About Wire Size Calculator

The Wire Size Calculator is an essential tool to determine the correct gauge of electrical wire for various electrical installations. Proper wire sizing minimizes energy loss, ensures safety, and prevents overheating or damage to electrical equipment. The calculator considers critical parameters such as current, voltage drop, conductor material, cable length, and operating temperature.

Mathematical Formula

The wire cross-sectional area (\(A\)) is calculated based on the type of electrical system:

For DC and Single-Phase AC Systems:

The formula is given by:

\[ A = \frac{2 \cdot \rho \cdot I \cdot L}{V_d} \]

Where:

• \(A\): Wire cross-sectional area (\(\text{m}^2\))
• \(\rho\): Resistivity of the conductor (\(\Omega \cdot \text{m}\))
• \(I\): Current (\(\text{A}\))
• \(L\): One-way cable length (\(\text{m}\))
• \(V_d\): Allowable voltage drop (\(\text{V}\))

For Three-Phase AC Systems:

The formula for three-phase systems includes the \(\sqrt{3}\) factor to account for phase relationships:

\[ A = \frac{\sqrt{3} \cdot \rho \cdot I \cdot L}{V_d} \]

The variables are the same as those for DC systems, with the inclusion of the \(\sqrt{3}\) factor for three-phase systems.

Wire Diameter Calculation:

Once the wire cross-sectional area is calculated, the wire diameter (\(D\)) can be determined using the formula:

\[ D = 2 \cdot \sqrt{\frac{A}{\pi}} \]

Key Principles

• Ohm's Law: Describes the relationship between voltage, current, and resistance: \(V = IR\).
• Voltage Drop: Refers to the reduction in voltage along the length of the wire due to resistance.
• Conductor Material: Copper and aluminum are commonly used, with copper having lower resistivity than aluminum.
• Temperature Effects: Wire resistivity increases with temperature, which is accounted for in the calculations.
• Safety Standards: Voltage drop should generally not exceed 3-5% to ensure efficiency and safety.

Example Calculations

Example 1: DC Circuit

Input:

• Voltage: 120 V
• Current: 25 A
• Distance: 100 m
• Material: Copper
• Voltage Drop: 3%
• Temperature: 50°C

Calculation:

Resistivity of copper (\(\rho\)) adjusted for temperature:

\[ \rho_{\text{adjusted}} = 1.68 \times 10^{-8} \cdot (1 + 0.00393 \cdot (50 - 20)) = 1.88 \times 10^{-8} \, \Omega \cdot \text{m} \]

Allowable voltage drop:

\[ V_d = 120 \cdot 0.03 = 3.6 \, \text{V} \]

Wire cross-sectional area:

\[ A = \frac{2 \cdot 1.88 \times 10^{-8} \cdot 25 \cdot 100}{3.6} = 2.61 \times 10^{-5} \, \text{m}^2 = 26.08 \, \text{mm}^2 \]

Wire diameter:

\[ D = 2 \cdot \sqrt{\frac{26.08}{\pi}} \approx 5.77 \, \text{mm} \]

Output:

• Required Wire Cross-sectional Area: 26.08 mm²
• Wire Diameter: 5.77 mm
• Recommended Wire Gauge: 3 AWG

Example 2: Three-Phase AC Circuit

Input:

• Voltage: 415 V
• Current: 50 A
• Distance: 150 m
• Material: Aluminum
• Voltage Drop: 5%
• Temperature: 60°C

Calculation:

Resistivity of aluminum (\(\rho\)) adjusted for temperature:

\[ \rho_{\text{adjusted}} = 2.82 \times 10^{-8} \cdot (1 + 0.00403 \cdot (60 - 20)) = 3.27 \times 10^{-8} \, \Omega \cdot \text{m} \]

Allowable voltage drop:

\[ V_d = 415 \cdot 0.05 = 20.75 \, \text{V} \]

Wire cross-sectional area for three-phase system (\(\sqrt{3}\) factor applied):

\[ A = \frac{\sqrt{3} \cdot 3.27 \times 10^{-8} \cdot 50 \cdot 150}{20.75} = 2.5 \times 10^{-5} \, \text{m}^2 = 20.5 \, \text{mm}^2 \]

Wire diameter:

\[ D = 2 \cdot \sqrt{\frac{20.5}{\pi}} \approx 5.11 \, \text{mm} \]

Output:

• Required Wire Cross-sectional Area: 20.5 mm²
• Wire Diameter: 5.11 mm
• Recommended Wire Gauge: 4 AWG