Learn how to calculate voltage drop in single-phase and three-phase circuits, interpret the formulas, and apply the limits of NBR 5410.
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Voltage drop calculation determines how much of the voltage available at the source is lost along the conductors before reaching the load. A correct calculation considers design current, circuit length, conductor cross-section and material, resistance, reactance, power factor, and electrical system type.
In direct terms, voltage drop in volts is calculated from circuit impedance and the current flowing through it. The result is then converted into a percentage of nominal voltage and compared with the applicable limits of ABNT NBR 5410.
Simply multiplying current by distance or using a generic table is not sufficient. Single-phase and three-phase circuits use different relationships. Conductor resistance also changes with temperature, and reactance can become relevant in long feeders, larger conductors, low-power-factor loads, and industrial installations.
What is voltage drop?
Voltage drop is the difference between the voltage at the source of a circuit and the voltage that actually reaches the point of utilization while current is flowing.
Every conductor has impedance. Current flow therefore produces a potential difference along the line. The greater the current, length, and impedance, the greater the voltage drop tends to be.
In general terms:
ΔV = voltage at source − voltage at load
The percentage is calculated as:
ΔV% = (ΔV / Vn) × 100
Where:
- ΔV is voltage drop, in volts;
- Vn is the nominal voltage used as reference;
- ΔV% is percentage voltage drop.
Voltage drop is a normal phenomenon. It becomes a problem when it exceeds the design value or compromises load operation.
Are voltage drop, undervoltage, and voltage sag the same thing?
No. These phenomena may produce similar symptoms, but they have different causes and durations.
Circuit voltage drop results from current flowing through conductor impedance. It can be estimated during design and verified in the field.
Undervoltage is a condition in which voltage remains below the expected range for a longer period. Its cause may lie in the utility network, transformers, connections, excessive loading, or the installation itself.
A voltage sag is a temporary reduction, normally associated with faults, starting of large motors, or transient events.
This distinction matters. Increasing conductor cross-section can reduce internal voltage drop, but it does not correct inadequate voltage already present at the point of supply. When the cause is unclear, Power Quality Analysis and Diagnosis helps distinguish supply, internal distribution, and load problems.
What data is required to calculate voltage drop?
Before applying any formula, the actual circuit data must be defined.
Electrical data
- nominal voltage;
- design current;
- single-phase, phase-to-phase, three-phase, or direct-current system;
- power factor;
- load characteristics;
- presence of harmonics;
- steady-state or starting condition.
Conductor data
- material, such as copper or aluminum;
- nominal cross-section;
- route length;
- resistance per unit length;
- reactance per unit length;
- operating temperature;
- physical cable arrangement;
- number of parallel conductors.
System data
- point from which voltage drop is to be accounted for;
- voltage available at the source;
- upstream feeder sections;
- transformer, generator, or UPS involved;
- limits of the supplied equipment;
- planned load expansion.
Resistance and reactance values should preferably come from the technical data for the actual cable and configuration used.
What is the voltage-drop formula?
The formula depends on circuit type and available quantities. When resistance and reactance are given per unit length, the following relationships can be used.
Single-phase circuit or two active conductors
For a phase-to-neutral single-phase circuit or a phase-to-phase load supplied by two conductors:
ΔV = 2 × L × I × (R × cosφ + X × sinφ)
Balanced three-phase circuit
For a three-phase circuit:
ΔV = √3 × L × I × (R × cosφ + X × sinφ)
Direct-current circuit with outgoing and return conductors
When reactance does not apply:
ΔV = 2 × L × I × R
In these expressions:
- L is the one-way circuit length;
- I is the design current;
- R is conductor resistance per unit length;
- X is reactance per unit length;
- cosφ is the power factor;
- sinφ represents the component associated with reactance.
Units must be consistent. If R and X are in ohms per kilometer, L must be expressed in kilometers.
Simplified resistivity formula
For certain applications, particularly short circuits with smaller conductors, an approximation based mainly on resistance may be used:
ΔV ≈ 2 × ρ × L × I / S — circuit with outgoing and return conductors
ΔV ≈ √3 × ρ × L × I / S — three-phase circuit
Where:
- ρ is the resistivity adopted for the material and temperature;
- S is the conductor cross-section.
This approximation should not be applied automatically to every feeder. When reactance, temperature, cable arrangement, or power factor are relevant, the complete formula provides a better representation.
The simplified formula is not universal.
