Wire is usually chosen from a current-carrying table: pick a gauge that will not get hot at the motor’s rated current, and move on. For a permanent magnet DC motor that is not enough, because the gauge really decides how much voltage arrives at the terminals, and the speed of a permanent magnet motor is very nearly proportional to the voltage it sees. A cable that is too thin therefore does not announce itself by warming up. It announces itself as a machine that runs slow, or one that will not start.

Speed Is Set by the Voltage at the Terminals

A permanent magnet DC motor‘s no-load speed follows its terminal voltage, and stall torque does the same. The current determines how much torque is produced at that speed, but the voltage sets the ceiling.

That has a direct consequence for cable choice. A drop of nine percent in the cable is a machine running nine percent slower and starting with nine percent less torque, with nothing wrong anywhere inside the motor. This is the mechanism behind the most common entry in any troubleshooting list, low voltage at the motor, and it is decided at the drawing board by a wire gauge rather than at the machine by a fault.

The Drop Is a Round Trip, and It Has More Than One Term

The arithmetic is short. Voltage drop equals two times the current, times the one-way length, times the resistivity of copper, divided by the cross-sectional area. The factor of two is the return conductor, which is the part usually forgotten.

Take 12 V, 3 A, a five metre run and 0.5 mm² wire. With copper at 0.0175 ohm square millimetres per metre, one conductor is 0.175 ohm, the loop is 0.35 ohm, and the drop is 1.05 V. That is nearly nine percent of the supply, spent before the current reaches the motor. Moving to 1.0 mm² halves it to about 4.4 percent, which is usually the right answer and costs very little.

The sum has other terms. Connectors are the ones most often left out, and their share depends on the length. On a three metre run the wire dominates. On a short internal harness of 0.3 m the wire loop is about 0.02 ohm, while two contacts in an ordinary terminal can be 0.03 ohm between them, so the connector is the larger loss. A cheap connector can cost more than a metre of cable, and it is the part nobody re-specifies when a machine comes up short on speed.

Size It on Starting Current, Not Running Current

The wire has to carry the current the motor draws when it is doing the hardest thing it does, which is starting under load or stalling. That current is several times the running figure.

At stall the motor draws whatever the winding allows, and the drop scales with it. A four ampere starting surge through the same 0.35 ohm loop costs 1.4 V, nearly twelve percent of a 12 V supply, which removes the same proportion of the starting torque. A machine that starts perfectly on a bench supply and refuses to start through three metres of thin cable and a marginal connector is usually not a motor problem at all. It is a loop resistance problem, and the bench supply hid it because it was connected with short heavy leads.

There is a useful scale check here. A ZGB37RG at 12 V is quoted at 0.4 A running and 0.8 A at stall. Through five metres of 0.5 mm² the drop at rated current is about one percent, so for a motor of this size the cable is irrelevant and there is no reason to over-specify it. The calculation earns its keep when the current rises or the lead gets long, which is where actuators, multi-motor harnesses and outdoor runs live.

Voltage Halves the Penalty, Length Doubles It

Because the drop is a percentage of the supply, the same cable on a 24 V system costs half as much in relative terms. The 1.05 V above is nine percent of 12 V and about four percent of 24 V, and neither the wire nor the current changed.

That leads to a practical asymmetry. On 12 V systems, gauge by run length, because a modest length already matters. On 24 V systems there is roughly twice the tolerance, and the same wire may be entirely adequate. And when a design is being pushed from 12 V to 24 V for other reasons, the harness usually gets better as a side effect, which is worth knowing when a prototype is short on speed.

Both remaining variables scale predictably. Doubling the length doubles the drop. Doubling the area halves it. Nothing else in the calculation is negotiable.

Two Corrections Worth Applying

Copper resistance rises with temperature by about 0.4 percent per degree Celsius. In a warm housing at 70 °C the same conductor is roughly twenty percent more resistive than the 20 °C figure, so a drop calculated on a cold bench understates the drop in service. For a harness running near its limit, use the hot figure.

And a long lead is not only resistive. Coiled spare cable behaves as an inductor, which adds reactance, and a long unshielded run radiates. Neither changes the steady-state speed, but both can disturb a controller or a sensor sharing the harness, and a coil of excess cable tucked into a housing is a poor habit even when the gauge is correct.

What to Check

Three numbers settle it: the current at the hardest moment, the one-way length, and the smallest voltage the motor can tolerate. From those, the drop is a multiplication, and the required area follows. Measuring the voltage at the motor terminals while it runs under load is faster than calculating, and it settles the question in one reading. Then add the connectors to the same sum, because on short harnesses they carry more of it than the wire does.