Voltage drop is the loss of electrical potential along a conductor due to its resistance and reactance. The formula is ΔV = 2 × I × L × (R cosφ + X sinφ) ÷ 1000 for single-phase or DC, and ΔV = √3 × I × L × (R cosφ + X sinφ) ÷ 1000 for three-phase. Standards limits: 3% for lighting, 5% for power circuits per IEC 60364-5-52 / BS 7671 and NEC 210.19. Excessive voltage drop reduces motor torque, dims lighting, lengthens heating-element warm-up, and silently destroys electronic loads. This calculator handles DC, single-phase AC, and three-phase AC with full power-factor and reactance compensation.
Reviewed: April 23, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: IEC 60364-5-52 Annex G, NEC Article 210.19, BS 7671:2018+A2:2022.
Electrical safety notice. Voltage drop affects equipment performance and safety; it is not a substitute for ampacity sizing per the same standards. Always verify cable selection against both the voltage-drop limit AND the IEC/NEC ampacity tables (see our cable sizing calculator). Live-circuit work must be performed by a licensed electrician.
What is Voltage Drop?
Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. It is caused by the internal resistance and reactance of the cables over a distance.
By international standards like IEC 60364-5-52 and BS 7671, the voltage drop typically shouldn't exceed 3% for lighting and 5% for other uses.
Where:
- I = Current in Amperes (A)
- L = Length of cable in meters (m)
- mV/A/m = Millivolt drop per ampere per meter (dependent on cable size and material)
The full voltage-drop formulas — DC, single-phase, three-phase
The simplified mV/A/m approach is convenient but only accurate when reactance can be ignored (small cable sizes, unity power factor). For accurate calculations on larger cables, motor circuits, or low power factor loads, use the full impedance formulas below.
Where:
- I = current in amperes (A)
- L = one-way cable length in metres (m)
- R = AC resistance per metre, milliohms/m (varies with cable size, material, conductor temperature)
- X = inductive reactance per metre, milliohms/m (varies with cable size and installation method)
- cosφ = power factor of the load (0.85–0.95 for typical motor loads, 1.0 for purely resistive)
- sinφ = sine of the phase angle = √(1 − cos²φ)
Why √3 in three-phase? In a balanced 3-phase system, the line-to-line voltage is √3 times the line-to-neutral voltage. The factor of √3 (1.732) appears because we're computing voltage drop between two phase conductors rather than between a phase and the neutral.
Why a factor of 2 in single-phase but not three-phase? The factor 2 in the single-phase formula accounts for current flowing OUT through the line conductor and BACK through the neutral — both conductors contribute to the round-trip voltage drop. In a balanced 3-phase system the neutral current is zero (or nearly so), so only the line-conductor drop matters.
Percent voltage drop: ΔV% = (ΔV ÷ Vnominal) × 100. This is what compliance limits (3%/5%) apply to.
Voltage-drop limits by standard
| Standard | Lighting | Power / Other | Total (panel to load) |
|---|---|---|---|
| IEC 60364-5-52 Annex G | 3% | 5% | From origin of installation |
| BS 7671:2018+A2:2022 | 3% | 5% | From origin (UK 18th Edition) |
| NEC 210.19(A) Informational Note | 3% (branch) | 3% (branch) | 5% combined feeder + branch |
| AS/NZS 3000 | 5% | 5% | From point of supply |
| Sensitive equipment (medical, data centres) | 1–2% | 1–2% | Per equipment manufacturer spec |
| Solar PV DC strings (NEC 690.45) | — | 2% recommended (5% maximum) | Affects energy yield |
Why these limits matter: a 5% voltage drop on a 230 V supply is 11.5 V — the load only sees 218.5 V. Most equipment is rated to operate within ±10% of nominal, but performance degrades sharply with sustained under-voltage. Three-phase induction motors lose torque proportional to the SQUARE of voltage, so a 10% under-voltage means 19% torque loss. LED lighting flickers below ~85% nominal voltage. Switching power supplies in computers and electronics lose efficiency and overheat with sustained under-voltage.
Worked example 1 — residential 32 A circuit
Scenario: 230 V single-phase, 32 A continuous load (electric oven), 6 mm² copper PVC cable, 25 m run, power factor 1.0 (purely resistive heating element).
Cable parameters (6 mm² Cu, 70 °C operating): R = 3.08 mΩ/m, X = 0.085 mΩ/m.
= 2 × 32 × 25 × 3.08 ÷ 1000 = 4.93 V
Verdict: 6 mm² cable is acceptable for both ampacity (47 A in conduit) and voltage drop (2.14% < 5%). For lighting circuits with the same parameters but a 3% limit, the 6 mm² would still pass with margin.
Worked example 2 — three-phase motor with low power factor
Scenario: 22 kW, 415 V, 3-phase induction motor, FLC = 39.4 A (efficiency 92%, PF 0.85). 50 m run in 16 mm² copper XLPE cable.
Cable parameters (16 mm² Cu XLPE, 90 °C): R = 1.38 mΩ/m, X = 0.110 mΩ/m.
