Long cable runs lose voltage, which makes motors struggle and lights dim. Enter the supply, current, cable length and size to get the voltage drop and the smallest cable that keeps it within limits.
Choose the supply and enter the voltage and current.
Enter the one-way length and choose the cable size and material.
Check the drop against the limit.
Single phase: VD = 2 I L ρ ÷ A
Three phase: VD = √3 I L ρ ÷ A
Current flowing through a long cable loses some voltage to the cable's own resistance. This calculator estimates that voltage drop for copper or aluminium conductors in single-phase or three-phase circuits. You enter the supply voltage, load current, one-way cable length and conductor size in mm², and it gives the drop in volts and as a percentage of supply, tells you whether it is within your allowed limit, and finds the smallest conductor size that would meet it.
In India this comes up constantly: a submersible borewell pump at the end of a long cable, a farmhouse fed from a distant pole, an EV charger in a basement parking or a workshop machine far from the distribution board. Too much drop makes motors overheat and struggle to start and makes lights dim, so electricians and electrical engineers check it before choosing a cable.
1. Note the supply: single phase (typically 230 V) or three phase (typically 415 V between lines).
2. Measure the one-way cable length L in metres from the supply point to the load.
3. Take the resistivity ρ at 20 °C: about 0.0172 Ω·mm²/m for copper and 0.0282 for aluminium.
4. For single phase, VD = 2 × I × L × ρ ÷ A. For balanced three phase, VD = √3 × I × L × ρ ÷ A, with A in mm².
5. Express the drop as a percentage: VD ÷ V × 100.
6. If it is too high, find the minimum size: A = k × I × L × ρ ÷ (limit% ÷ 100 × V), where k is 2 or √3, and choose the next standard size up.
A conductor's resistance is R = ρL ÷ A. It grows with length and shrinks with cross-section, and ρ depends on the metal. Aluminium's resistivity is about 1.6 times copper's, so an aluminium cable needs roughly 1.6 times the area for the same drop. The voltage lost is simply current times the resistance of the conductors carrying it, from Ohm's law, V = IR. Because the drop is proportional to both current and length, long runs of heavy loads need thick cables.
In a single-phase circuit current goes out on the phase wire and returns on the neutral, so the total conductor length is twice the route length, hence the factor 2. In a balanced three-phase circuit the return currents cancel in the neutral. The drop in each line is ILρ ÷ A, and the drop in line-to-line voltage is √3 times that, because line voltages are √3 times phase voltages. That is why the three-phase percentage must be taken on the line voltage, typically 415 V.
The calculator uses resistance at 20 °C only. A cable running at full load may be at 70 °C or more, which raises copper's resistance by about 20%. For larger cables and motor loads, reactance and power factor also affect the drop. The calculation says nothing about heating: a cable can have an acceptable drop and still be too small for the current in its installation method. So also check the current rating, grouping and ambient temperature, and follow the applicable standards.
Mahesh is running a single-phase 230 V feed to a 12 A borewell pump 90 m from his farmhouse meter using a 2.5 mm² copper cable, and wants to stay within a 5% drop.
Voltage drop: 2 × I × L × ρ ÷ A = 2 × 12 × 90 × 0.0172 ÷ 2.5 = 14.861 V
As a percentage: 14.861 ÷ 230 × 100 = 6.46%
Minimum size for the limit: A ≥ 2 × 12 × 90 × 0.0172 ÷ (5% × 230) = 3.23 mm²
Answer: Voltage drop 14.861 V (6.46%); Minimum conductor size 3.23 mm²
Entering the out-and-back length for a single-phase circuit, which doubles the factor of 2 already in the formula.
Using 230 V as the supply for a three-phase line-to-line calculation instead of 415 V.
Ignoring the extra starting current of motors, which briefly causes much larger drops.
Choosing a cable only by voltage drop without checking its current-carrying capacity.
Forgetting to switch the material to aluminium when the cable is aluminium.
Sizing cables for borewell and submersible pumps on farms.
Planning feeders to outbuildings, workshops and EV chargers.
Checking long lighting circuits in warehouses and factories.
Electrical engineering coursework on distribution design.
Troubleshooting motors that run hot or lights that dim on long runs.
What drop is acceptable?
Commonly 3% for lighting and 5% for other loads from the supply point; check your local code.
Does this check cable heating?
No. Also confirm the cable's current rating for the installation method.