# Wire Size Calculator

Created by Kenneth Alambra
Last updated: Jul 24, 2022

If you need to find the correct cross-sectional area or diameter of an electrical wire that will suit your needs, then this electrical wire size calculator is for you. This tool works as an AC wire size calculator as it can also perform wire size and wire thickness calculations for AC electrical systems. Keep on reading to start learning:

• The importance of using the correct wire size;
• How to calculate wire sizes; and
• How to use this electrical wire size calculator.

## The importance of using the correct wire size

Choosing the proper wire size for your electrical system lets you become safe from fire hazards and can also help you save money by not spending too much on purchasing larger wires than needed. Passing high values of current on a small wire can heat the wire, melt its insulating cover, and potentially burn its surroundings.

Though a larger cross-sectional area can allow more current to flow safely than a small cross-section, choosing a large wire for small projects can be very expensive. That is why we calculate just the correct wire size for our needs.

## How to calculate wire sizes

To calculate wire sizes that will suit our needs, we have to use the formula derived from Pouillet's Law and Ohm's Law, as shown below:

$A = \frac{I\times \varrho\times c\ \times L}{V}$

where:

• $A$ is the wire's cross-sectional area in square meters;
• $I$ is the maximum current in amperes;
• $\varrho$ is the conducting wire's resistivity in ohm meters;
• $c$ is a constant equal to $2$ for single-phase AC or DC electrical systems, and $\sqrt 3$ for 3-phase electrical systemsl
• $L$ is the wire length in meters; and
• $V$ is the voltage drop, in volts, from the voltage source to the load.

The factor of $\sqrt 3$ is needed to convert between the system's phase current and line current. The factor of 2 disappears, as there is no return cable in a three-phase system.

For the wire's resistivity, $\varrho$, it's a good practice to consider the maximum operating temperature of your wires. Here is the formula we can use to calculate the resistivity of a wire at that temperature:

$\varrho = \varrho_\text{ref} (1 + \alpha \, (t_\text{max} - t_\text{ref}))$

where:

• $\varrho$ is the wire's resistivity at the maximum wire temperature;
• $\varrho_\text{ref}$ is the wire's resistivity at the reference temperature $t_\text{ref}$;
• $\alpha$ is the temperature coefficient of the conducting material;
• $t_\text{max}$ is the maximum wire temperature to find the resistivity $\varrho$; and
• $t_\text{ref}$ is the reference temperature where we can observe the resistivity value $\varrho_\text{ref}$.

🔎 Wondering if wire resistivity has something to do with wire resistance? Check our wire resistance calculator for some answers.

## How to use this electrical wire size calculator

Let's say we want to calculate the wire size for a direct current electrical system that we expect to draw 2 amperes of current from a 12-V battery, where we'll use copper wires for the conductors. We also expect the system to operate in a well-ventilated area that can result in a maximum wire temperature of 40°C, and the system can still run even at a 2% voltage drop. We'll also only need about 30 cm or 0.3 meters of wire to connect our load to our batter. To use this DC and AC wire size calculator:

1. Choose the DC/AC Single-phase option for the electrical system.
2. Input 12 V for the source voltage.
3. Enter 2% for the allowable voltage drop (V).
4. Select copper for the conductor material.
5. Type in 2 A for the current (I).
6. Enter 0.3 m for the one-way distance (D).
7. Lastly, input 40°C for the maximum wire temperature.

At this point, our DC and AC wire size calculator will already display a wire gauge of 24 AWG, a wire cross-sectional area (A) of 0.205 mm², and a wire diameter (d) of 0.519 mm.

🙋 Note that you can refer to the resulting wire diameter if you wish to use this tool as a wire thickness calculator.

Kenneth Alambra
Electrical system
DC/AC Single-phase
Source voltage
V
Allowable voltage drop (V)
%
Conductor material
Copper
Current (I)
A
One-way distance (D)
ft
Maximum wire temperature
°F
Recommended wire size
Wire gauge
AWG
Wire cross-sectional area (A)
kcmil
Wire diameter (d)
in
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