Power-factor terms: cosφ = 0.85, sinφ = √(1 − 0.85²) = 0.527.
= 1.732 × 39.4 × 50 × (1.173 + 0.058) ÷ 1000
= 1.732 × 39.4 × 50 × 1.231 ÷ 1000 = 4.20 V
The reactance contribution: at PF 0.85, the X × sinφ term contributes 0.058 mΩ/m to the effective impedance — about 5% of the total. For larger cables (50 mm²+) at lower power factor (PF 0.7), reactance can contribute 30–40% of total drop. Ignoring it underestimates voltage drop and can lead to motor under-voltage at startup.
Motor starting transient: the calculation above is for normal running. At motor startup, current can be 6–8× FLC for a few seconds. Voltage drop during starting becomes 6–8× the running drop — here, 8 × 1.01% = ~8%, which would prevent the motor from starting (motors typically need >85% rated voltage to develop starting torque). For motor circuits, our motor starting current calculator handles the transient analysis.
Worked example 3 — long DC solar PV string
Scenario: 600 V DC PV string, 12 A operating current, 6 mm² PV cable, 80 m run from rooftop to inverter.
Cable parameters (6 mm² Cu PV cable): R = 3.08 mΩ/m. Reactance ignored for DC.
Why this matters for solar: NEC 690.45 recommends keeping DC string voltage drop under 2% to maximise energy harvest. Every 1% of DC voltage drop is roughly 1% of lifetime energy lost — over 25 years of a system's operation, that's thousands of dollars per kW installed. For long rooftop-to-inverter runs (>30 m), upsizing the cable from 4 mm² to 6 mm² or 10 mm² usually pays back within 2–5 years through additional energy yield. This is a different optimisation than typical AC voltage drop, where the limit is equipment performance rather than energy yield.
Worked example 4 — Level 2 EV charger on a long garage run
Scenario: 240 V single-phase, 48 A continuous (60 A breaker per NEC 625 continuous-load 1.25× rule), 6 AWG copper THWN, 35 m garage-to-panel run, power factor 1.0. Continuous-load voltage-drop check.
6 AWG copper resistance: approximately 1.61 mΩ/m at 75 °C operating temperature. Reactance negligible at this size.
EV charging is treated as continuous load per NEC 625, so the 1.25 multiplier is already baked into the breaker sizing. Voltage drop on EV circuits is particularly important because chargers reduce output current under low-voltage conditions, slowing charging or refusing to start. The 2.25% here leaves comfortable margin; if the run extended to 60 m the drop would approach 4%, requiring upsizing to 4 AWG.
Common voltage-drop mistakes — six errors that cause real problems
- Ignoring reactance on large cables. The simplified V = I × R formula understates voltage drop on cables 50 mm² and larger by 10–30%. Always use the full impedance formula with sinφ for cables above ~25 mm².
- Forgetting the factor of 2 in single-phase calculations. Current flows OUT through the line and BACK through the neutral; both contribute. Without the factor of 2, you'll calculate half the actual voltage drop.
- Calculating at 20 °C (cold) when the cable runs at 70 °C or 90 °C (hot). Conductor resistance increases ~0.4% per °C above 20 °C. A cable at full load at 70 °C has 20% higher resistance than its cold table value — meaning 20% more voltage drop. IEC and NEC tables typically give R at the operating temperature; verify before using.
- Calculating only normal-running drop for motor circuits. Motor starting can briefly require 6–8× FLC. If your steady-state voltage drop is 4%, your starting voltage drop can be 25–30% — preventing motor start. Always check both conditions.
- Using line-to-neutral voltage in three-phase % calculation. 3-phase voltage drop is line-to-line; the limit % applies to the line-to-line nominal voltage (415 V or 480 V), not the line-to-neutral voltage (240 V or 277 V).
- Treating voltage drop and ampacity as independent. They are linked: a cable that's "just right" for ampacity at maximum derating may have unacceptable voltage drop on long runs, and a cable upsized for voltage drop may need confirmation that the protective device still coordinates with the new (larger) ampacity.
Approximate voltage drop per metre per ampere — copper cables (mV/A/m)
Quick-reference values for typical installations (cosφ = 0.85, conductor temperature 70 °C). Multiply by current (A), length (m), and divide by 1000 for single-phase volts; multiply also by √3 for three-phase.
| Conductor (mm²) | Single-phase (mV/A/m) | Three-phase (mV/A/m) |
|---|---|---|
| 1.5 | 29 | 25 |
| 2.5 | 18 | 15 |
| 4 | 11 | 9.5 |
| 6 | 7.3 | 6.4 |
| 10 | 4.4 | 3.8 |
| 16 | 2.8 | 2.4 |
| 25 | 1.75 | 1.50 |
| 35 | 1.25 | 1.10 |
| 50 | 0.93 | 0.81 |
| 70 | 0.65 | 0.57 |
| 95 | 0.49 | 0.42 |
| 120 | 0.41 | 0.36 |
Aluminium: multiply the copper value by approximately 1.6 (since aluminium has 60% the conductivity of copper).
