V

where L is the length [km], R = Rac and X = XL [Ω/km] are the section’s resistance and reactance, cosφ = PF and sinφ = √(1−PF²). For single-phase, √3 becomes 2 and the reference voltage is V/√3; with n parallel cables, R and X are divided by n. The usual limit is 3% for general loads and 4% for motors (which tolerate more because of starting), per NBR 5410 (6.2.7).

On short circuits ampacity governs; on long circuits the drop grows linearly with length and may force one or more sizes up just to keep the load voltage within the limit — even with ample ampacity.

Coordination with the protection

The chosen section does not stand alone: it must be protected by the breaker. NBR 5410 (6.3.4.1) requires:

Ib ≤ In ≤ Iz and I2 ≤ 1.45·Iz

where In is the breaker rated current, Iz = Iz_table·Ft·Fa·n_cables is the cable capacity already corrected for the installation (not the raw table value, which would overstate the protection) and I2 = 1.45·In is the conventional tripping current (IEC 60898/60947). For a motor, overload is handled by the thermal relay of the motor protector and the breaker only covers the short circuit; in that case Ib ≤ Iz suffices.

Cable composition: phase, neutral and earth

Sizing also delivers the cable notation (KxLc#Ymm²: K cables, L conductors per cable, Y the size):

• Neutral: only the single-phase circuit has a neutral, carrying the full current (equal to the phase). A balanced three-phase circuit carries no sized neutral.
• Protective conductor (PE): follows Table 58 — PE = phase up to 16 mm², 16 mm² between 16 and 35 mm², and half the phase above 35 mm².
• When the neutral or PE share the same size as the phase, they merge into the same conductor group; if smaller, they become separate single-core cables.

Practical design considerations

• Do not skip the correction factors: Ft and Fa are the difference between a cable that lasts and one that cooks its insulation.
• Always check ampacity AND drop: the final size is the larger of the two requirements, and on long runs the drop usually wins.
• Get the installation method right: it sets which table column applies — and the ampacity changes nearly 50% between conduit and tray.
• Coordinate with the protection: Ib ≤ In ≤ Iz closes the loop; without it, the breaker does not protect the cable.

Following this chain — design current, correction factors, selection by ampacity, voltage-drop check and coordination with the protection — yields a cable sizing that is numerically rigorous and stands up to installation reality.