How to Work Out Voltage Drop: Wire Sizing Formulas and Real-World Fixes

Voltage drop is the reduction in electrical potential between the power source and the load, caused by the inherent resistance of the conductors carrying the current. You can size a breaker perfectly and use wire that meets the minimum ampacity requirements, but if the run is too long, the equipment at the end of the line will still starve for power. Understanding how to work out voltage drop is the difference between a circuit that merely passes inspection and one that actually performs under load.

What Voltage Drop Actually Changes in Your Circuit

To design reliable systems, you need to know exactly what voltage drop alters in a physical installation, and what it leaves alone.

What it changes:

• Available Load Voltage: The most direct impact. A 120V nominal circuit experiencing a 6V drop delivers only 114V to the receptacle.
• Conductor Temperature: The "lost" voltage doesn't disappear; it converts to heat (P = I²R) inside the wire insulation. Over time, this accelerates insulation degradation.
• Motor Starting Torque: AC induction motors produce starting torque proportional to the square of the applied voltage. A 10% voltage drop results in a 19% loss in starting torque.

What it does NOT change:

• Source Voltage: The utility transformer or main panel busbars still output their nominal voltage.
• Breaker Trip Curves: Voltage drop does not cause a breaker to trip. In fact, because undervoltage causes motors to draw more current to compensate for lost power, a severe voltage drop can push a motor into a continuous overcurrent state that slowly overheats the windings before the breaker's magnetic trip ever engages.

The Core Math: How to Work Out Voltage Drop Step-by-Step

For standard single-phase AC and DC branch circuits, the industry-standard formula relies on the circular mil (CM) area of the conductor.

The Formula:
VD = (2 × K × I × D) / CM

• VD: Voltage Drop (in Volts)
• 2: Multiplier for the out-and-back path of a single-phase circuit.
• K: Specific resistance of the wire. Use 12.9 for copper at 75°C operating temperature, or 21.2 for aluminum.
• I: Current in Amps (use the continuous load or Full Load Amps).
• D: One-way distance from source to load in feet.
• CM: Circular mils of the wire cross-section.

Reference Table: AWG to Circular Mils (Solid/Stranded Copper)

Worked Numeric Example

Let's calculate the drop for a 120V branch circuit powering a 15A continuous space heater. The one-way run from the panel is 100 feet, and we are proposing 12 AWG copper wire.

1. Identify variables: K = 12.9, I = 15A, D = 100 ft, CM = 6,530 (for 12 AWG).
2. Calculate numerator: 2 × 12.9 × 15 × 100 = 38,700.
3. Divide by CM: 38,700 / 6,530 = 5.92V drop.
4. Calculate percentage: (5.92V / 120V) × 100 = 4.93%.

The National Electrical Code (NEC) recommends a maximum 3% voltage drop on branch circuits. At 4.93%, 12 AWG is legally permissible for ampacity (it handles 20A), but practically inadequate for this 100-foot run. You must upsize to 10 AWG to keep the drop under 3%.

Where You Meet This in Practice

Voltage drop isn't just a textbook exercise; it dictates material costs and equipment survival in specific real-world installations.

• Outbuilding Subpanels: Running a feeder 150 feet to a detached garage or shed. Even if 6 AWG copper handles the 60A breaker, the voltage drop at 50A continuous load might force you to install 4 AWG or 3 AWG aluminum to maintain usable voltage at the subpanel bus.
• Low-Voltage DC Systems: 12V and 24V systems (like solar arrays, LED strip lighting, or RV wiring) are hyper-sensitive. A 2V drop on a 120V circuit is a nuisance; a 2V drop on a 12V circuit is a catastrophic 16% loss that will prevent LED drivers from firing or cause solar charge controllers to misread battery state-of-charge.
• Heavy Motor Starts: Well pumps, HVAC compressors, and workshop table saws draw massive inrush currents (Locked Rotor Amps) for a fraction of a second. If the wire is undersized, the voltage collapses during startup, and the motor stalls.

Scenario Walkthrough: The 120V Workshop Subpanel Disaster

To understand why ampacity alone is a trap, let's look at a real-world failure mode involving a DIY workshop build.

The Setup:
A hobbyist runs 100 feet of 10 AWG NM-B cable from the main house panel to a shed subpanel. They install a 30A breaker. The 10 AWG wire is perfectly rated for 30A ampacity. In the shed, they plug in a 120V cabinet table saw with a Full Load Amp (FLA) rating of 15A and a Locked Rotor Amp (LRA) starting surge of 90A.

The Numbers (During Motor Start):
When the saw motor starts, it briefly draws the 90A LRA. Let's work out the voltage drop during that critical half-second using our formula:

• VD = (2 × 12.9 × 90A × 100 ft) / 10,380 CM
• VD = 232,200 / 10,380 = 22.3V drop

The Outcome:
The voltage at the saw's plug drops from 120V to 97.7V during startup. Because motor starting torque drops with the square of the voltage, the saw only produces 66% of its rated starting torque. If there is a piece of oak on the blade, the motor lacks the torque to spin up. It stalls, continues drawing 90A, and the internal thermal overload protector trips, shutting the saw down. The 30A breaker in the house never trips because the thermal overload acts first.

What Went Wrong:
The builder sized the wire for running ampacity (15A FLA), completely ignoring the starting voltage drop (90A LRA). The fix requires upsizing the feeder to 6 AWG copper or 4 AWG aluminum to ensure the voltage at the receptacle stays above 108V during the inrush surge. Tools like the Cerro Wire Voltage Drop Calculator can automate these checks, but understanding the underlying math prevents costly material mistakes.

Common Confusions: Voltage Drop vs. Sag vs. High Resistance

When a multimeter reads low voltage at a receptacle, voltage drop is only one of three possible culprits. Confusing them leads to the wrong fix.

1. Steady-State Voltage Drop

This is what we calculated above. It is proportional to the load. If you turn off the space heater, the voltage at the receptacle immediately recovers to 120V. It is distributed evenly across the entire length of the wire.

2. Voltage Sag (Dip)

A sag is a transient, grid-side event. It happens when the utility transformer experiences a massive sudden load (like a neighbor's AC compressor kicking on) or a fault. It affects the entire house simultaneously, lasts for a few cycles to a few seconds, and has nothing to do with your internal wire sizing.

3. High-Resistance Connection

This is a localized failure. If a neutral wire is loose under a receptacle terminal, or a breaker lug wasn't torqued to spec, that single point of contact introduces massive resistance. Danger: Unlike distributed voltage drop, which warms the wire safely, a high-resistance connection concentrates heat into a single square millimeter, melting insulation and causing arc faults. If your voltage reads 118V with no load, but drops to 90V when you plug in a 5A lamp, you don't have a wire sizing problem; you have a loose termination that needs immediate tightening.