Voltage Drop Calculator
Calculate voltage drop in single-phase or three-phase copper or aluminium wire runs.
About the Voltage Drop Calculator
Calculates the electrical voltage drop along a conductor run using material resistivity, wire size, circuit phase, current, and distance. This tool calculates both the absolute voltage drop in volts and the percentage loss relative to the supply voltage.
$$ V_d = \frac{k \cdot L \cdot I \cdot \rho}{A} $$
How to use this calculator
- Enter the **One-way wire length** in meters.
- Enter the load **Current** in Amperes (A).
- Enter the **Conductor cross-sectional area** in \(\text{mm}^2\) (e.g. \(1.5\), \(2.5\), \(4\), \(6\), \(10\)).
- Enter the source **Supply voltage** (e.g., \(230\,\text{V}\) for domestic single-phase, \(400\,\text{V}\) for industrial three-phase).
- Select the conductor **Material** (Copper or Aluminium).
- Select the circuit **Phase** (Single-phase or Three-phase).
- Click **Calculate** to see the step-by-step math and percentage drop.
The formula explained
The voltage drop formula computes line loss using Ohm's Law and material properties: \(\delta = \frac{k \cdot L \cdot I \cdot \rho}{A}\).
- k (Phase Factor): - For **Single-phase**, \(k = 2\) because current must travel out through the phase wire and return through the neutral wire. - For **Three-phase**, \(k = \sqrt{3} \approx 1.732\) due to the vector summation of balanced currents in a three-wire system.
- L: One-way length of the cable in meters.
- I: Circuit load current in Amperes.
- \(\rho\) (Resistivity): The electrical resistivity of the conductor material: - **Copper:** \(\approx 0.0172\,\Omega\cdot\text{mm}^2/\text{m}\) at room temperature. - **Aluminium:** \(\approx 0.0282\,\Omega\cdot\text{mm}^2/\text{m}\) (aluminium is less conductive, creating higher drop).
- A: Cross-sectional area of the wire in \(\text{mm}^2\).
Worked Examples
Example 1: Single-Phase Domestic Run
Problem: A \(30\,\text{m}\) copper run feeds a \(16\,\text{A}\) load at \(230\,\text{V}\) using a \(2.5\,\text{mm}^2\) cable. Find the voltage drop.
- Use Single-phase \(k = 2\) and Copper \(\rho = 0.0172\).
- Substitute: \(V_d = \frac{2 \cdot 30 \cdot 16 \cdot 0.0172}{2.5}\).
- Calculate: \(V_d = \frac{16.512}{2.5} \approx 6.60\,\text{V}\).
- Percentage drop: \((6.60 / 230) \times 100 \approx 2.87\%\).
Answer: Voltage drop is \(6.60\,\text{V}\) (\(2.87\%\)), which is within acceptable limits.
Example 2: Three-Phase Industrial Run
Problem: A \(50\,\text{m}\) aluminium run feeds a \(40\,\text{A}\) load at \(400\,\text{V}\) using a \(16\,\text{mm}^2\) cable. Find the voltage drop.
- Use Three-phase \(k = 1.732\) and Aluminium \(\rho = 0.0282\).
- Substitute: \(V_d = \frac{1.732 \cdot 50 \cdot 40 \cdot 0.0282}{16}\).
- Calculate: \(V_d = \frac{97.6848}{16} \approx 6.11\,\text{V}\).
- Percentage drop: \((6.11 / 400) \times 100 \approx 1.53\%\).
Answer: Voltage drop is \(6.11\,\text{V}\) (\(1.53\%\)).
Frequently asked questions
What voltage drop is acceptable?+
Electrical safety codes recommend keeping total drop under 3% for branch circuits, and under 5% for combined main and branch feeders to ensure electrical appliances run efficiently.
Why does conductor material matter?+
Aluminium has higher resistance than copper. Aluminium resistivity is approximately 0.0282 compared to copper's 0.0172. To match the conductivity of a copper run, an aluminium run requires a thicker wire size.
Why do three-phase calculations use a different factor?+
Single phase circuits carry current out and back through 2 wires (hence a factor of 2). Balanced three-phase systems carry three line wires out where phases cancel neutral current, utilizing a geometric phase offset factor of \(\sqrt{3} \approx 1.732\).
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