Work out the voltage drop on a cable run from its size, length and load, and the smallest cable that keeps it within 3% or 5%.
390.5at the load2.38drop126.1longest run within 3%
Every copper size on this run
Voltage drop, line-to-line
9.519V
2.38% of the 400 V nominal, balanced three-phase, 35 mm² copper.
Check the values to see a result.
Single-phase and DC ΔU = 2 × I × L × (R cos φ + X sin φ)Balanced three-phase ΔU = √3 × I × L × (R cos φ + X sin φ)
100 A in each line over 100 m of 35 mm² copper at 400 V balanced three-phase drops 9.519 V, 2.38% of the supply. The smallest size within 3% is 35 mm².
Tip: 3% and 5% are common design targets, not limits. Your wiring rules set the limit for each type of circuit.
Voltage drop is the current times the cable’s resistance and reactance over the route length, counted twice on a single-phase or DC circuit and multiplied by √3 on a balanced three-phase circuit. The calculator works it out for a standard IEC 60228 cable size or for the resistance and reactance the manufacturer states, and names the smallest standard size that keeps the run within 3% and within 5%.
ΔU = 2 × I × L × (R cos φ + X sin φ)
Current flows out on the line and back on the neutral, so the route length counts twice. L is the one-way route length in km, R and X are per conductor in Ω/km, and cos φ is the power factor.
ΔU = √3 × I × L × (R cos φ + X sin φ)
This is the drop between lines. A balanced load puts no current in the neutral, and √3 converts the drop in one line to a line-to-line figure.
ΔU = 2 × I × L × R
There is no reactance and no power factor, so the drop is the current times the loop resistance. On a 24 V supply, a 1.2 V drop is already 5%.
ΔU% = ΔU ÷ U0 × 100
Divide by the nominal supply voltage, line-to-line for three-phase. Wiring rules state their limits in this form, from the origin of the installation to the load.
For a standard size, R is the IEC 60228 maximum resistance at 20 °C, corrected to the operating temperature: 70 °C for PVC insulation and 90 °C for XLPE. Copper at 70 °C has 19.6% more resistance than at 20 °C. X is fixed at 0.08 Ω/km for every size, the value the Schneider Electric Electrical Installation Guide gives for use when the manufacturer states none.
A sub-main to a plant room carries 63 A in each line at a power factor of 0.8. It runs 80 m from the main board on 16 mm² copper PVC cable. The drop is 10.03 V, or 2.51% of 400 V. 10 mm² gives 3.93% and 25 mm² gives 1.62%.
The 2.51% comes out of the budget for the whole installation. Final circuits fed from the plant-room board have 2.49% left against a 5% target, and 0.49% against 3% for lighting.
Voltage drop, line-to-line 10.03 V Open in the calculator
A 15 kW pump motor at 400 V, 92% efficient with a power factor of 0.85, draws 27.69 A at full load (see the motor full-load current calculator). Direct on line, it starts at 5 to 7 times that current, at a power factor near 0.35. Take 6 times, 166 A.
On 60 m of 10 mm² copper, the running drop is 5.477 V, 1.37%. The starting drop is 14.51 V, 3.63%. Six times the current gives only 2.6 times the drop, because R is multiplied by cos φ, and cos φ falls from 0.85 to 0.35. On 6 mm², the formula gives 23.54 V, 5.89%, but the full cable impedance drop, current times impedance, is about 16% of the supply. The first-order formula holds only up to 10%, so the calculator does not show the voltage at the load.
The 3% and 5% limits apply in steady state, not during a start. Check the starting drop against what the motor and its starter need. The dip that other loads see comes from the cables upstream, so run the sub-main at the starting current too.
Voltage drop, line-to-line 14.51 V Open in the calculator
5 A on 1.5 mm² copper over a 50 m route loses 7.239 V at 70 °C. That leaves 16.76 V at the far end. IEC 61131-2 sets 20.4 V, 24 V less 15%, as the lowest supply for 24 V DC PLC equipment. At 20 °C the drop is still 6.05 V. A cable carrying 5 A runs well below 70 °C, so the true figure is between the two.
4 mm² keeps the far end at 21.24 V, and 10 mm² keeps the drop within 5%. A power supply near the load is usually cheaper than 10 mm² cable.
