Electrical Engineering Calculator

Voltage Drop Calculator

Calculate voltage drop in DC, single-phase and three-phase electrical circuits using conductor resistivity or direct resistance values.

System Configuration

Select system type and calculation method

System Type

Calculation Method

Input Parameters

Metric units (A, m, mm², V, Ω/km)

Load Current (I)

Operating current of the load.

One-way Length (L)

One-way conductor length (not round-trip).

Supply Voltage (V)

Nominal system voltage.

Conductor Material

Cross-Section Area (A)

mm²

Conductor cross-sectional area.

Max Allowed Drop (%)

Typical limit: 3 % (branch) or 5 % (feeder+branch).

Engineering Tip

For motors, always check voltage drop at starting current (typically 5–7 × FLA). A circuit that is acceptable at full load may still fail during motor start-up.

Voltage Drop

7.58V

1.89 % of supply voltage

Voltage at Load

392.42 V

Conductor R

1.094 Ω/km

PASS — Voltage drop is within the allowable limit

Calculated drop is 1.89 % compared with the limit of 3 %.

Governing Formulas

V_d = √3 × I × L × R / 1000

% Drop = (V_d / V) × 100

V_dV

Voltage drop

Load current

One-way length

RΩ/km

Conductor resistance

Supply voltage

Percentage drop

Assumptions & Notes

Resistive approximation (R only)
Balanced three-phase system
Constant conductor temperature
One-way length (not round-trip)

Engineering Code

Reuse the voltage drop calculation in your own engineering workflow.

Python

import math

def voltage_drop(system, I, L, V, R):
    """
    Calculate voltage drop.

    system: 'dc', 'single' or 'three'
    I: current (A)
    L: one-way length (m)
    V: supply voltage (V)
    R: conductor resistance (Ω/km)
    """

    if system == 'three':
        Vd = (math.sqrt(3) * I * L * R) / 1000
    else:
        Vd = (2 * I * L * R) / 1000

    percent = (Vd / V) * 100
    Vload = V - Vd
    return {"Vd_V": Vd, "percent": percent, "Vload_V": Vload}


# Example
R = ((0.0175 / 16) * 1000)  # Ω/km
results = voltage_drop('three', 50, 80, 400, R)
print(results)

MATLAB

function results = voltage_drop(system, I, L, V, R)
    % Voltage drop calculation
    % system: 'dc', 'single', 'three'
    % R in Ω/km, L in m

    if strcmp(system, 'three')
        Vd = (sqrt(3) * I * L * R) / 1000;
    else
        Vd = (2 * I * L * R) / 1000;
    end

    results.Vd = Vd;
    results.percent = (Vd / V) * 100;
    results.Vload = V - Vd;
end

% Example
R = ((0.0175/16)*1000);
r = voltage_drop('three', 50, 80, 400, R);
disp(r);

Excel Formulas

Vd = SQRT(3)*I*L*R/1000
%Drop = Vd/V*100
Vload = V-Vd

Example Calculation

Three-phase system, I = 50 A, one-way length L = 80 m, copper cable 16 mm² (ρ ≈ 0.0175 Ω·mm²/m), supply voltage 400 V:

R = ρ / A = 1.094 Ω/km

V_d = √3 × I × L × R / 1000 = 7.58 V

Voltage Drop % = 1.90 %

Voltage at Load = 392.42 V

Technical Explanation: Voltage Drop in Electrical Circuits

Voltage drop is the reduction in electrical potential that occurs as current flows through the inherent resistance of a conductor. In any practical electrical distribution system, wires are not perfect conductors; they possess a measurable electrical resistance determined by their material, cross-sectional area, and length. When current (I) travels through this resistance (R), Ohm's Law (V = I × R) dictates that a portion of the source voltage is expended simply to push the electrons through the wire. Consequently, the voltage delivered to the load at the end of the circuit is always lower than the voltage at the source.

Calculating voltage drop is a fundamental requirement in electrical engineering. If the voltage supplied to a piece of equipment falls below its rated tolerance, the equipment may malfunction, draw excessive current, or suffer permanent damage. This calculator allows engineers to properly size conductors by verifying that the anticipated voltage drop remains within acceptable code limits.

Governing Formulas and Circuit Types

The mathematical approach to calculating voltage drop depends heavily on the geometry of the power supply (DC, Single-Phase AC, or Three-Phase AC). This calculator utilizes the standard resistive voltage drop formulas:

DC and Single-Phase AC: In these systems, the electrical current must travel from the source to the load along the phase (or positive) conductor, and then return to the source along the neutral (or negative) conductor. Because the current traverses the physical distance twice, the formula incorporates a multiplier of 2:
V_d = (2 × I × L × R) / 1000
Three-Phase AC: In a balanced three-phase system, the power is transmitted across three phase conductors separated by 120 electrical degrees. The return currents cancel out perfectly at the neutral point. The voltage drop across the line-to-line voltage is calculated using the square root of 3 (√3 ≈ 1.732):
V_d = (√3 × I × L × R) / 1000

In the formulas above, I is the load current in Amperes, L is the one-way cable length in meters, and R is the conductor resistance in Ohms per kilometer (Ω/km).

