How to Calculate Voltage Drop
Learn the resistance-based voltage drop formulas for DC, single-phase AC and balanced three-phase circuits, with a worked cable example.
What Is Voltage Drop?
Voltage drop is the voltage lost between a source and a load because the conductors and other circuit elements have impedance. In a resistance-dominated cable model, the main variables are current, cable length, conductor area and conductor resistivity.
Step 1: Calculate Conductor Resistance
Here, ρ is conductor resistivity in ohm-metres, L is conductor length in metres and A is conductor cross-sectional area in square metres. When using a value in mm², convert the area to m² inside the equation.
ToolVault converts mm² to m² automatically and can also convert the selected AWG size to an equivalent cross-sectional area.
Step 2: Apply the Circuit Formula
For DC and single-phase circuits, the outgoing and return paths produce a factor of two:
For a balanced three-phase circuit using line-to-line voltage:
Step 3: Calculate Voltage Drop Percentage
The receiving-end voltage is then:
Worked Example: 48 V DC, 20 A, 30 m, 6 mm² Copper
Use copper resistivity of approximately 1.724 × 10⁻⁸ Ω·m at the reference condition.
Resistance per metre = 1.724 × 10⁻⁸ ÷ 0.000006 ≈ 0.002873 Ω/m.
For 30 m one-way, one-conductor resistance = 0.002873 × 30 ≈ 0.08620 Ω.
DC voltage drop = 2 × 20 × 0.08620 ≈ 3.448 V.
Voltage drop percentage = 3.448 ÷ 48 × 100 ≈ 7.18%.
Load-end voltage ≈ 44.55 V.
How Cable Size Changes Voltage Drop
For the same material, current and length, a larger conductor area reduces resistance. Because voltage drop is proportional to resistance in this model, increasing mm² or moving to a larger conductor size generally lowers voltage drop.
Maximum Cable Length for a Target Drop
To solve the equation for length, first determine the maximum voltage drop allowed:
Then:
Required Conductor Area for a Target Drop
For the resistance-only model, the theoretical minimum area is:
This is a voltage-drop constraint, not a final cable-size recommendation.
AWG vs mm²
AWG is a conductor-gauge system; the gauge number decreases as conductor diameter increases. Metric cable sizes use cross-sectional area in mm². ToolVault converts the selected AWG value into area for its resistance calculation, while metric mode accepts the area directly.
Important Electrical Design Limits
Voltage-drop calculations do not replace ampacity, protective-device selection, temperature correction, short-circuit withstand or installation-method checks. AC circuits can also require impedance and power-factor treatment beyond this simple resistance model. Final design should use manufacturer data and the applicable electrical requirements.
Use the Free Voltage Drop Calculator
ToolVault's Voltage Drop Calculator performs these calculations for DC, single-phase and balanced three-phase systems with mm² and AWG options.
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