Voltage drop 7.239 V Open in the calculator
Copper cable to IEC 60228 at a power factor of 0.8 lagging. Multiply by the current in amps and the one-way length in metres, then divide by 1000, for the drop in volts. Single-phase figures count both conductors; three-phase figures are line-to-line.
| Size (mm²) | Single-phase, 70 °C (mV/A/m) | Three-phase, 70 °C (mV/A/m) | Three-phase, 90 °C (mV/A/m) |
|---|---|---|---|
| 1.5 | 23.3 | 20.1 | 21.5 |
| 2.5 | 14.3 | 12.4 | 13.2 |
| 4 | 8.92 | 7.73 | 8.23 |
| 6 | 5.99 | 5.19 | 5.52 |
| 10 | 3.60 | 3.12 | 3.32 |
| 16 | 2.30 | 1.99 | 2.11 |
| 25 | 1.49 | 1.29 | 1.37 |
| 35 | 1.10 | 0.952 | 1.01 |
| 50 | 0.837 | 0.725 | 0.767 |
| 70 | 0.609 | 0.527 | 0.557 |
| 95 | 0.465 | 0.403 | 0.424 |
| 120 | 0.389 | 0.337 | 0.353 |
| 150 | 0.333 | 0.289 | 0.302 |
| 185 | 0.286 | 0.247 | 0.258 |
| 240 | 0.240 | 0.208 | 0.216 |
| 300 | 0.211 | 0.183 | 0.189 |
IEC 60228 maximum DC resistance per kilometre for plain copper and aluminium conductors. A cable that conforms is at or below these values. IEC 60228 lists aluminium conductors from 10 mm².
| Size (mm²) | Copper, stranded | Copper, flexible | Aluminium, stranded |
|---|---|---|---|
| 0.5 | 36.0 | 39.0 | Not listed |
| 0.75 | 24.5 | 26.0 | Not listed |
| 1 | 18.1 | 19.5 | Not listed |
| 1.5 | 12.1 | 13.3 | Not listed |
| 2.5 | 7.41 | 7.98 | Not listed |
| 4 | 4.61 | 4.95 | Not listed |
| 6 | 3.08 | 3.30 | Not listed |
| 10 | 1.83 | 1.91 | 3.08 |
| 16 | 1.15 | 1.21 | 1.91 |
| 25 | 0.727 | 0.780 | 1.20 |
| 35 | 0.524 | 0.554 | 0.868 |
| 50 | 0.387 | 0.386 | 0.641 |
| 70 | 0.268 | 0.272 | 0.443 |
| 95 | 0.193 | 0.206 | 0.320 |
| 120 | 0.153 | 0.161 | 0.253 |
| 150 | 0.124 | 0.129 | 0.206 |
| 185 | 0.0991 | 0.106 | 0.164 |
| 240 | 0.0754 | 0.0801 | 0.125 |
| 300 | 0.0601 | 0.0641 | 0.100 |
| 400 | 0.0470 | 0.0486 | 0.0778 |
| 500 | 0.0366 | 0.0384 | 0.0605 |
| 630 | 0.0283 | 0.0287 | 0.0469 |
| 800 | 0.0221 | Not listed | 0.0367 |
| 1000 | 0.0176 | Not listed | 0.0291 |
Source: Classification of conductors according to IEC 60228, February 2021
IEC 60364-5-52 Annex G recommends a maximum from the origin of the installation to any load point. From a public LV network, it is 3% for lighting and 5% for other uses. From a private supply, such as a site’s own HV/LV substation, it is 6% and 8%. BS 7671 Appendix 4 uses the same four figures. The NEC gives 3% for a branch circuit and 5% for feeder and branch together, in informational notes that are advisory. The calculator uses 3% and 5% as design targets. Your wiring rules set the limit.
No. The limit runs from the origin of the installation to the load, so the drops of cables in series add. On a balanced three-phase cable, the percentage of line-to-line voltage equals the percentage of line-to-neutral voltage, so a single-phase circuit off a three-phase sub-main adds directly. After the 2.51% sub-main in the first example, a 32 A EV charger 40 m away on 6 mm² copper adds 4.10%, which makes 6.61% in total. On 10 mm² it adds 2.44%, 4.95% in total. The smallest sizes the calculator names assume the whole 3% or 5% is available to one cable.
On small cables, resistance dominates. At a power factor of 0.8, the reactance term is 9% of the drop on 35 mm² copper, 25% on 120 mm² and 40% on 240 mm². At unity power factor it is zero. The fixed 0.08 Ω/km is typical of multicore cable. Single-core cables, and single-core cables laid apart in particular, have a higher reactance. For a large single-core run, the standard-size result is therefore low. Enter the manufacturer’s R and X instead.
It is one of three checks. The cable must also carry the design current in its installation method without exceeding its insulation temperature. Its protective device must also disconnect a fault in the required time. On long runs, 24 V DC circuits and motor circuits, voltage drop often decides the size. On short runs, current-carrying capacity usually decides it.
The calculation assumes one steady current at one power factor. A ZEM at the load end measures the voltage that the load actually receives as its current and power factor change.
