Cable & load
Cable details
How it's calculated
Vd = 2 × I × L × (R cos φ + X sin φ)Vd = √3 × I × L × (R cos φ + X sin φ)% = Vd / V × 100R_t = R_ref × [1 + α (t − t_ref)]R and X are divided by the number of runsV_load = V − VdP = n × I² × R × L / runs, n = 2 or 3 conductorsmV/A/m = 2 × R (Ω/km)I is the load current per phase, L the one-way length of the cable, R the conductor resistance per unit length at its operating temperature, X the reactance per unit length and φ the power-factor angle. The length is counted once: the factor 2 (or √3 for three-phase) already accounts for the return path. Resistance comes from the standard tables, which give it at 20 °C for IEC 60228 and at 75 °C for NEC Chapter 9 Table 8, and is corrected to the operating temperature with α = 0.00393 per °C for copper and 0.00403 for aluminium (0.00323 and 0.00330 at the NEC 75 °C reference). The limit check compares the drop with the percentage you choose, and the smallest size is the first size of the same material, in the same standard, whose drop is within it. If you enter power instead of current, the current comes from the power calculator relations.
Worked examples
| Case | Working | Result |
|---|---|---|
| Single-phase 230 V, 20 A, 30 m of 2.5 mm² copper at 70 °C | R = 7.41 × (1 + 0.00393 × 50) = 8.87 Ω/km | 8.87 Ω/km |
| Its drop | Vd = 2 × 20 × 0.030 × 8.87 | 10.64 V, 4.63% |
| Smallest size within 3% (6.9 V) | 4 mm²: 2 × 20 × 0.030 × 4.61 × 1.1965 | 4 mm², 6.62 V |
| Three-phase 400 V, 100 A, 50 m of 35 mm² copper, PF 0.85 | √3 × 100 × 0.050 × (0.627 × 0.85 + 0.08 × 0.527) | 4.98 V, 1.25% |
| 120 V, 16 A, 100 ft of 12 AWG copper at 75 °C (NEC) | 2 × 16 × 100 × 1.98 / 1000 | 6.34 V, 5.28% |
| Three-phase 400 V, 150 A, 120 m of 95 mm² aluminium at 90 °C, PF 0.9 | R = 0.320 × 1.2821 = 0.410 Ω/km | 12.60 V, 3.15% |
Assumptions
- The length is the one-way route length from the supply to the load, not the length of the loop.
- The conductor is taken at its operating temperature, by default the maximum for the insulation (70 °C PVC, 90 °C XLPE or EPR, 60/75/90 °C NEC). That is conservative: a cable that is not fully loaded runs cooler and drops less.
- Resistances are the standard maximum values (IEC 60228 Class 2 stranded, NEC Table 8 stranded uncoated), so a real cable is usually slightly better. NEC Table 8 is DC resistance and ignores the small skin and proximity effects.
- Reactance defaults to 0.08 Ω/km (0.05 Ω/1000 ft), typical of multicore cable and cable in conduit. Single-core cables in trefoil or flat formation differ, so edit it for those. It only matters when the power factor is below 1.
- Balanced, steady loads. Motor starting current, harmonics and unbalanced three-phase loads are not covered.
- The smallest size meets the voltage drop limit only. It does not check current-carrying capacity, short-circuit withstand, protective devices or grouping and ambient derating.
- The 3% and 5% limits are common recommendations (see the FAQ), not a rule for every installation. Your project specification or local wiring rules decide.
- Metric (IEC mm²) and imperial (NEC AWG and kcmil) sizes are different series. Switching between them picks the nearest cross-sectional area.
Frequently asked questions
What is an acceptable voltage drop?
In the UK, BS 7671 (Appendix 4) gives 3% for lighting and 5% for other uses for an installation supplied from the public low-voltage network, with higher figures (6% and 8%) allowed for a private supply. IEC 60364-5-52 also gives informative guidance, and the limit depends on the supply and the country. The NEC informational notes to 210.19 and 215.2 suggest 3% on a branch circuit and 5% for feeder plus branch circuit together, and are recommendations only. Motors need the voltage at their terminals during starting to stay above what the motor and the starter allow, which this calculator does not check.
What is the 3-phase voltage drop formula?
Vd = √3 × I × L × (R cos φ + X sin φ), with I the line current, L the one-way cable length and R and X the resistance and reactance per unit length. For a 3-phase voltage drop calculation, divide Vd by the line-to-line voltage and multiply by 100 for the percentage. Example: 100 A over 50 m of 35 mm² copper at 400 V and PF 0.85 is 4.98 V, or 1.25%.
What is the single-phase voltage drop formula?
Vd = 2 × I × L × (R cos φ + X sin φ). The factor 2 covers the live and neutral (or return) conductors. At power factor 1 this is the same as 2 × I × L × R, which is how the mV/A/m tables are built.
How do I calculate voltage drop for a cable?
Find the load current, enter the one-way length, the cable size and material, and the supply voltage. The calculator takes the resistance from the standard tables, corrects it to the operating temperature, and returns the drop in volts and percent with a check against the 3% or 5% limit. The worked examples above show the arithmetic step by step.
How do I reduce voltage drop?
Use a larger conductor, shorten the route, run conductors in parallel, use copper instead of aluminium, or use a higher supply voltage for the same power, because the same power then needs less current.
Why is the length one-way?
The formula already includes the return path: the factor 2 for DC and single-phase, and √3 for three-phase. Enter the distance from the supply to the load.
How does this compare with the mV/A/m tables?
For a load at unity power factor the drop in mV per ampere per metre is twice the resistance in Ω/km at the operating temperature: for 2.5 mm² copper at 70 °C that is about 17.7 mV/A/m, which agrees with the roughly 18 mV/A/m in the BS 7671 tables for a two-core cable. This calculator works from resistance and reactance, so it also covers other power factors, aluminium and parallel runs.
Can I use the smallest size shown?
Only if it also carries the current safely. The cable must meet current-carrying capacity (heating) limits, which depend on the installation method, grouping and ambient temperature, and be protected by a suitable device. Check it against the cable tables of your wiring code. The cable size calculator combines the voltage drop with a short-circuit check and tells you the rating the cable needs after derating.
How many amps for my load?
Choose "Power (kW)" under "Load given as", or use the power calculator to convert kW, kVA or motor hp to amps first.
Standards and references
- IEC 60364-5-52: selection and erection of wiring systems, with informative guidance on voltage drop.
- BS 7671 (IET Wiring Regulations), Appendix 4: current-carrying capacity and voltage drop.
- IEC 60228: conductors of insulated cables, including the maximum resistance of each size.
- NFPA 70 (NEC) Chapter 9 Tables 8 and 9, and the informational notes to 210.19(A) and 215.2(A).
- IEC 60038: standard voltages.
This calculator estimates voltage drop. It does not size cables for heating, short circuit or protection, and it does not check any code requirement. Have the design checked by a qualified engineer.