When a cable runs over a long distance, voltage at the load end is always lower than at the source. If the drop is too large, motors lose torque, instruments give wrong readings, and the cable itself runs hotter than designed.
This guide covers the full calculation procedure for DC, single phase, and three phase circuits, with two worked examples and an interactive calculator for all three circuit types.
Every electrical installation has a maximum allowable voltage drop defined by its applicable standard. IEC 60364 limits voltage drop to 3% for lighting and 5% for other loads. Exceeding these limits is one of the most common commissioning failures in industrial plants.
What Is Voltage Drop and Why It Matters
Voltage drop is the reduction in voltage along a cable caused by the resistance of the conductor. When current flows, the conductor's resistance consumes a portion of the supply voltage before the remaining voltage reaches the load.
This is a direct application of Ohm's Law: voltage lost across a conductor equals the current multiplied by the conductor resistance (V = IR). For a long cable, that resistance is significant enough to matter.
In process plants, the practical consequences of excessive voltage drop include:
- Motors running at lower speed than rated, with reduced torque and higher slip
- Contactor coils that fail to pick up or drop out at incorrect setpoints
- 4 to 20 mA loop powered instruments losing accuracy at the far end of long runs
- Overheating in the cable from power being dissipated as heat
- Nuisance tripping of thermal overloads and contactors. The power factor correction guide covers how reactive current compounds the drop in motor circuits
The Voltage Drop Formula: Three Versions
The correct formula depends on the circuit type. There are three cases: DC, single phase AC, and three phase AC.
For most practical low voltage calculations, the simplified resistive formula is sufficient. For longer runs or inductive loads, the full impedance method is used.
DC Circuits and Resistive AC Loads
For DC circuits and short AC runs where reactance is negligible (power factor close to 1), the formula is:
I = Load current (A)
L = One way cable length (m)
R = Cable resistance per metre (Ω/m), from IEC 60228 or cable datasheet
The factor 2 accounts for both the line conductor and the return (neutral) conductor.
Cable resistance values are published in cable manufacturer datasheets and in IEC 60228. A typical 2.5 mm² copper conductor has a resistance of approximately 7.41 mΩ/m at 20°C, rising to around 9.18 mΩ/m at the maximum operating temperature of 70°C (PVC insulation).
Single Phase AC Circuits
For single phase AC, reactance starts to matter when cable runs exceed roughly 50 m at LV. The IEC and BS 7671 method uses the mV/A/m value from the cable manufacturer's table:
I = Design current (A)
L = One way cable length (m)
1000 = Converts millivolts to volts
Three Phase AC Circuits
For balanced three phase AC circuits, the formula uses the √3 factor because voltage drop appears line to line and the neutral carries no current in a balanced system:
I = Line current (A)
L = One way cable length (m)
R = Conductor resistance per km (Ω/km) from the cable datasheet
1000 = Converts Ω/km to Ω/m
Using mV/A/m method: Vdrop = (mV/A/m × I × L) ÷ 1000 -- the √3 factor is already embedded in the three phase column of the manufacturer's table.
Percentage Voltage Drop: The Compliance Check
The absolute voltage drop in volts is useful for design, but standards limit voltage drop as a percentage of nominal supply voltage. This is the number inspectors check.
| Standard | Circuit Type | Max Allowable Drop |
|---|---|---|
| IEC 60364-5-52 | Lighting | 3% |
| IEC 60364-5-52 | Other loads (motor, heat, etc.) | 5% |
| BS 7671 (public supply) | Lighting | 3% |
| BS 7671 (public supply) | Other circuits | 5% |
| BS 7671 (private supply) | Lighting | 6% |
| BS 7671 (private supply) | Other loads | 8% |
| NEC (NFPA 70) | Branch circuit | 3% recommended |
| NEC (NFPA 70) | Feeder + branch total | 5% combined |
| AS/NZS 3000 (Australia) | General | 5% |
Worked Example 1: Three Phase Motor Feeder (IEC Method)
This is the most common calculation in industrial plants. A 415V three phase motor sits 150 m from the panel, drawing 85 A.
Cable: 25 mm² copper, 3-core PVC, R = 0.780 Ω/km at 70°C (from the manufacturer's datasheet).
R = 0.780 Ω/km at 70°C.Vdrop = 1.732 × I × L × R ÷ 1000Vdrop = 1.732 × 85 × 150 × 0.780 ÷ 10001.732 × 85 = 147.22 → × 150 = 22,083 → × 0.780 = 17,225 → ÷ 1000 = 17.23 VVdrop% = 17.23 ÷ 415 × 100 = 4.15%If the result had exceeded 5%, the next step would be to upsize the cable to 35 mm² (R = 0.554 Ω/km) and recalculate, which would bring the drop down to approximately 2.95%.
