Voltage Drop Calculation: Formula, Limits and Cable Sizing

Voltage drop is the voltage lost along a conductor between the source and the load. It is calculated from current, one-way length, conductor resistivity and cross-section — for a three-phase feeder, ΔV = √3 × I × L × ρ / A. The number that decides cable size is not the drop in volts but the drop as a percentage of nominal voltage, compared against the limit the installation is designed to.

What voltage drop actually measures

A conductor is a resistor. Every metre of it dissipates a small amount of energy, and the voltage at the far end is therefore always lower than at the source. That difference is voltage drop, and it is not the same thing as power loss, although the two are related: the energy dissipated in the conductor is the drop multiplied by the current.

The practical consequence is that a cable can be perfectly adequate for current-carrying capacity and still be the wrong cable. A 10 mm² copper feeder may run cool at 100 A and still drop more than 3% over 50 m, which will make a motor start badly, dim lamps at the far end, or push an appliance below its acceptable input range. Ampacity answers “will this conductor survive?”; voltage drop answers “will the load still work?”

The formula, single-phase and three-phase

Both forms use the same four inputs: current in amperes, one-way route length in metres, conductor resistivity in ohm square-millimetres per metre, and cross-section in square millimetres.

• Single-phase (line and neutral): ΔV = 2 × I × L × ρ / A
• Three-phase (line conductors only): ΔV = √3 × I × L × ρ / A
• Percentage: ΔV% = ΔV / V_nominal × 100

The factor of two in the single-phase form is not a safety margin. Current flows out along the line and back along the neutral, so the conductor length carrying current is twice the route length. Three-phase uses √3 instead because the three line currents sum vectorially. Resistivity is 0.0175 Ω·mm²/m for copper and roughly 0.0282 Ω·mm²/m for aluminium at 20 °C — about 60% higher, which is why an aluminium feeder needs a larger cross-section for the same drop.

Worked example: 100 A over 80 m

A 400 V three-phase feeder carries 100 A over a one-way route of 80 m in copper. Using ρ = 0.0175 Ω·mm²/m and A = 35 mm²:

ΔV = 1.732 × 100 × 80 × 0.0175 / 35 = 6.9 V, which is 1.7% of 400 V. That passes a 3% limit comfortably, so 35 mm² is decided by ampacity and derating rather than by drop.

Dropping to 25 mm² on the same route gives 9.7 V, or 2.4%: still inside 3%, but the margin is gone once the conductor runs hot or the route grows. This is the calculation a designer should run before shortening a cable to save cost.

The shorter route is to read the drop per ampere per metre, which is fixed for a given material and cross-section. The table below gives copper values at 20 °C for three-phase 400 V circuits, with the maximum one-way length that keeps drop at 3% while carrying 100 A.

Read the table as a planning aid, not a substitute for a calculation. Resistivity changes with temperature, joints add resistance, and a single-phase circuit needs roughly twice the cross-section for the same length and current.

Temperature turns a passing design into a failing one

The values above are at 20 °C. A conductor carrying its rated current runs far hotter: at 70 °C, copper resistance is about 20% higher than at 20 °C, and at 90 °C it is about 27% higher. A feeder that calculates 2.8% cold will sit above 3% in service.

This is why the honest way to check voltage drop is to use the conductor resistance at the expected operating temperature, not the textbook 20 °C figure. In practice, most designs use tabulated mV/A/m values that already embed a working temperature, which is why a hand calculation and a cable-sizing table can disagree by a few tenths of a percent.

Where voltage drop is ignored and where it dominates

For a distribution board a few metres from its transformer, voltage drop is a rounding error and ampacity decides everything. It dominates in four situations: long rural feeders, low-voltage single-phase runs of more than about 30 m, generator cables where the source is already at nominal, and any circuit feeding a motor whose starting current is five to seven times its running current.

Motor circuits deserve separate treatment. A 5% drop at running current becomes a much deeper dip during a direct-on-line start, and the contactor may chatter or drop out. If the load is a motor, calculate the drop at starting current, not at rated current.

A sizing sequence that avoids rework

1. Establish the actual load current, not the breaker rating. A 63 A breaker on a 40 A load must be sized for 40 A.
2. Pick a cross-section from the ampacity tables for the installation method, ambient temperature and grouping.
3. Calculate voltage drop at operating temperature and compare it with the project limit.
4. If the drop fails, increase the cross-section one step and repeat — do not add a second parallel run unless the route allows it and the protection is rated for the combined current.
5. Check that protection still coordinates with the final cross-section, and that the earth conductor meets the adiabatic requirement.
6. Confirm the lug or terminal accepts the conductor and the stud, then order terminations with the cable.

The last step is the one that delays projects. A 240 mm² conductor needs a lug whose barrel and palm are both correct for the strand class, and a terminal block rated for the current. If you are converting between AWG and metric sizes, use the AWG to mm² conversion chart before choosing the barrel, and if the circuit is a final branch, cross-check the conductor against the 60 amp breaker wire sizing guide.

Terminating the conductor you selected

Voltage drop calculations end in a cross-section, and that cross-section has to be terminated. YOMIN supplies crimp terminations for the sizes these calculations produce, including ROHS-certified two-hole copper cable lugs for bolted joints, DL series aluminium lugs where the conductor is aluminium, and copper cable lugs across the common metric range.

Two details decide whether the joint behaves like the conductor or becomes the weakest point: the barrel must match the strand class and the actual cross-section, and the palm must match the stud and the pad it bolts to. Aluminium-to-copper joints also need a bimetallic interface or a suitable compound, otherwise the joint resistance climbs and the voltage drop you calculated never appears at the load.

Frequently asked questions

What is an acceptable voltage drop?

Design limits vary by code and by project. IEC 60364-5-52 Annex G gives guidance of 3% for lighting and 5% for other uses in public low-voltage distribution, while North American practice commonly applies 3% on a branch circuit and 5% overall. What matters is that the limit is stated before the cable is sized.

Does voltage drop depend on the load or on the cable?

Both. The cable fixes the resistance per metre, and the load fixes the current through it. That is why the same 80 m run can be acceptable at 40 A and unacceptable at 100 A without changing a single cable.

Why is the single-phase formula multiplied by two?

Because the current travels out on the line conductor and back on the neutral, so the length of conductor carrying current is twice the physical route length. Three-phase circuits use the square root of three instead, because the return path is the other two phases.

Can I fix voltage drop with a bigger breaker?

No. Protection does not change the resistance of the conductor. Increasing the breaker rating makes the installation less safe without improving the voltage at the load; the only effective remedies are a larger cross-section, a shorter route, or a higher distribution voltage.