# 24V Wire Size Calculator

Created by Luis Hoyos
Reviewed by Wojciech Sas, PhD
Last updated: Jul 04, 2023

Calculating the proper wire size can prevent you from wasting money on unnecessary big cables, so we've created this 24V wire size calculator to get the optimal size.

As a calculation example, we'll see what wire size for a 24V trolling motor is needed.

You can also look at the FAQ list for other common electrical problems, like the wire size needed for a 20 amp 220-volt circuit.

## Formula to calculate the wire size for a 24V system.

The equation varies depending on the type of electrical system used.

### DC/ single-phase systems

To calculate a 24 V wire size in a direct current (DC) or an alternating current (AC) single-phase system, use this formula:

$\footnotesize A = \frac{Iϱ2L}{V}$

where:

• $V$ — Voltage drop between the source and the farthest end of the wire, measured in volts;
• $I$ — Electric current through the wire, in amperes;
• $ϱ$ — Resistivity of the conductor material, in Ω⋅m;
• $L$ — Length of the wire (one-way), in meters;
• $A$ — Cross-sectional area of the wire, in square meters; and

The 2 coefficient before L accounts for the return path after the current passes the load.

### Three-phase systems

For a three-phase AC system, three cables are used instead of one. The calculator accepts the total line voltage and current of the combined three wires.

The equation for a single wire is modified with a √3 factor, which is needed to convert between the system's phase current and line current. For each of the three cables, the area is given by:

$\footnotesize A = \frac{\sqrt{3}IϱL}{V}$

The factor of 2 disappears, as three-phase systems don't possess a return cable.

🙋 Important:

• The result given by the three-phase formula accounts for the area of only one wire. Therefore, you'll need three wires of that size to build your three-phase cable.
• This 24V wire size calculator has the three-phase system option enabled, but, for most applications, 24 V systems will work in DC or AC single-phase.
• For source voltages of more than 50 V, if L<16 m, this calculator assumes a distance of 16 m so that the wire doesn't result in excessively tiny sizes for small lengths.
• V is the voltage drop, not the source voltage magnitude.
• ϱ varies with temperature.

## Example: What wire size for a 24V trolling motor is needed

Suppose you're choosing the wire size of a trolling motor operating at 48 amps. The one-way distance (from source to load) is 25 ft, and the maximum operating temperature is 50°C. What is the required size for this operation?

Use our 24V wire size calculator following these steps to know the answer:

1. As trolling motors and 24 V systems operate in DC, choose "DC/AC Single-phase" as the electrical system.
2. As recommended in most applications, choose a 3% allowable voltage drop.
3. Copper is the most common wire material. Therefore, you can choose it as your conductor material.
4. Type 56 A in the "Current (I)" box.
5. Type 25 ft in the "One-way distance" box.
6. Type 50°C in the "Maximum wire temperature" box.

That's it. The required wire size should be 97.95 mm² or 0000 (4/0) AWG.

## Other interesting wire size tools

We've also created other tools to ease your life and solve similar problems:

## FAQ

### What wire size for a 20 amp 220-volt circuit should I use?

The wire size for 20 amp 220-volt circuits is 10 AWG for cable lengths below 40 m. This answer assumes using a copper cable at a maximum operating temperature of 100°C and an allowable 3% voltage drop. For longer wires, use our wire size calculator.

### What wire size for a 24V trolling motor should I use?

Usually, a 4 AWG will be more than enough for 24 V trolling motors. Even so, to calculate the optimum wire size, follow these steps:

1. Determine the trolling motor electric current (in amps), cable length L (in meters), conductor resistivity ϱ (in Ω⋅m), and allowable voltage drop V (usually 3% of the source voltage).
2. Input the values in this formula:
A = (2IϱL) / V
3. Now you know the wire size for your 24V trolling motor!!! The formula provides the wire area in m². Multiply it by 1,000,000 to convert it to square millimeters.

## Disclaimer

These results are solely for educational purposes. Before beginning any electrical project, always get the advice of an experienced electrician.

Luis Hoyos
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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