Worked Example 2: Single Phase Lighting Circuit
A single phase 230V lighting circuit runs 80 m from the distribution board, carrying 16 A.
Cable: 4 mm² copper, mV/A/m = 11 from the BS 7671 voltage drop table at 70°C.
11 mV/A/m for 4 mm² single phase copper at 70°C.Vdrop = mV/A/m × I × L ÷ 1000Vdrop = 11 × 16 × 80 ÷ 1000 = 14,080 ÷ 1000 = 14.08 VVdrop% = 14.08 ÷ 230 × 100 = 6.12%Upsizing to 10 mm² copper (mV/A/m = 4.4 mV/A/m) gives: 4.4 × 16 × 80 ÷ 1000 = 5.63 V = 2.45%. This is now within the 3% limit.
Copper Conductor Resistance: IEC 60228 Reference Table
Use the 70°C column for PVC insulated cables and multiply 20°C values by 1.30 for XLPE cables at 90°C. For aluminium conductors, multiply copper resistance by approximately 1.64. See the earth conductor sizing guide for IEC 60364 selection rules.
| Cable Size (mm²) | Resistance at 20°C (Ω/km) | Resistance at 70°C (Ω/km) | Typical Use |
|---|---|---|---|
| 1.5 | 12.10 | 15.00 | Lighting, control wiring |
| 2.5 | 7.41 | 9.18 | Power outlets, small loads |
| 4 | 4.61 | 5.72 | Lighting distribution, small motors |
| 6 | 3.08 | 3.82 | Motor feeders up to 5 kW |
| 10 | 1.83 | 2.27 | Motor feeders up to 10 kW |
| 16 | 1.15 | 1.43 | Motor feeders up to 16 kW |
| 25 | 0.727 | 0.780 | Motor feeders up to 25 kW |
| 35 | 0.524 | 0.554 | Motor feeders up to 37 kW |
| 50 | 0.387 | 0.420 | Feeder cables, large motors |
| 70 | 0.268 | 0.332 | Feeder cables, very large motors |
| 95 | 0.193 | 0.247 | Main distribution feeders |
| 120 | 0.153 | 0.196 | Main distribution feeders |
| 150 | 0.124 | 0.159 | Busbar risers and transformer feeds |
Interactive Voltage Drop Calculator
Effect of Cable Length on Voltage Drop
This table shows how voltage drop changes with length for a 415V three phase motor drawing 50 A, using 16 mm² copper cable (R = 1.43 Ω/km at 70°C). It shows the point where upsizing becomes necessary.
| One Way Length (m) | V_drop (V) | V_drop% | Status vs 5% | Action |
|---|---|---|---|---|
| 50 | 6.2 | 1.5% | PASS | No action |
| 100 | 12.4 | 3.0% | PASS | No action |
| 150 | 18.6 | 4.5% | PASS | No action |
| 175 | 21.7 | 5.2% | FAIL | Upsize to 25 mm² |
| 200 | 24.8 | 6.0% | FAIL | Upsize to 25 mm² |
| 250 | 31.0 | 7.5% | FAIL | Upsize to 35 mm² |
| 300 | 37.2 | 9.0% | FAIL | Upsize to 50 mm² |
Voltage Drop in Instrument Cable Runs: A Different Concern
For 4 to 20 mA instrument loops, voltage drop works differently. Long cable runs raise loop resistance, which limits the maximum output voltage a transmitter can develop across the loop.
The maximum loop resistance a transmitter can tolerate is published in its datasheet as a compliance voltage specification. For a transmitter with 17.4V compliance:
The total loop resistance (cable resistance + barriers + DCS input impedance) must stay below this limit. See the electrical calculations guide and the MCB rating calculation article and the short circuit current article for related calculation methods used in the same design workflow.
6 Practical Rules for Keeping Voltage Drop Under Control
Watch: Voltage Drop Calculation Step by Step
Voltage Drop Calculation Questions
External References
- IEC 60364-5-52 -- Wiring Systems: Selection and Erection
- NEC (NFPA 70) -- National Electrical Code, Article 215
What We Learn Today
- V_drop = 2 × I × L × R / 1000 (single phase/DC); factor 1.732 for three phase
- IEC 60364: 3% limit for lighting, 5% for other loads
- Always use resistance at operating temperature -- 70°C for PVC, 24% higher than 20°C
- Enter one way length -- the factor 2 or 1.732 already accounts for both conductors
- Instrument loops check compliance voltage, not percentage voltage drop
- Doubling cable length doubles the drop -- upsize conductor cross section to compensate