The resistivity approximation can be useful, but it does not replace analysis of resistance at operating temperature, reactance, power factor, and cable configuration when these quantities are relevant.
Should circuit length be counted once or twice?
In the formulas shown, L represents the physical one-way length between source and load.
In single-phase or DC circuits, the factor 2 already represents the outgoing and return path. The length must therefore not be doubled again.
In a balanced three-phase circuit, the √3 factor is used instead of 2.
This is one of the most frequent errors in calculators, spreadsheets, and calculation reports. Entering the total round-trip distance in a formula that already contains the factor 2 doubles the result.
How is three-phase voltage drop calculated?
Consider a three-phase feeder with the following illustrative data:
- nominal voltage: 380 V;
- design current: 55 A;
- one-way length: 70 m, or 0.070 km;
- power factor: 0.90;
sinφ: approximately 0.436;- conductor resistance under the adopted condition: 0.87 Ω/km;
- configuration reactance: 0.08 Ω/km.
Applying the formula:
ΔV = √3 × 0.070 × 55 × [(0.87 × 0.90) + (0.08 × 0.436)]
First, calculate the impedance term:
(0.87 × 0.90) + (0.08 × 0.436) ≈ 0.818 Ω/km
Thus:
ΔV ≈ 5.45 V
The percentage drop is:
ΔV% = (5.45 / 380) × 100
ΔV% ≈ 1.43%
The result for this section is approximately 1.43%. It must, however, be added to the drops in upstream sections from the applicable reference point to the load.
The resistance and reactance values in this example are illustrative. In a design, they must be replaced with data for the actual cable, temperature, and physical arrangement specified.
How are circuits with multiple loads along the route calculated?
When loads are distributed, it is incorrect to apply the total current to the full circuit length if part of that current stops flowing after each branch.
The circuit should be divided into sections. For each section, consider:
- the length of that section;
- the current actually flowing through it;
- the corresponding cross-section and impedance.
Total voltage drop is the sum of the drops in each section:
ΔVtotal = ΔV1 + ΔV2 + ΔV3 + ...
This method applies, for example, to feeders with intermediate switchboards, long lighting circuits, lines with distributed loads, and internal networks in industrial plants.
What are the NBR 5410 voltage-drop limits?
ABNT NBR 5410 establishes limits according to the point from which voltage drop is calculated.
| Reference origin | Limit to point of utilization |
| Secondary terminals of the consumer unit’s own MV/LV transformer | 7% |
| Secondary terminals of the utility transformer when the point of supply is located there | 7% |
| Point of supply for other low-voltage supplies | 5% |
| Output terminals of an on-site generator | 7% |
In addition to these overall limits, the standard requires voltage drop in final circuits not to exceed 4%.
This does not mean that every installation has a universal 4% limit. The 4% value applies to the final circuit. The total limit depends on the reference origin and must include upstream distribution sections.
For certain main lines longer than 100 m, the standard permits a limited increase in cases associated with a transformer or generator. This allowance must be assessed carefully and does not eliminate the limit applicable to final circuits.
The standard also requires the calculation to use the design current, including relevant harmonic components.
The 4% limit does not represent the entire installation.
The maximum drop in the final circuit must be combined with the drop in upstream feeders. The total limit depends on the point of origin defined by NBR 5410.
How should voltage drop be allocated between feeders and final circuits?
NBR 5410 defines maximum limits, but the designer must establish how the available margin will be distributed among the different levels of the installation.
A system may include:
- transformer or point of supply;
- LVMSB;
- distribution boards;
- secondary feeders;
- final circuits;
- internal equipment cables.
Using the entire margin in the first feeders may leave no allowance for final circuits. More robust designs therefore adopt internal criteria for each section and record cumulative voltage drop in the load schedule, calculation report, or circuit spreadsheet.
The allocation should also consider future expansion. A feeder operating close to the limit on day one may become inadequate after new loads are added.
Does power factor affect voltage drop?
Yes. In AC systems, voltage drop depends on the relationship between resistance, reactance, and current phase angle.
As power factor decreases, the reactive component becomes more significant. In lines where reactance is not negligible, this can increase voltage drop.
In addition, for the same active power, a lower power factor requires higher current. This increase in current also raises voltage drop and thermal losses.
Power-factor correction can reduce current and losses in certain sections, but it should not be treated as an automatic substitute for adequate conductor sizing.
Does cable temperature affect the result?
Yes. The electrical resistance of metals increases with temperature.
