How to use this calculator
Enter the circuit voltage, current, one-way length and conductor size. Select copper or aluminium and the circuit type.
Inputs
Results
The equation, and the two terms this page leaves out
What is being computed, and the size of what is not.
Voltage drop along a conductor is an impedance problem, not a resistance problem. The general form for a balanced circuit is
ΔV = k · I · L · (R′·cosφ + X′·sinφ) k = 2 for DC and single-phase, √3 for balanced three-phasewhere R′ and X′ are resistance and reactance per unit length and L is the one-way route length. The factor of 2 on a single-phase circuit accounts for the return conductor; the √3 on a three-phase circuit is the line-to-line relationship, not a third conductor — a frequent source of error when the two are mixed up.
Conductor resistance is temperature dependent:
R₂₀ = ρ₂₀ / A R(T) = R₂₀ · [1 + α(T − 20)]with ρ₂₀ = 1.724 × 10⁻⁸ Ω·m and α = 0.00393 /K for annealed copper, 2.826 × 10⁻⁸ Ω·m and 0.00403 /K for aluminium. Running a copper conductor at its 70 °C rated temperature rather than 20 °C raises its resistance by 20%; at 90 °C, by 28%.
What the calculator above does: it applies temperature correction and computes ΔV = k·I·L·R(T)·cosφ — the resistive term only. It has no reactance input. For small conductors that is a good approximation; for large ones it is not, and the next two sections quantify when the difference starts to matter.
Worked example: a 120 m three-phase submain
400 V, 80 A, copper, power factor 0.85, conductors at 70 °C.
A 400 V three-phase submain feeds an 80 A load 120 m away. Trial size 35 mm² copper, power factor 0.85 (so sinφ = 0.527), conductors assumed at their 70 °C operating temperature. For a 35 mm² multicore LV cable the reactance is about 0.08 Ω/km.
R₂₀ = 1.724×10⁻⁸ / 35×10⁻⁶ = 0.493 Ω/km → R₇₀ = 0.493 × 1.197 = 0.589 Ω/km ΔV = √3 × 80 × 0.120 × (0.589×0.85 + 0.080×0.527) = 9.03 V → 2.26%Now the same circuit with each refinement removed in turn:
| Method | ΔV | % of 400 V | Relative to full calculation |
|---|---|---|---|
| R at 70 °C, with reactance | 9.03 V | 2.26% | 100% |
| R at 70 °C, no reactance (this calculator) | 8.33 V | 2.08% | 92% |
| R at 20 °C, with reactance | 7.66 V | 1.92% | 85% |
| R at 20 °C, no reactance | 6.96 V | 1.74% | 77% |
Every omission runs the same way: it makes the cable look better than it is. Taking the bottom row and comparing it against a 2% internal design target would pass a circuit that actually sits at 2.26%. Neither error is large on its own; together they are 23%, and they are both non-conservative.
Two further points this example does not show. Real stranded cable resistance runs roughly 5–10% above the ρ/A figure because of the lay of the strands — manufacturer or standard tabulated values are preferable to the ideal calculation where the margin is tight. And the load current here is the design current; for a continuous load a code may require the circuit to be assessed at 125% of it.
When reactance stops being negligible
Cable reactance is roughly constant with size. Resistance is not.
For LV multicore cables the reactance per unit length sits near 0.07–0.09 Ω/km almost regardless of conductor area — it is set by conductor spacing and geometry, not by cross-section. Resistance, meanwhile, falls in inverse proportion to area. So the X/R ratio climbs steadily with cable size:
| Copper conductor | R at 70 °C | X (typical multicore) | X / R | Reactance contribution at pf 0.85 |
|---|---|---|---|---|
| 2.5 mm² | 8.25 Ω/km | 0.08 | 0.01 | negligible |
| 16 mm² | 1.29 Ω/km | 0.08 | 0.06 | under 4% |
| 35 mm² | 0.589 Ω/km | 0.08 | 0.14 | about 8% |
| 95 mm² | 0.217 Ω/km | 0.08 | 0.37 | about 19% |
| 185 mm² | 0.112 Ω/km | 0.08 | 0.72 | about 32% |
| 240 mm² | 0.086 Ω/km | 0.08 | 0.93 | about 37% |
| 400 mm² | 0.052 Ω/km | 0.08 | 1.55 | about 49% |
Reactance overtakes resistance somewhere around 240–300 mm². Above that point a resistance-only calculation is not an approximation, it is half the answer — and the error grows worse as power factor falls, because the reactive term scales with sinφ. At pf 0.7 the reactive contribution on a 240 mm² run is larger again.
