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 voltage that occurs as current flows through the resistance (and reactance) of conductors. Excessive voltage drop can cause equipment to malfunction, motors to overheat, and lights to dim.

Most electrical codes recommend limiting voltage drop to 3 % for branch circuits and 5 % for the total of feeder + branch circuit.

How to Use This Calculator

System Type: Select DC, Single-phase AC or Three-phase AC.
Method: Choose Resistivity (material + cross-section) or Direct Resistance (Ω/km).
Current & Length: Enter load current (A) and one-way conductor length (m).
Supply Voltage: Enter the nominal system voltage to obtain percentage drop.

Key Formulas

DC / Single-phase: V_d = 2 × I × L × R / 1000
Three-phase: V_d = √3 × I × L × R / 1000
Resistance from resistivity: R (Ω/km) = ρ / A × 1000

Typical Resistivity Values

Copper (Cu): ρ ≈ 0.0175 Ω·mm²/m
Aluminum (Al): ρ ≈ 0.0282 Ω·mm²/m

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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.