Using only the resistance specified at 20 °C can therefore underestimate voltage drop when the conductor operates at a higher temperature. The calculation should use resistance corresponding to the service condition or apply the correction specified in the technical documentation.
Operating temperature depends on loading, insulation, installation method, grouping, and environmental conditions. This directly connects voltage-drop calculation to electrical cable sizing.
Do copper and aluminum produce the same voltage drop?
Not for the same cross-section and condition.
Copper and aluminum have different electrical resistances. In general, an aluminum conductor requires a larger cross-section to achieve electrical performance similar to that of a copper conductor.
The comparison should also consider:
- operating temperature;
- terminals and connections;
- physical arrangement;
- reactance;
- initial cost;
- lifecycle losses;
- maintenance.
Simply replacing one material with another while retaining the same cross-section can change voltage drop, current-carrying capacity, and protection coordination.
How is voltage drop calculated during motor starting?
Motor starting must be analyzed separately from steady-state operation.
During starting, current may be several times higher than rated current. Consequently, the temporary voltage drop can affect:
- acceleration torque;
- starting time;
- contactors and control devices;
- other motors;
- lighting;
- electronic equipment;
- source stability.
For motor circuits, NBR 5410 relates sizing to the general steady-state limits and establishes a specific criterion during starting at the starter device, allowing a dedicated assessment according to the application.
The calculation must consider the impedance of the complete circuit, including source, transformer, feeders, and motor. The starting method and possibility of simultaneous starts must also be assessed.
The article Motor Circuit Breaker: What It Is, How It Works, and When to Use It explains the protection and control functions associated with the circuit.
Steady-state operation and starting are different verifications.
A circuit may have acceptable voltage drop during normal operation and still impair motor acceleration or other loads during starting.
How should voltage drop be assessed with a generator or UPS?
Alternative sources have their own impedance and dynamic behavior.
A generator may exhibit more significant voltage variation during load steps or motor starting. A UPS may limit current, transfer to bypass, or operate under specific overload restrictions.
In these systems, cable calculation is only part of the analysis. The following should also be considered:
- source power and impedance;
- voltage regulation;
- overload capacity;
- available short-circuit current;
- load-starting sequence;
- autonomy and battery conditions;
- normal, emergency, and maintenance operation;
- protection selectivity.
In critical installations, Critical and Uninterruptible Power Systems Design integrates cables, sources, distribution, protection, and operational continuity.
What is the relationship between voltage drop and energy losses?
Voltage drop and conductor losses are related to resistance and current.
Active losses can be represented, in simplified form, by:
Plosses = I² × R
Increasing conductor cross-section reduces resistance. This can reduce both voltage drop and operating losses.
ABNT NBR 16819 highlights economic assessment of conductor cross-sections. In certain applications, especially industrial installations with long operating periods, the most economical cross-section may be larger than the minimum required solely by thermal and safety criteria.
Therefore, meeting the maximum voltage-drop limit does not necessarily result in the lowest lifecycle cost.
How can voltage drop be reduced?
The most common measures are:
- increase conductor cross-section;
- reduce feeder length;
- locate transformers and switchboards closer to major loads;
- use a higher distribution voltage where technically applicable;
- improve load distribution;
- correct power factor near the relevant loads;
- reduce high-resistance connections;
- use parallel conductors with controlled current sharing;
- limit simultaneous starts;
- select an appropriate motor-starting method;
- review the distribution architecture.
The best solution is not necessarily to increase every cable size. In some cases, reorganizing switchboards or changing distribution voltage provides a better technical and economic result.
Common errors in voltage-drop calculations
Using power without calculating the correct current
Current depends on voltage, number of phases, power factor, and, for some loads, efficiency.
Confusing one-way distance with round-trip distance
When the formula already includes the factor 2, entering the total length doubles the calculated drop.
Ignoring reactance
A resistive approximation may be inadequate for long feeders, large conductors, and low-power-factor loads.
Using resistance at 20 °C as if it were the operating value
Conductor resistance increases with temperature and can increase the actual result.
Applying 4% as the total limit for every installation
The 4% limit is specific to final circuits. The overall limit depends on the point of origin established by the standard.
Calculating only the last section
The load experiences the cumulative effect of the feeders and final circuit.
Treating low measured voltage as proof of an undersized cable
The cause may be the utility, transformer, connections, imbalance, or transient events.
Ignoring motor starting
A circuit may comply in steady state and still perform inadequately during acceleration.
Trusting a calculator without checking assumptions
Online calculators may use resistivity, temperature, power factor, or length conventions that differ from actual conditions.
