# 24V Cable Size Calculator

Created by Luis Hoyos
Last updated: Feb 18, 2023

This 24V cable size calculator will determine the optimum size of the wire of a 24V system. 24 V source voltages are usually present in direct current (DC) and single-phase systems.

If you need to know the size of the wire of a 24-volt three-phase system, you can select the option in the calculator. In three-phase, three wires are used instead of one. The calculator provides the area of a single wire, but it accepts the total line voltage and current of the combined three wires.

## Formula to calculate a 24V cable size

To calculate the wire size of a 24V system, we use the same formulas used in our wire size calculator, which arise from algebraically combining Ohm's law and Pouillet's Law. The formula is:

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

, where:

• $A$ — Wire's cross-sectional area, in square meters ($\text m^2$);
• $I$ — Maximum current, in amperes ($\text A$);
• $\varrho$ — Resistivity of the conducting 24V wire, in ohm meters ($\mathrm{\Omega \cdot m}$);
• $\phi$ — Phase factor, equal to $1$ for single-phase or DC, and $\sqrt 3$ for three-phase systems.
• $L$ — Wire length, in $\text m$; and
• $\Delta V$ — Voltage drop from the voltage source to the load, in volts ($\text V$).

Once you've obtained the cross-sectional area, you can convert it to the American wire gauge (AWG) standard using this 24v cable size calculator or our wire gauge calculator, where you can learn more about it.

Some important aspects to consider about the previous formula:

• Since square meters are not a sensible unit for electrical wires, the area ($A$) usually requires to be in square millimeters (mm²). To convert the result of the formula to mm², multiply it by 1,000,000 or use our area conversion calculator.
• In three-phase, three wires are used instead of one. We designed the 24V wire size calculator to accept the total line voltage and current of the combined three wires, and the calculator provides the area of a single wire (this is thanks to the $\phi = \sqrt 3$ factor).
• An allowable voltage drop of 3% is usually recommended. For example, for our 24V system, this would correspond to $\Delta V = 24\ \text V \times 0.03 = 0.72\ \text V$.
• For DC and single-phase systems, the 24V wire length equals two times the one-way distance $L = 2D$, as we need a return cable. For three-phase, $L = D$, as there's no return cable in this type of system. If your distances are in feet($\text {ft}$), use our length converter to convert them to $\text m$.

## Influence of wire temperature

The resistivity used in the previous formula depends on the wire material and operating temperature. The following equation can model the relationship:

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

, where:

• $T_\text{ref}$ — Reference temperature corresponding to the reference resistivity $\varrho_\text{ref}$ at that temperature;
• $T$ — Temperature at which you want to find the resistivity $\varrho$; and
• $\alpha$ — Temperature coefficient, different for each material.

Higher temperatures increase the resistivity of the wire and, therefore, the required wire size. To warrant an appropriate wire for the 24V application, we must calculate the resistivity using the maximum operating temperature ($T = T_\text{max}$).

🙋 We can express $T$ and $T_\text{ref}$ in $\mathrm {\ \degree C}$ or Kelvin as long the unit is the same for both temperatures.

• For copper, $\alpha = 0.00404$, and at $T_\text{ref} = 20\mathrm {\ \degree C}$ the resistivity equals $\varrho_\text{ref} = 1.68 × 10^{−8} \mathrm{\ \Omega \cdot m}$
• For aluminum, $\alpha = 0.00404$, and at $T_\text{ref} = 20\mathrm {\ \degree C}$ the resistivity equals $\varrho_\text{ref} = 2.65 × 10^{−8} \mathrm{\ \Omega \cdot m}$

## 24-volt wire size chart for DC and single-phase systems

If you need to compare the result of different amperages and distances, the following 24-volt wire size chart for your DC system can be helpful. It assumes an allowable voltage drop of 3% and 75°C as the maximum operating temperature. Note you can get the same result with our 24V wire size calculator.

Amps

Wire length (in ft)

10

15

20

25

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

5

14

13

11

10

10

8

7

7

6

5

5

4

4

4

3

3

3

2

2

10

11

10

8

7

7

5

4

4

3

2

2

1

1

1

1/0

1/0

1/0

2/0

2/0

15

10

8

7

6

5

4

3

2

1

1

1/0

1/0

2/0

2/0

3/0

3/0

3/0

3/0

4/0

20

8

7

5

4

4

2

1

1

1/0

2/0

2/0

3/0

3/0

3/0

4/0

4/0

4/0

25

7

6

4

3

3

1

1/0

1/0

2/0

3/0

3/0

4/0

4/0

4/0

30

7

5

4

3

2

1

1/0

2/0

3/0

3/0

4/0

4/0

40

5

4

2

1

1

2/0

3/0

3/0

4/0

50

4

3

1

1/0

1/0

3/0

4/0

4/0

60

4

2

1

1/0

2/0

3/0

4/0

70

3

1

1/0

2/0

3/0

4/0

80

2

1

2/0

3/0

3/0

90

2

1/0

2/0

3/0

4/0

100

1

1/0

3/0

4/0

4/0

Luis Hoyos
Electrical system
DC or 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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