Practical boundary: use the resistance-only result up to roughly 95 mm² / 3/0 AWG and at power factors above 0.9, where the omission is a few percent. Beyond that, take R and X from the cable manufacturer's data or from the tabulated (r, x) values in IEC 60364-5-52 Annex G or NEC Chapter 9 Table 9, and compute the impedance drop properly. Note also that increasing conductor size above the crossover buys progressively less voltage-drop improvement — paralleling smaller cables or raising the distribution voltage becomes the better move.
What counts as too much drop
The headline figures, and the widely misunderstood status of the American ones.
| Framework | Lighting | Other uses | Status |
|---|---|---|---|
| NEC (US) — branch circuit | 3% | 3% | Informational note, not a requirement |
| NEC (US) — feeder + branch total | 5% | 5% | Informational note, not a requirement |
| BS 7671 (UK), public LV supply | 3% | 5% | Appendix 4, from origin of installation |
| IEC 60364-5-52, public LV supply | 3% | 5% | Annex G recommendation |
| IEC 60364-5-52, private supply | 6% | 8% | Annex G recommendation |
The NEC point is worth dwelling on, because it is misquoted constantly. NEC 210.19(A) and 215.2(A)(1) place their voltage-drop figures in informational notes, which Article 90 states are not enforceable as Code requirements. They are good engineering practice and most specifications adopt them, but a circuit exceeding 3% is not by itself a Code violation in general-purpose work. Some articles do impose mandatory limits for specific applications — sensitive electronic equipment, fire pumps and certain PV circuits among them — and a project specification or local amendment can make the 3%/5% figures contractual. Check which applies before arguing either way.
BS 7671 and IEC 60364 are stated differently: the limit applies from the origin of the installation to the point of use, so the distribution drop and the final-circuit drop share one budget. Spending 4% on a long submain leaves 1% for everything downstream of it.
Why the limit exists at all
- Equipment tolerance. Motors are the binding case. Torque varies with the square of terminal voltage, so a 10% drop is a 19% torque loss — a motor that starts marginally at nominal may not start at all at the end of a long run, and will draw more current trying.
- Energy. The drop is dissipated as heat in the cable. The I²R loss figure in the results panel is that waste, continuously, for the life of the installation. Over a long run it frequently justifies the next conductor size on operating cost alone.
- Headroom. The supply itself varies. European LV distribution is nominally 230/400 V with a tolerance of +10%/−10% (EN 50160); if the supply is already low, your drop sits on top of that, not within it.
What this calculation does not check
- Ampacity. A conductor can pass the voltage-drop check and still be thermally undersized, or vice versa. Short runs are almost always ampacity-governed; long runs are almost always voltage-drop-governed. Both must pass — see cable ampacity and derating.
- Short-circuit withstand. The adiabatic check S ≥ √(I²t)/k is a separate and sometimes governing constraint, handled on the cable sizing page.
- Protective-device coordination and earth-fault loop impedance. Disconnection times depend on loop impedance, which the same conductor length drives. A cable that satisfies voltage drop can still fail the disconnection-time requirement.
- Harmonics and neutral loading. Non-linear loads put triplen harmonics in the neutral, which can carry more current than the phases. The √3 three-phase form assumes a balanced sinusoidal system and does not apply.
- Starting and inrush. This is a steady-state calculation. Motor starting current of 6–8 × full load at a poor power factor produces a momentary drop far larger than the running figure, and voltage dip rather than running drop is often what sets the cable.
- Skin and proximity effect. Significant above roughly 150 mm² at 50/60 Hz, and already folded into tabulated AC resistance values — which is another reason to prefer them over ρ/A at large sizes.
Frequently Asked Questions
Practical questions about assumptions, inputs, interpretation and limitations.
Enter the one-way route length. The calculator applies the appropriate current path for DC, single-phase AC and balanced three-phase calculations.
