How to Select Cable Size Based on Voltage Drop

When designing an electrical installation, many engineers and electricians focus primarily on the cable's current-carrying capacity (ampacity). However, there is another critical factor that often determines the final cable size: voltage drop. A cable that is perfectly adequate for current may still be too small if the voltage drop along its length is excessive. Voltage drop is the reduction in voltage that occurs as current flows through the resistance of the conductor. If the voltage drop is too high, equipment may not operate correctly, lights may dim, motors may overheat, and sensitive electronics may malfunction.

This article explains how to select the correct cable size based on voltage drop, providing a step-by-step guide and practical examples.

1. What Is Voltage Drop?

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Voltage drop is the decrease in voltage measured across a load compared to the voltage at the source. It is a natural consequence of the resistance of the conductor. As current flows through a cable, some voltage is "lost" as heat due to the resistance of the conductor.

The voltage drop is calculated using Ohm's Law:

Vd = I × R

Where:

• Vd = Voltage drop (volts)

• I = Load current (amperes)

• R = Total resistance of the conductor (ohms)

For a cable of length L (metres) and cross-sectional area A (mm²), with resistivity ρ (Ω·mm²/m), the resistance is:

R = ρ × (2L / A) (for single-phase circuits, because the current travels out and back)

For three-phase circuits, the voltage drop is calculated using:

Vd = √3 × I × (ρ × L / A) (where L is the one-way length)

The voltage drop is typically expressed as a percentage of the nominal supply voltage.

Example: A 230 V single-phase circuit with a voltage drop of 5 V has a drop of 5/230 × 100 = 2.2%.

2. Why Voltage Drop Matters

Voltage drop is not just a theoretical concern—it has real-world consequences:

• Dim lights – Incandescent and some LED lights become noticeably dimmer at lower voltages.

• Motor overheating – Induction motors draw more current at lower voltage, causing overheating and reduced motor life.

• Poor performance – Tools, heaters, and electronic devices may operate less efficiently or malfunction.

• Energy waste – The lost voltage is dissipated as heat in the cables, which is pure energy waste.

• Equipment failure – Sensitive electronics may shut down or be damaged by low voltage.

Voltage drop limits: Most electrical codes (e.g., IEC 60364, NEC, BS 7671) recommend that voltage drop be kept below:

• 3% for branch circuits (lighting, sockets).

• 5% for the total system (feeder + branch).

These limits are not just recommendations; they are often legal requirements for safety and performance.

3. The Voltage Drop Formula: Understanding the Variables

The voltage drop formula is the key to sizing cables based on voltage drop. The formula is:

Vd = I × R

Where:

• Vd = Voltage drop (volts)

• I = Load current (amperes)

• R = Resistance of the conductor (ohms)

For a cable, the resistance is calculated from:

R = ρ × (L / A)

Where:

• ρ = Resistivity of the conductor material (Ω·mm²/m). For copper, ρ = 0.0175 Ω·mm²/m at 20°C; for aluminium, ρ = 0.0282 Ω·mm²/m.

• L = Length of the conductor (metres) — for single-phase, use 2L (out and back); for three-phase, use L (one-way) and multiply by √3.

• A = Cross-sectional area of the conductor (mm²).

Important: The resistance of the conductor increases with temperature. At 90°C (operating temperature for XLPE), the resistance is about 30% higher than at 20°C. This must be accounted for in accurate calculations.

4. Step-by-Step Guide: Selecting Cable Size Based on Voltage Drop

Selecting the cable size based on voltage drop involves the following steps:

Step 1: Determine the Load Current (I)
Calculate the full-load current from the load power (kW or kVA). For three-phase: I = P / (√3 × V × pf). For single-phase: I = P / (V × pf).

Step 2: Determine the Cable Length (L)
Measure the one-way distance from the source to the load. For single-phase circuits, the total conductor length is 2L. For three-phase, it is L (but multiplied by √3).

Step 3: Determine the Maximum Allowed Voltage Drop (Vd_max)

• For a 230 V single-phase circuit with a 3% limit, Vd_max = 230 × 0.03 = 6.9 V.

• For a 400 V three-phase circuit with a 5% limit, Vd_max = 400 × 0.05 = 20 V.

Step 4: Calculate the Required Conductor Resistance (R_max)
Rearrange the voltage drop formula to solve for the maximum allowable resistance:

• For single-phase: R_max = Vd_max / (2 × I)

• For three-phase: R_max = Vd_max / (√3 × I)

Step 5: Determine the Minimum Cross-Sectional Area (A_min)
Using the resistivity of the conductor material, calculate the minimum area:

• A_min = ρ × L / R_max (for three-phase)

• A_min = ρ × 2L / R_max (for single-phase)

Step 6: Select the Nearest Standard Cable Size
Choose a standard conductor size that is equal to or greater than A_min. Also, check that the selected cable size meets the ampacity requirements for the load (it usually will, but this must be verified).

