How to Calculate Voltage Drop

A practical guide for electricians, engineers and installers: what voltage drop is, the formulas for single-phase and three-phase circuits, the 3% and 5% rules of thumb, and how conductor size and run length change the result.

What Is Voltage Drop?

Every conductor has resistance. When current flows through a cable, some of the supply voltage is lost as that current pushes against the resistance of the copper or aluminium. The voltage that actually reaches the load is therefore lower than the voltage at the source. That difference is the voltage drop.

A small drop is harmless. A large one means lights dim, motors run hot and lose torque, electronics misbehave, and energy is wasted as heat in the cable rather than delivered to the load. The longer the run and the smaller the conductor, the worse it gets. Calculating voltage drop before you pull cable is how you make sure the load sees the voltage it needs.

The Single-Phase Voltage Drop Formula

For a single-phase circuit, the standard approximation is:

V_d = 2 × I × L × R / 1000

Where:

V_d is the voltage drop in volts.
I is the load current in amperes.
L is the one-way length of the run in metres.
R is the conductor resistance in ohms per kilometre (ohms/km).

The factor of 2 is the key to the single-phase formula. Current has to travel out to the load and back again, so the total conductor length carrying current is twice the one-way run. Dividing by 1000 simply converts the resistance, quoted per kilometre, to match a length measured in metres.

To express the drop as a percentage, divide by the supply voltage and multiply by 100: %V_d = (V_d / V_supply) × 100. The percentage is what most standards and rules of thumb are written against, so it is the figure to watch.

Single-phase worked example

A 230 V single-phase circuit feeds a 20 A load over a 30 m one-way run using a conductor with a resistance of 7.41 ohms/km (roughly 2.5 mm² copper). What is the voltage drop?

V_d = 2 × 20 × 30 × 7.41 / 1000 = 8.89 V
As a percentage: 8.89 / 230 × 100 = 3.87%

That 3.87% already exceeds the common 3% target for branch circuits, so this run would call for a larger conductor. You can check any combination of current, length and conductor in seconds with the voltage drop calculator rather than working through the arithmetic by hand.

The Three-Phase Voltage Drop Formula

For a balanced three-phase circuit, the factor of 2 is replaced by the square root of 3:

V_d = √3 × I × L × R / 1000

The change from 2 to √3 (approximately 1.732) comes from the geometry of three phases displaced by 120 degrees and the fact that the return current is shared across the phase conductors rather than flowing back through a single neutral. For the same current, length and conductor, a three-phase circuit therefore has a lower line-to-line voltage drop than the single-phase equivalent. This is one of the reasons three-phase distribution is favoured for long runs and large loads.

Note that the resistance figure R should ideally be the AC resistance of the conductor at its operating temperature, not the cold DC value. On large conductors and long runs the reactance of the cable also contributes, but for most practical sizing the resistive approximation above is accurate enough and is the basis of the rules of thumb below.

Three-phase worked example

A 400 V three-phase feeder carries 50 A over a 60 m run using a conductor rated at 1.83 ohms/km (roughly 10 mm² copper). What is the line-to-line voltage drop?

V_d = √3 × 50 × 60 × 1.83 / 1000 = 9.51 V
As a percentage: 9.51 / 400 × 100 = 2.38%

At 2.38% this feeder sits comfortably inside the 3% guideline. Had the same load been wired single-phase at 230 V, the drop would have been markedly worse, which is exactly why the √3 factor matters.

The 3% and 5% Rules of Thumb

The US National Electrical Code does not mandate a hard voltage drop limit, but it gives a widely followed recommendation in its informational notes:

3% on a branch circuit: the drop from the final distribution board to the load should not exceed 3% of the nominal voltage.
5% total: the combined drop across the feeder and the branch circuit together should not exceed 5%.

So a feeder might be allowed up to 2% and the branch up to 3%, adding up to the 5% overall ceiling. UK practice under BS 7671 works to a similar idea, recommending the drop between the origin of the installation and any point of use stays within roughly 3% for lighting and 5% for other uses. Whichever standard applies in your region, the principle is the same: keep enough voltage at the load for it to work correctly, and keep cable losses sensible.

These are design targets, not absolute laws of physics, but ignoring them leads to nuisance problems that are expensive to fix once the cable is installed. Sizing to the rule of thumb up front is far cheaper than re-pulling a run.