Input Parameters and Conductor Resistance

To accurately predict voltage drop, the resistance of the cable must be established. This calculator allows for two methods:

Resistivity Method: You input the material's specific electrical resistivity (ρ) and the cable's cross-sectional area (A) in mm². The resistance is derived as R = ρ / A. Standard resistivity at 20°C is roughly 0.0175 Ω·mm²/m for annealed Copper, and 0.0282 Ω·mm²/m for Aluminum.
Direct Resistance Method: You input the manufacturer's specified resistance in Ω/km directly. This is the preferred method for professional design, as manufacturer data accounts for stranding classes, alloy compositions, and operating temperatures.

It is critical to enter the one-way length of the circuit. The calculator's internal formulas already account for the return path geometry where applicable.

Engineering Interpretation and Code Compliance

The absolute voltage drop (V_d) is evaluated as a percentage of the nominal supply voltage. Most international electrical codes (such as the NEC in the United States and the IEC globally) strongly recommend specific limits to ensure equipment longevity:

A maximum of 3% voltage drop for individual branch circuits (e.g., from a distribution panel to a specific motor or outlet).
A maximum of 5% total accumulated voltage drop for the combination of the main feeder and the branch circuit (from the utility service entrance to the furthest load).

When the calculated percentage exceeds these thresholds, the engineer must mitigate the issue by increasing the conductor's cross-sectional area. "Upsizing" the cable lowers its resistance, thereby reducing the voltage drop, even if a smaller wire was theoretically capable of carrying the current (ampacity).

Assumptions and High-Power Limitations

This calculator employs the simplified resistive voltage drop approximation. It assumes that the cable's impedance is entirely resistive (Z ≈ R) and ignores both the inductive reactance of the cable (X_L) and the power factor of the load (cos φ).

For small-to-medium electrical installations (cables smaller than 35 mm² or loads with a power factor close to 1.0), this resistive approximation is highly accurate. However, for large industrial feeder cables carrying heavy AC currents, or for circuits feeding highly inductive loads like large induction motors, the inductive reactance of the cable becomes a dominant factor. In those scenarios, engineers must use the exact impedance voltage drop formula:V_d = I × L × (R × cos φ + X × sin φ). Using the simplified resistive calculator for highly reactive loads will slightly underestimate the true voltage drop.

Additionally, this calculator assumes the resistance is static. In reality, wire resistance increases with temperature. If a cable is operating near its maximum thermal ampacity (e.g., 90°C), its resistance will be approximately 25% higher than its 20°C baseline. Professional designs should always use elevated-temperature resistance values when calculating voltage drop for fully loaded circuits.

Practical Engineering Application

Voltage drop calculations are the driving factor in the design of long electrical runs. Common applications include sizing the DC cables that connect distant solar panel arrays to inverters (where minimizing voltage drop directly maximizes revenue generation), sizing the supply lines for agricultural irrigation pumps located far from utility transformers, and ensuring that temporary construction site generators can successfully start heavy electric motors without causing a severe voltage dip (brownout) that trips sensitive control electronics.

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Real-World Engineering Cases

Long Feeder Causing Motor Starting Problems

A 75 kW motor at the end of a 180 m feeder experienced severe voltage drop during start-up. The starting current caused the voltage at the motor terminals to fall below 80 % of nominal, leading to overheating and eventual failure of the starter contactor.

Engineering Lesson

Always check voltage drop under both running and starting (inrush) currents. Motors are especially sensitive to low voltage during acceleration.

LED Lighting Flicker in Commercial Buildings

Several floors of LED panel lights flickered noticeably in the late afternoon. Investigation revealed that the long branch circuits had voltage drops exceeding 4 % under full lighting load, pushing the drivers into unstable operating regions.

Engineering Lesson

Modern electronic loads (LED drivers, switch-mode power supplies) can be more sensitive to voltage drop than traditional loads. Keep branch-circuit voltage drop well within recommended limits.

Frequently Asked Questions

What is an acceptable voltage drop?

Most standards recommend a maximum of 3 % voltage drop for branch circuits and 5 % for the combination of feeder and branch circuit under full load.

Why is there a factor of 2 in the single-phase formula?

The factor 2 accounts for the outgoing and return conductors. Current flows to the load and back, so the total conductor length is twice the one-way distance.

Does this calculator include reactance (X)?

This version uses the resistive approximation (R only). For long cables or high power-factor loads the reactive component can become significant and a more detailed calculation with cable impedance is recommended.

What units should I use?

Current in amperes (A), length in metres (m), cross-section in mm², resistance in Ω/km, voltage in volts (V). Results are given in volts and percent.

Copper or aluminium – which resistivity should I use?

Typical values at 20 °C: Copper ≈ 0.0175 Ω·mm²/m, Aluminium ≈ 0.0282 Ω·mm²/m. For precise work use the manufacturer’s resistance data at the operating temperature.