How should the calculation be documented in the electrical design?
The result must be traceable. For each relevant circuit, it is advisable to record:
- identification and origin;
- supplied load or switchboard;
- voltage and number of phases;
- design current;
- length of each section;
- material and cross-section;
- adopted resistance and reactance;
- power factor;
- voltage drop in volts;
- percentage drop for the section;
- cumulative drop;
- adopted limit;
- starting condition, where applicable;
- source of the data used.
This information can be included in the load schedule, calculation report, circuit lists, and single-line diagram.
The article Stages of a Low-Voltage Electrical Design shows how calculations connect to design documents.
When is an isolated calculation not enough?
A simple verification may be sufficient for a clearly defined circuit. However, the analysis must be integrated when there are:
- multiple distribution levels;
- on-site transformers;
- generators and UPS systems;
- large motors;
- long distances;
- parallel cables;
- nonlinear loads;
- future expansions;
- low voltage measured in the field;
- selectivity requirements;
- critical processes.
In these situations, the calculation must remain consistent with cable sizing, short-circuit studies, protection, motor starting, power quality, and source capacity.
The Low-Voltage Electrical Design service consolidates these verifications into executable documents and traceable calculation reports.
Voltage drop should be analyzed as part of the system.
In installations with multiple switchboards, alternative sources, motors, and critical processes, the analysis must integrate cables, protection, selectivity, power quality, and operating conditions.
Conclusion
Voltage-drop calculation determines the difference between voltage at the source and voltage available at the load. The result depends on current, length, resistance, reactance, power factor, conductor cross-section, material, and conductor temperature.
The formula must correspond to the circuit type. The different sections must also be added and the cumulative drop compared with the limits of ABNT NBR 5410.
Beyond meeting a maximum percentage, the design should ensure adequate performance, allowance for expansion, and consistency among sources, cables, and protection. In industrial and critical installations, reducing voltage drop can also reduce losses and improve lifecycle operating cost.
Technical references
[1] BRAZILIAN ASSOCIATION OF TECHNICAL STANDARDS. ABNT NBR 5410:2004 — Low-voltage electrical installations. Sections consulted: 6.2.6.1.2, 6.2.7, 6.5.1.2.1, 6.5.1.3.2 e 6.5.1.3.3. Rio de Janeiro: ABNT, 2004.
[2] BRAZILIAN ASSOCIATION OF TECHNICAL STANDARDS. ABNT NBR 16819:2020 — Low-voltage electrical installations — Energy efficiency. Section consulted: 6.5 — Conductor losses. Rio de Janeiro: ABNT, 2020.
[3] Before applying the standard in a design, confirm the current edition and any amendments in the official ABNT Catalog.
Frequently asked questions
Define the design current, one-way length, conductor resistance and reactance, power factor, and circuit type. Calculate the drop in volts, convert it to a percentage of nominal voltage, and compare it with the applicable limit.
For a circuit with two active conductors, ΔV = 2 × L × I × (R × cosφ + X × sinφ) can be used, with consistent units and L representing one-way length.
For a balanced three-phase circuit, ΔV = √3 × L × I × (R × cosφ + X × sinφ) can be used.
The overall limit depends on the reference origin and may be 5% or 7%. In final circuits, voltage drop must not exceed 4%.
In formulas containing the factor 2 or √3, L represents the physical one-way length. The route must not be doubled again.
Yes. It changes the relationship between the resistive and reactive components and also affects the current required to transmit a given active power.
Only when its influence is demonstrably small. In long feeders, larger conductors, and low-power-factor loads, reactance may be relevant.
Yes. Metal resistance increases with temperature, increasing voltage drop. Data compatible with the operating condition should be used.
Divide the route into sections and calculate each section using the current that actually flows through it. Total voltage drop is the sum of the section drops.
Not for the same cross-section and condition. The materials have different resistances and require comparison using technical data and appropriate cross-sections.
Use the current and power factor corresponding to starting and consider the complete impedance of the source and feeders, as well as the starting method and duration.
No. Internal voltage drop results from current in the conductors. Undervoltage may originate in the supply, transformers, connections, or loading and requires diagnosis of the cause.
It reduces resistance and normally reduces voltage drop, but changes to architecture, distribution voltage, switchboard location, or load sequence may be more effective.
No. Assumptions, units, temperature, power factor, reactance, limits, and data for the cable used must be checked.
Because the voltage available at the load reflects losses in all upstream sections from the reference point to the equipment.
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