Voltage Drop Calculator for a Cable Run

Voltage Drop Formula for a Cable Run

Voltage drop is not a separate phenomenon that needs its own theory. It is Ohm’s law applied to a resistor you did not intend to install — the cable — which sits in series with the load and divides the supply with it. Everything below follows from that one observation.

The drop is Ohm’s law on the wire

Whatever current the load draws also passes through the cable, and the cable has resistance, so there is a voltage across it:

And what reaches the load is what is left. The cable and the load form a voltage divider, with the cable taking a share proportional to its resistance:

Both legs of the circuit count

This is the error that halves more voltage-drop calculations than any other. Current has to return, so in an ordinary two-wire circuit it travels the distance twice — out along one conductor and back along the other. The resistance in the path uses twice the one-way length:

As a percentage, and why three per cent

A drop in volts means little on its own; what matters is what fraction of the supply it is, because that is what the load actually sees:

Three per cent on a branch circuit is the conventional limit, and the reasoning behind it is simply that most equipment tolerates a few per cent without measurable harm, while the losses stay small. Note what the formula says about low voltages: the supply is in the denominator, so the same cable, the same distance and the same power delivered gives a percentage drop that scales inversely with voltage. A 12 V system has around 370 times the percentage drop of a 230 V one delivering the same power, because the current is 19 times higher and the supply it is compared against is 19 times lower.

The heat that goes with the drop

The energy that disappears from the supply voltage does not vanish. It warms the cable, at a rate given by the power law:

The square is what makes this bite. Doubling the current doubles the voltage drop but QUADRUPLES the heat in the cable, so a run that was comfortable at 5 A is not merely twice as warm at 10 A. It is also why cable ratings fall when cables are bundled: the heat is the same, and the escape route is worse.

Worked example

Seventeen per cent, from wire that looks perfectly substantial — and 20.8 W going into warming a conduit, which is more than many of the loads such a run would be feeding. Getting inside 3 % here needs AWG 4 — eight sizes thicker and more than six times the copper. On a low-voltage run that answer is often to move the supply closer or raise the voltage instead.

Why Low-Voltage Runs Suffer Most

The same cable behaves completely differently at 12 V and at 230 V, and the reason is worth working through because it explains most surprising drop results.

To deliver a given power at a lower voltage you need proportionally more current. The drop in volts rises with that current, and it is then compared against a smaller supply — so the percentage suffers twice:

Delivering 120 W at 230 V takes 0.52 A; at 12 V it takes 10 A. Through the same cable the 12 V case has 19 times the drop in volts and one nineteenth of the supply to measure it against.

This is why solar, automotive, marine and LED-strip installations are dominated by cable sizing in a way that mains wiring is not, and why long runs at 12 V are often better done at 24 V or 48 V — doubling the voltage quarters the percentage drop for the same delivered power, at no cost in copper.

Sizing a Cable for a Drop Limit

Working forwards from a cable to a drop is easy. The useful direction is backwards — from an acceptable drop to the cross-section that achieves it. Rearranging R = ρL/A with the round trip included:

That gives a minimum area, which then has to be rounded up to a size that exists — you cannot buy 3.7 mm². The calculator above does this for you and names the smallest AWG size that stays inside 3 %.

Two limits, and the larger one wins

Cable has a current rating (ampacity) as well as a drop consequence, and they are different constraints. Ampacity is about the insulation surviving the heat; voltage drop is about the load receiving enough voltage. On short runs ampacity usually decides the size; on long runs voltage drop does, often by a wide margin. Size for both and take the thicker answer.

Note also that a cable sized for drop is a cable that runs cooler, since the losses scale the same way. Sizing generously is not purely a voltage decision.

What the Percentage Actually Costs You

Three per cent sounds like a tolerance. Here is what different amounts of drop do to real loads, and why some of them care far more than others.