Where voltage-drop checks matter most
- Long branch circuits — rural homes, large warehouses, agricultural buildings; runs over 30 m almost always need voltage-drop verification.
- Motor circuits — both running and starting must be checked.
- Solar PV systems — DC string drops directly cost annual energy yield (NEC 690.45 recommends 2%).
- EV charging — Level 2 chargers (32–48 A continuous) over a long garage run frequently need cable upsizing for voltage drop.
- Outdoor lighting — landscape and parking-lot circuits regularly span 50–150 m, often making voltage drop the limiting design factor.
- Submarine and underwater installations — very long cable runs at low voltage for marine equipment.
- Data centres — UPS and PDU branch circuits; tight 1–2% drop limits for sensitive server power supplies.
- Medical facilities — NFPA 99 requires tight voltage regulation for patient-care equipment; calculations follow IEC/NEC plus extra margin.
Sources & further reading
- IEC 60364-5-52 — Selection and erection of electrical equipment, wiring systems (Annex G covers voltage-drop requirements).
- NEC (NFPA 70) — National Electrical Code (Article 210.19 informational note on voltage drop).
- BS 7671:2018+A2:2022 — UK wiring regulations (IET Wiring Regulations 18th Edition).
- IEEE 141 (Red Book) — Recommended Practice for Electric Power Distribution for Industrial Plants.
- Hayt, Kemmerly, Durbin. Engineering Circuit Analysis, 9th ed. McGraw-Hill. ISBN 978-0073545516. Chapters 10–11 cover AC steady-state and impedance.
Frequently Asked Questions
By international standards such as IEC 60364-5-52 and BS 7671, voltage drop should typically not exceed 3% for lighting circuits and 5% for other uses (from the origin of the installation). NEC recommends a maximum 3% voltage drop for branch circuits.
The formula for a 3-phase circuit is: Voltage Drop (V) = (√3 × I × L × (R cos Φ + X sin Φ)) / 1000, where I is the current, L is the length of the cable, R is the resistance per km, X is the reactance per km, and Φ is the phase angle.
Voltage drop is the reduction in electrical potential (voltage) as current flows through the resistance of a conductor (cable or wire). It occurs because every conductor has some resistance, and per Ohm's Law (V = I × R), current flowing through resistance causes a voltage loss.
Per IEC 60364, NEC (USA), and most international standards, the maximum allowable voltage drop is 3% for branch circuits and 5% total (from supply to final load). Exceeding these limits causes equipment malfunction, overheating, and energy waste.
Common causes of excessive voltage drop include: undersized cable (too thin for the current load); excessively long cable run; high ambient temperature reducing conductor capacity; loose or corroded connections adding resistance; and load currents higher than originally designed.
To reduce voltage drop: use a larger conductor cross-section (thicker cable); shorten the cable run where possible; increase the supply voltage; use a higher-conductivity material (copper vs aluminium); or split the load across multiple circuits.
The voltage drop formula is: VD = (2 × L × I × R) / 1000, where VD is voltage drop in volts, L is the one-way cable length in metres, I is the load current in amperes, and R is the conductor resistance in Ω/km. The factor of 2 accounts for both the live and return conductor.
Inductive reactance X becomes significant on cables 25 mm² and larger, especially at lower power factors. For a 240 mm² cable at PF 0.7, the X·sinφ term contributes roughly 40% of total impedance. Ignoring reactance underestimates voltage drop for motor and transformer circuits, and can cause motor under-voltage at startup. Always use the full R cosφ + X sinφ formula for cables above ~25 mm².
Conductor resistance increases by approximately 0.4% per °C above 20 °C for copper. A cable at full load at 70 °C (typical PVC operating temperature) has ~20% higher resistance than the cold (20 °C) table value. IEC and NEC ampacity tables usually cite R at the conductor operating temperature; verify before use. For solar PV cables exposed to 60–80 °C rooftop ambient, use the hot-cable resistance.
Motor starting current is typically 6-8× the full-load current (FLC) for direct-on-line starting. Multiply the normal-running voltage drop by the LRA (locked-rotor amps) ratio to get the starting drop. A motor needs at least 85% of rated voltage to develop starting torque — so the starting voltage drop should stay below 15%. If not, consider soft-starter or VFD starting, or upsize the supply cable.
Yes. A 5% voltage drop at a resistive load means 5% of the supplied power is dissipated as heat in the cable rather than doing useful work at the load. Over thousands of operating hours per year, the cumulative energy loss can justify larger-cable capital cost on economic grounds alone. Solar PV DC strings particularly benefit from cable upsizing: every 1% lower voltage drop translates to ~1% more annual energy harvest.
Yes, completely free. No signup, no account, no email required. Every calculation runs in your browser; values are never sent to our servers. Handles DC, single-phase AC, and three-phase AC with full impedance (R and X) per IEC 60364-5-52 and NEC 210.19.