5. Practical Examples

Example 1: Single-Phase Circuit

• Supply voltage: 230 V

• Load current: 20 A

• Cable length: 50 m (one-way)

• Allowable voltage drop: 3% (6.9 V)

• Conductor material: Copper (ρ = 0.0175 Ω·mm²/m)

Calculation:
Total conductor length = 2 × 50 = 100 m

Maximum allowable resistance = Vd_max / (2 × I) = 6.9 / (2 × 20) = 0.1725 Ω

Minimum cross-sectional area = ρ × 2L / R_max = 0.0175 × 100 / 0.1725 = 10.14 mm²

Select: 16 mm² cable (since 10 mm² is slightly below the calculated value, 16 mm² is the nearest standard size that meets the requirement).

Verification:
Using 16 mm²: R = 0.0175 × 100 / 16 = 0.1094 Ω; Vd = 20 × 0.1094 = 2.19 V (0.95%). This is well within the limit. You could also consider 10 mm² cable if it just meets the limit or if the load is non-critical.

Example 2: Three-Phase Circuit

• Supply voltage: 400 V (line-to-line)

• Load current: 50 A

• Cable length: 100 m (one-way)

• Allowable voltage drop: 5% (20 V)

• Conductor material: Copper (ρ = 0.0175 Ω·mm²/m)

Calculation:
R_max = Vd_max / (√3 × I) = 20 / (1.732 × 50) = 0.2309 Ω

Minimum cross-sectional area = ρ × L / R_max = 0.0175 × 100 / 0.2309 = 7.58 mm²

Select: 10 mm² cable (nearest standard size above 7.58 mm²).

Verification:
Using 10 mm²: R = 0.0175 × 100 / 10 = 0.175 Ω; Vd = √3 × 50 × 0.175 = 15.16 V (3.8%). This is within the 5% limit.

Note: Always check that the selected cable also meets the ampacity (current-carrying capacity) requirement for the load. In this example, a 10 mm² cable may also need to be checked for ampacity, depending on the installation method and ambient temperature.

6. The Effect of Temperature on Voltage Drop

The resistance of a conductor increases with temperature. The temperature coefficient of resistance for copper is approximately 0.004 per °C. At 90°C (normal operating temperature for XLPE), the resistance is about 30% higher than at 20°C.

For voltage drop calculations, it is recommended to use the resistance at the maximum operating temperature, which is:

R_t = R_20 × (1 + α × (T - 20))

Where:

• R_t = Resistance at temperature T (°C)

• R_20 = Resistance at 20°C (from tables)

• α = Temperature coefficient (0.004 per °C for copper, 0.0043 for aluminium)

• T = Maximum operating temperature of the cable (e.g., 90°C for XLPE)

Example: A copper conductor with a 20°C resistance of 1 Ω/km will have a resistance of 1 × (1 + 0.004 × 70) = 1 × 1.28 = 1.28 Ω/km at 90°C.

This temperature correction should be applied for accurate voltage drop calculations, especially for long cables and high loads.

7. Voltage Drop in AC Circuits: Reactance

In AC circuits, the voltage drop is not purely resistive—there is also an inductive reactance component (XL) due to the magnetic field around the conductor. This is especially significant for large cables and high currents.

The impedance of the conductor is:

Z = √(R² + XL²)

Where XL = 2πfL (inductive reactance) and L is the inductance of the cable. The voltage drop is then:

Vd = I × Z

For most low and medium voltage cables, the reactance is small compared to the resistance at 50/60 Hz, so the simple resistive formula is sufficient for practical purposes. For very large cables (> 300 mm²) or long circuits, reactance should be considered.

8. Common Mistakes in Voltage Drop Sizing

9. Voltage Drop and Ampacity: Which Governs?

For short cables (less than about 50 m), ampacity (current-carrying capacity) is usually the governing factor. The cable is sized to carry the load current without overheating.

For long cables (more than about 50 m), voltage drop often becomes the governing factor. The cable must be sized not just for current, but to keep the voltage drop within acceptable limits.

In practice: You should calculate both the required size for ampacity and the required size for voltage drop. The larger of the two is the correct cable size for the installation.

10. Quick Reference: Voltage Drop Limits by Application

Always check the specific requirements of your project and the relevant electrical code.

Voltage drop is not just a number—it is a design constraint that affects the performance, efficiency, and safety of an electrical installation. A cable that is oversized for current may still be required to meet voltage drop limits for long runs. Conversely, a cable that is adequate for voltage drop will almost always meet the ampacity requirement.

By understanding the voltage drop formula, applying temperature correction, and following a systematic sizing process, you can select the correct cable size for any application. The extra effort in calculating voltage drop will pay off in years of reliable, efficient, and safe operation. In the world of power cables, voltage drop is not the enemy—it is a parameter to be understood and managed.