How Conductor Size and Length Affect the Drop

Two variables dominate voltage drop once the current is fixed: the length of the run and the cross-sectional area of the conductor.

Length is directly proportional. Double the run and you double the resistance in the circuit, so you double the voltage drop. This is why long runs, such as a sub-panel in a detached garage or a pump at the far end of a field, are the classic voltage drop problem.

Conductor size is inversely proportional. Resistance falls as cross-sectional area rises, so going up a conductor size reduces the drop. Stepping up one AWG size increases the area by roughly 26% and cuts resistance, and so voltage drop, by a similar proportion. Going up two sizes roughly halves the resistance. The usual fix for a run that fails the 3% test is simply to specify the next conductor size up.

Rather than guess, work backwards from your target. The wire size calculator takes the current, run length and an acceptable voltage drop and tells you the smallest conductor that will stay inside the limit. If you are moving between metric and imperial conductor systems, the AWG conversion calculator converts between AWG, square millimetres and circular mils so you can match a spec sheet to the cable on your van.

Practical ways to reduce voltage drop

Increase the conductor size (the most common and reliable fix).
Shorten the run, or relocate the distribution board closer to the load.
Raise the system voltage where possible, since a higher voltage means lower current for the same power.
Use copper instead of aluminium for the same cross-section, as copper has lower resistance.
Distribute large loads across three phases rather than a single phase.

Recommended gear

Tools and materials for measuring and correcting voltage drop on site. Amazon affiliate links, commissions help keep this site free.

Digital True-RMS Multimeter
Measure the voltage at the supply and again at the load to confirm the actual drop under real load conditions. A true-RMS meter reads accurately on non-sinusoidal waveforms and is the single most useful instrument for diagnosing a suspected voltage drop problem.
THHN/THWN Building Wire (per reel)
When a run fails the 3% test, the fix is usually heavier copper. THHN/THWN building wire is the workhorse conductor for conduit and panel feeds. Buying the next size up on a full reel is cheaper than re-pulling an undersized run later.
Clamp Meter with Inrush Capture
Voltage drop depends on actual current, so measuring real load current is half the job. A clamp meter lets you read current without breaking the circuit, and inrush capture is handy for motor starting currents where the worst drop occurs.

Frequently Asked Questions

What is an acceptable voltage drop?

As a rule of thumb, keep the drop on a branch circuit within 3% of the nominal voltage and the total drop across feeder plus branch within 5%. These figures come from the recommendations in the US National Electrical Code, and UK practice under BS 7671 follows a similar 3% for lighting and 5% for other loads. They are design targets rather than hard legal limits, but staying inside them avoids dim lights, weak motors and wasted energy.

Why does the single-phase formula use a factor of 2?

In a single-phase circuit the current flows out to the load along one conductor and returns along another, so the total length of conductor carrying current is twice the one-way run. The factor of 2 in V_d = 2 times I times L times R / 1000 accounts for both the outgoing and return legs. In a balanced three-phase circuit the factor becomes the square root of 3 (about 1.732) because the return current is shared across the phases rather than flowing back through a single conductor.

How does cable length affect voltage drop?

Voltage drop is directly proportional to the length of the run. Doubling the cable length doubles the resistance in the circuit and therefore doubles the drop. This is why long runs to detached buildings, pumps or remote equipment are the most common source of voltage drop problems, and why such runs often need a larger conductor than the load current alone would suggest.

How do I reduce voltage drop on a long run?

The most reliable fix is to increase the conductor size, since resistance falls as cross-sectional area rises. Stepping up one or two conductor sizes is the usual remedy for a run that fails the 3% test. Other options are shortening the run, raising the system voltage so the same power needs less current, choosing copper over aluminium, and spreading large loads across three phases. A wire size calculator will tell you the smallest conductor that keeps the drop inside your target.

Is voltage drop the same in single-phase and three-phase circuits?

No. For the same current, length and conductor, a three-phase circuit has a lower line-to-line voltage drop than a single-phase one because the formula uses a factor of the square root of 3 (about 1.732) rather than 2. That is one reason three-phase distribution is preferred for long runs and large loads. The conductor resistance and the load current are the same in both cases, but the multiplying factor differs.