There is no single universal value. Allowable or recommended voltage drop depends on the installation, circuit purpose and governing electrical rules or project standard.
Copper and aluminium resistance rises as conductor temperature increases. A warmer conductor therefore produces more voltage drop and I²R loss for the same current.
For a balanced three-phase circuit using line-to-line voltage and line current, the voltage-drop relationship uses the √3 geometry of the three-phase system. Single-phase and DC circuits use the outgoing and return current path.
No. Voltage drop is only one design check. Cable sizing and protective-device selection also require ampacity, installation method, ambient conditions, grouping, fault current, disconnection requirements and applicable electrical standards.
No. It computes the resistive drop with temperature correction, which is the term that dominates for small and medium conductors. For a 35 mm2 copper cable at power factor 0.85 the omitted reactive term is about 8% of the total; by 240 mm2 it is nearly 40%. Above roughly 95 mm2 or 3/0 AWG, use tabulated R and X values and compute the impedance drop.
Generally no. The 3% branch-circuit and 5% total figures appear in NEC informational notes at 210.19(A) and 215.2(A)(1), and Article 90 states that informational notes are not enforceable as Code requirements. They are accepted good practice and most specifications adopt them, but specific articles do impose mandatory limits for certain applications, and a project specification or local amendment can make them contractual.
One-way route length. The factor of 2 in the single-phase and DC formula already accounts for the return conductor. Entering the round trip doubles the answer. The square-root-of-three factor on a three-phase circuit is the line-to-line relationship, not a conductor count, and is not a doubling.
The temperature the conductor will actually run at, not ambient. A cable loaded near its rating sits close to its insulation rating: 70 C for general-purpose thermoplastic, 90 C for thermoset. Using 20 C understates the drop by about 20% for copper at 70 C and 28% at 90 C. Where you need a defensible worst case, use the maximum permitted operating temperature of the insulation.
Because ampacity depends on current and installation conditions while voltage drop depends on current and length. Short runs are almost always ampacity-governed. Beyond a few tens of metres the drop limit takes over and can force a conductor one or two sizes above what thermal rating alone would need. Both checks must pass, along with short-circuit withstand and earth-fault loop impedance.
Only up to a point. Resistance falls in inverse proportion to area but cable reactance stays near 0.07 to 0.09 ohm per km regardless of size, so above roughly 240 to 300 mm2 the reactive term dominates and further upsizing buys very little. At that stage paralleling conductors, improving power factor, or raising the distribution voltage is more effective than a larger cable.
Where this sits in a cable calculation
Voltage drop is one of four checks. A conductor has to pass all of them.
- Step 01Design current Convert the connected load to a design current, apply diversity and the continuous-load uplift, and establish the protective device rating.
- Step 02Ampacity and derating Base ampacity for the conductor and insulation, corrected for ambient temperature, grouping and installation method. The derated value must exceed the device rating.
- Step 03 — this pageVoltage drop Check the drop at the design current over the route length against the applicable limit. On long runs this usually governs and forces a size above the ampacity answer.
- Step 04Short-circuit withstand and final size Adiabatic check against prospective fault current and clearing time, then the governing size across all four checks.
Working the steps out of order wastes effort: sizing for voltage drop before the ampacity answer is known often produces a conductor that then fails the fault check anyway, and the final size is whichever of the four is largest.
Sources
- NFPA 70 (National Electrical Code), Art. 210.19(A) and 215.2(A)(1) informational notes; Art. 90.5 on the status of informational notes; Chapter 9 Tables 8 and 9 for conductor resistance and reactance.
- BS 7671, Requirements for Electrical Installations (IET Wiring Regulations), Appendix 4 — voltage drop limits and tabulated (r, x) values.
- IEC 60364-5-52, Low-voltage electrical installations — Selection and erection of wiring systems, Annex G — recommended voltage drop.
- IEC 60228, Conductors of insulated cables — standard conductor classes and maximum resistance values, which account for stranding.
- EN 50160, Voltage characteristics of electricity supplied by public distribution networks — supply tolerance that the installation drop sits on top of.
- Conductor resistivity and temperature coefficients: annealed copper 1.724 × 10⁻⁸ Ω·m (100% IACS), aluminium 2.826 × 10⁻⁸ Ω·m (61% IACS).