# Wire Size Calculator

Created by Steven Wooding
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Feb 27, 2023

The wire size calculator will help you select the correct gauge of electrical wire for your next electrical project, such as installing a pump in your garden pond, wiring up your tiny house, or getting power to your shed.

This wire size calculator is very versatile as it also contains the functionality of a:

• DC wire size calculator;
• AC wire size calculator;
• 12V wire size calculator;
• Low-voltage lighting wire size calculator; and
• Much more!

You can even use it instead of a difficult-to-use wire size chart.

## How do you calculate wire size?

The size of an electrical wire means the cross-sectional area it has (and in turn its diameter). The larger the area, the more current the wire can transmit with lower resistance. It is pretty similar to water flowing in a pipe. Using a larger pipe allows more water to flow at a lower pressure.

Let's derive the equation for the cross-sectional area of a wire carrying an electrical current from Ohm's law and Pouillet's law:

$\tag{Ohm's law} V = IR$
$\tag{Pouillets law} R = \varrho \frac{L}{A}$

where:

• $V$Voltage drop calculated between the source and the farthest end of the wire, measured in volts;
• $I$ — Maximum current running through the wire, measured in amps;
• $R$ — Resistance of the wire, measured in ohms. We learned how to calculate it at the wire resistance calculator;
• $\varrho$ — Resistivity of the conductor material, measured in ohm meters;
• $L$ — Length of the wire (one-way), measured in meters; and
• $A$ — Cross-sectional area of the wire, measured in square meters.

After combining and rearranging these two equations, the cross-sectional area is given by the equation:

$A = \frac{I \varrho 2 L}{V}$

Since square meters are not a sensible unit for electrical wires, the result is usually in mm² (if using the metric system). This conversion can be achieved by multiplying the result of the equation above by 1,000,000.

It is common for wire sizes to be given in AWG (American Wire Gauge) units in the US. For more information about the relationship between cross-sectional area and AWG, please refer to our wire gauge calculator.

The calculator will give you the next AWG size up, as it is always better to have a thicker wire to be safe, if possible.

### Calculating wire sizes for three-phase AC

For a three-phase AC electrical, three cables are used instead of one. The calculator is designed to accept the total line voltage and current of the combined three cables. The equation for the area of a single wire is modified to:

$A = \frac{\sqrt 3 I \varrho L}{V}$

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.

## Correcting for operating temperature

The resistivity of a conductor depends on its temperature, so the environment you will be installing your wire in will affect the wire size. When specifying a temperature, try to think of the maximum temperature the wire is likely to operate in, to be on the safe side.

The resistivity is given at a reference temperature, denoted by $\varrho_1$. Each material has a temperature coefficient, $\alpha$, associated with it that specifies how much more the resistivity increases by per degree of temperature. We can use the following formula to calculate the resistivity of a substance at any temperature:

$\varrho_2 = \varrho_1 (1 + \alpha \, (t_2 - t_1))$

where:

• $t_1$ — Reference temperature corresponding to the resistivity $\varrho_1$ at that temperature; and
• $t_2$ — Target temperature at which you want to find the resistivity $\varrho_2$.

Let's look at an example. Copper has a resistivity at 20 °C of $1.68 \times 10^{-8} \ \Omega \cdot \text{m}$ and a temperature coefficient $\alpha$ equal to $0.00404$. What would be the resistivity of copper at 50 °C?

\scriptsize \begin{align*} \varrho_2 &= 1.68 \times 10^{-8} (1 + 0.00404(50 - 20)) \\ &= 1.88 \times 10^{-8} \ \Omega \cdot \text{m} \end{align*}

You can set the temperature at which the calculator performs the calculation within the calculator, and the above analysis is done for you.

## How do you use this electrical wire size calculator?

Here is a step-by-step guide on how to use the wire size calculator:

1. Select which electrical system you will be using. Either DC/AC Single-phase or AC Three-phase. That means the calculator can be a simple DC wire size calculator, all the way up to an AC three-phase tool.
2. Enter a value for the source voltage, e.g., 12 V.
3. Input what percentage voltage drop is allowable. The smaller, the better, but the limit is 5% to keep devices working properly.
4. Select the wire conductor material, either copper or aluminum. You can also use Advanced mode to set a custom material resistivity at a fixed temperature.
5. Input a value for the current of the system. This figure should be the peak current so that the cable can be sized for the worst case.
6. Enter the one-way distance of the cable run from its source to the farthest point.
7. Change the temperature, if necessary. The value should be the maximum operating temperature that is expected for the wire.
8. You will then see results for the cross-sectional area, wire gauge in AWG, and the diameter of the cable. Much easier to use than a wire size chart!

💡 The unit of area circular mil (cmil) is equal to the area of a circle with a diameter of one mil, which is a thousandth of an inch (0.0254 mm). That's about 5.067 × 10-4 mm2. It then follows that the unit kilo circular mil (kcmil) equals 1000 times a cmil.

## Example of using this AC wire size calculator

Let's say that we are using an AC single-phase system operating at 120 V; a 3% allowable voltage drop; a copper conductor; 25 A peak current; a one-way cable run of 100 m (328 ft); and 50 °C max operating temperature.

Using the result for the resistivity for copper at 50 °C above, let's go ahead and enter the values into the equation for wire size:

\begin{align*} A &= \frac{I \varrho_2 L}{V} \\ \\ &= \frac{25 \times 1.88 \times 10^{-8} \times (2 \times 100)}{0.03 \times 120} \\ \\ &= 2.61 \times 10^{-5} \ \text{m}^2 \times 1000000 \\ \\ &= 26.1 \ \text{mm}^2 \\ \\ &= 51.6 \ \text{kcmil} \\ \\ &= 3 \ \text{AWG} \end{align*}

It's pretty straightforward, but using our super-duper wire size calculator is so much faster.

🙋 If you need to find the recommended size of your electrical boxes, you can check our box fill calculator for that.

## FAQ

### How do I calculate wire size for motors?

Perform the following calculation to get the cross-sectional area that's required for the wire:

1. Multiply the resistivity (Ω•m) of the conductor material by the peak motor current (A), the number 1.25, and the total length of the cable (m).
2. Divide the result by the voltage drop from the power source to the motor.
3. Multiply by 1,000,000 to get the result in mm2.

### How do I calculate wire size for 3 phase?

To calculate the wire size for a 3 phase electrical system, multiple the result for a single-phase supply by √3/2.

### How do I calculate AWG wire size?

Here's how you calculate AWG (American Wire Gauge) from the diameter of a wire:

1. Find the ratio (R) of the wire diameter to either 0.005 inches or 0.127 mm.
2. Use the equation n = -39 × log92(R) + 36 to find the AWG number.

### How do I calculate wire size for distance?

The wire size is proportional to the length of the cable distance. So, if you double the distance, the cross-sectional area of the wire needs to be doubled.

## Disclaimer

These results are only a guide for informational purposes only. Always consult a qualified electrician before proceeding with any electrical installation.

Steven Wooding
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 per cable
Wire gauge
AWG
Wire cross-sectional area (A)
kcmil
Wire diameter (d)
in
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