Voltage Drop Calculation Guide — Formulas, Methods & Limits

Voltage drop is the reduction in voltage along a cable caused by the cable's electrical impedance. When current flows through a conductor, the cable's resistance and reactance consume a portion of the supply voltage, delivering less voltage to the load than is available at the source.

Excessive voltage drop causes real problems: motors lose torque and overheat, lighting dims or flickers, electronic control equipment malfunctions, and energy is wasted as heat in the cable. Every major electrical standard sets maximum permissible limits, and voltage drop verification is a mandatory step in any cable sizing calculation.

This guide covers the fundamental voltage drop formulas, the practical mV/A/m tabulated method used by most standards, allowable limits across AS/NZS 3008, BS 7671, IEC 60364, and NEC, and a complete worked example demonstrating the calculation process.

The voltage drop across a cable depends on the current, cable length, and cable impedance. The impedance has two components: resistance (R) which dissipates energy as heat, and reactance (X) which stores and releases energy in the cable's magnetic field.

Single-phase AC circuits:

ΔV = 2 × I × L × (R×cosφ + X×sinφ) / 1000 — (Eq. 1)

Three-phase AC circuits:

ΔV = √3 × I × L × (R×cosφ + X×sinφ) / 1000 — (Eq. 2)

DC circuits:

ΔV = 2 × I × R × L / 1000 — (Eq. 3)

Where:

The factor of 2 in the single-phase and DC formulas accounts for the go-and-return path (current flows out on the active conductor and returns via the neutral or negative conductor). The √3 factor in the three-phase formula arises from the 120° phase displacement between the three conductors.

Rather than looking up separate R and X values and applying the full impedance formula, most standards provide pre-calculated voltage drop values in millivolts per ampere per metre (mV/A/m). This tabulated approach combines resistance, reactance, and the circuit configuration (single-phase or three-phase) into a single lookup value.

Simplified voltage drop formula:

ΔV = mV/A/m × I × L / 1000 — (Eq. 4)

The mV/A/m values are tabulated for specific cable types, sizes, and installation conditions. The key voltage drop tables in each standard are:

Most tables provide separate columns for resistive (R) and reactive (X) components, allowing you to calculate the effective impedance at any power factor:

mV/A/m = mV/A/m_R × cosφ + mV/A/m_X × sinφ — (Eq. 5)

Some tables (notably AS/NZS 3008 Tables 35–42) provide a single combined column for unity power factor (cosφ = 1), which is conservative for most loads since resistive voltage drop dominates at typical cable sizes.

Each electrical standard specifies maximum permissible voltage drop limits, typically expressed as a percentage of the nominal supply voltage. These limits represent the maximum acceptable voltage loss between the origin of the installation and the point of utilisation.

In the NEC, the 3% and 5% values are informational notes (not enforceable requirements), but they are universally adopted as best practice. Local authorities having jurisdiction (AHJ) may enforce them as requirements.

For installations with a sub-distribution board, the total voltage drop is split between the feeder (origin to sub-board) and the final circuit (sub-board to load). A common design rule is to allocate half the total budget to each section — for example, 2.5% feeder + 2.5% final circuit = 5% total under AS/NZS 3000.

Several factors influence the magnitude of voltage drop in a cable installation:

• Cable length: Voltage drop is directly proportional to length. Doubling the cable run doubles the voltage drop. This is the single most significant factor for long installations.
• Load current: Voltage drop is directly proportional to current. Higher loads produce proportionally higher voltage drops.
• Conductor cross-section: Larger cables have lower resistance per metre. Doubling the cable cross-section roughly halves the resistive voltage drop.
• Conductor material: Copper has a resistivity of approximately 17.2 nΩ·m at 20°C, while aluminium is approximately 28.3 nΩ·m — about 1.64× higher. Aluminium cables therefore have approximately 64% higher voltage drop than equivalent copper cables of the same cross-section.
• Power factor: At lower power factors, the reactive component of voltage drop becomes more significant. For highly inductive loads (motors, transformers), the reactive voltage drop can be comparable to or exceed the resistive component, particularly for larger cable sizes where reactance is relatively higher.
• Conductor temperature: Resistance increases with temperature. A cable operating at 75°C has approximately 20% higher resistance than the same cable at 20°C. Most tabulated mV/A/m values are given at the cable's operating temperature, not ambient temperature.
• Cable construction: Single-core cables in trefoil formation have different reactance than flat-spaced cables. Steel-wire-armoured (SWA) cables have higher reactance than unarmoured cables due to the magnetic effect of the steel armouring.

Calculate the voltage drop for a three-phase motor circuit with the following parameters:

Step 1: Look up mV/A/m values

From BS 7671 Table 4E4A, Column 3 (4-core XLPE/SWA), for 16 mm²:

• mV/A/m (resistive component, r) = 2.8
• mV/A/m (reactive component, x) = 0.170

Step 2: Calculate effective mV/A/m at load power factor

cosφ = 0.85, therefore sinφ = √(1 − 0.85²) = 0.527

mV/A/m_eff = 2.8 × 0.85 + 0.170 × 0.527 = 2.380 + 0.090 = 2.470

Step 3: Calculate voltage drop

ΔV = 2.470 × 63 × 50 / 1000 = 7.78 V

Step 4: Calculate percentage voltage drop

ΔV% = 7.78 / 415 × 100 = 1.87%

Result: The voltage drop is 1.87%, which is well within the BS 7671 limit of 5% for power circuits. ✓ PASS

For cable runs exceeding approximately 50 metres, voltage drop frequently becomes the governing factor for cable selection rather than current-carrying capacity. This is common in:

• Rural and agricultural installations with long overhead or underground runs
• Large commercial buildings with distant sub-distribution boards
• Industrial plants with motor control centres far from the main switchboard
• Mining and tunnelling installations
• Solar PV string cables running from arrays to the inverter

Strategies to manage voltage drop in long cable runs include:

1. Increase cable size: The most straightforward solution, though it increases cost and may require larger containment systems.
2. Increase supply voltage: Moving from 230/400 V to 415/690 V distribution reduces current for the same power, significantly reducing voltage drop. Common in industrial installations.
3. Relocate the distribution board: Positioning the switchboard closer to the major loads reduces the longest cable run.
4. Use a local transformer: For very long distances, stepping up to medium voltage (e.g., 11 kV) for the cable run and stepping back down at the load end virtually eliminates the voltage drop problem.
5. Power factor correction: Installing capacitors at the motor terminals improves power factor and reduces the reactive component of voltage drop. This is particularly effective for large motor loads.

When voltage drop governs cable size, the resulting cable is larger than needed purely for current capacity. This provides extra thermal margin, which can be beneficial in installations with variable loading or future load growth.

Voltage drop calculations involve multiple lookup steps and factor adjustments that benefit from automation. A reliable calculation workflow should:

• Look up the correct mV/A/m values from the applicable standard's impedance tables
• Apply temperature correction where required
• Calculate voltage drop using the full impedance method (R×cosφ + X×sinφ)
• Compare the result against the applicable standard's limit
• Clearly indicate pass/fail status with the exact percentage and absolute voltage drop
• Document all intermediate calculation steps with specific standard references

Each standard uses different impedance tables and voltage drop limits. Professional tools should handle the correct table selection automatically when switching between AS/NZS 3008, BS 7671, IEC 60364, and NEC.