• Resistive heaters and incandescent lamps — output falls with the SQUARE of the voltage. A 10 % drop is a 19 % loss of heat or light.
• Motors — torque falls roughly with the square of the voltage, and the current rises to compensate, which worsens the drop and the heating together. This is the load most likely to fail outright on a marginal run.
• LED strips — brightness falls visibly and unevenly along the run, which is why a long strip looks dim at the far end. Feeding from both ends halves the effective length.
• Switching power supplies — the most tolerant. They draw MORE current as the voltage falls to keep their output constant, which means a drop that is marginal can run away rather than settle.
• Battery charging — a drop in the cable subtracts directly from the charge voltage, and a few hundred millivolts can be the difference between a full charge and a chronically undercharged battery.

The switching-supply case deserves attention because it is counter-intuitive. Constant-power loads have a negative incremental resistance: less voltage means more current, which means more drop. A run that is stable at 90 % of nominal may not be stable at 85 %.

Assumptions, and Where They Break

Stated plainly, because a drop figure without its assumptions is not a number you can plan around:

• DC, or AC into a resistive load. On long AC runs the cable’s inductive reactance adds to the impedance, and with a poor power factor the drop is worse than resistance alone predicts.
• The steady-state current. A motor or a compressor draws several times its running current while starting, and the momentary drop can be enough to stall it — size for the inrush where one exists.
• The conductor temperature you entered. Under load the cable warms, its resistance rises, and the drop rises with it. A figure calculated at 20 °C is the best case.
• Solid conductor of the nominal gauge. Stranded cable has 2 to 5 % more resistance, and terminations, connectors and fuse holders add more still.
• Resistance only in the cable. Contact resistance at every joint is in series with it, and a corroded connector can exceed the whole cable run.

The practical upshot: treat the calculated drop as a floor, add margin for temperature and terminations, and where the answer is close to the limit, choose the next size up rather than defending the calculation.

Common mistakes

• Using the one-way distance. Current has to return, so a two-wire circuit has twice the cable length in the path — forgetting it halves the answer, in the direction that looks safe.
• Judging a drop in volts rather than as a percentage. Two volts is trivial at 230 V and catastrophic at 12 V.
• Sizing on ampacity alone. Ampacity keeps the insulation intact; it says nothing about whether the load receives enough voltage, and on long runs drop is the binding limit.
• Using the running current for a motor. Starting current is several times higher, and the momentary drop is what prevents it starting at all.
• Calculating at 20 °C for a cable that will be hot under load. The resistance rises about 0.4 % per degree, and so does the drop.
• Ignoring connectors and joints. Contact resistance is in series with the cable, and one poor crimp can exceed the entire run.

Frequently asked questions

How do you calculate voltage drop?

Multiply the current by the resistance of the cable: V drop = I × R. For a two-wire circuit the resistance is that of both conductors, so use twice the one-way length in R = ρL/A. Ten amps through 208 mΩ of cable is a 2.08 V drop.

What is an acceptable voltage drop?

Three per cent on a branch circuit is the conventional limit, and five per cent total from the supply to the point of use. Some loads tolerate more; motors, heaters and battery charging tolerate considerably less before the effect is noticeable.

Do you use one-way or round-trip length for voltage drop?

Round trip, for any ordinary two-wire circuit. The current flows out along one conductor and back along the other, so it passes through twice the distance. Using the one-way figure halves the calculated drop.

Why is voltage drop worse on 12 V systems?

Because delivering the same power at a lower voltage needs proportionally more current, and the resulting drop is then compared against a smaller supply. The percentage scales with P/V², so halving the voltage quadruples the percentage drop.

What size cable do I need for a given voltage drop?

Rearrange for the area: A ≥ 2ρLI / V drop max, then round up to a size that is sold. The calculator above names the smallest AWG conductor that stays inside 3 % for your run, and says so plainly when no listed size is enough.

How much power is lost in a cable?

I² × R, which is also the drop times the current. Ten amps through 208 mΩ dissipates 20.8 W as heat in the cable. Because of the square, doubling the current quadruples that loss while only doubling the voltage drop.

Does voltage drop matter if the equipment still works?

Often yes. The energy lost in the cable is paid for and produces nothing; heaters and lamps lose output with the square of the voltage; motors run hotter and produce less torque; and a switching supply draws more current as the voltage falls, which makes the drop worse rather than better.