How to Calculate Voltage Drop (With Examples)

A 200-hp motor 400 feet from the MCC won't start. The breaker trips on undervoltage. The cables are sized correctly for ampacity — but nobody checked voltage drop. The motor terminals are seeing 430V instead of the 460V they need.

Voltage drop is the reduction in voltage between the source and the load, caused by current flowing through the impedance of the conductors. The NEC doesn't set hard limits, but recommends no more than 3% drop on branch circuits and 5% total from the service entrance to the final outlet (see informational notes in NEC 210.19(A) and 215.2(A)).

The Formula

For single-phase circuits:

Vd = 2 x L x I x Z / 1000

For three-phase circuits:

Vd = 1.732 x L x I x Z / 1000

Where:

• Vd = voltage drop in volts
• L = one-way circuit length in feet
• I = load current in amperes
• Z = conductor impedance in ohms per 1000 feet
• 1000 = conversion factor (impedance is per 1000 ft)

The factor of 2 in the single-phase formula accounts for the round-trip current path through two current-carrying conductors (phase out and return). The 1.732 (square root of 3) replaces the factor of 2 for three-phase circuits.

To express voltage drop as a percentage: Vd% = (Vd / V_source) x 100

Where to Find Impedance Values

Use NEC Chapter 9, Table 9: "Alternating-Current Resistance and Reactance for 600-Volt Cables, 3-Phase, 60 Hz, 75°C." This table provides resistance (R) and reactance (X) values for various conductor sizes and conduit types, plus an effective impedance (Z effective) column calculated at 0.85 power factor.

For most calculations, the Z effective column at 0.85 PF gives you a single number to plug into the formula. For loads at a significantly different power factor, calculate Z effective from the R and X columns using the formula in the table notes. The table has separate columns for steel (magnetic), PVC, and aluminum conduit.

If you're using the simplified DC resistance method for shorter runs, NEC Chapter 9, Table 8 provides DC resistance values. This works for resistive loads at short distances, but for longer runs with inductive loads, the AC impedance from Table 9 gives more accurate results.

Worked Example: Three-Phase Feeder

A three-phase, 480V feeder supplies 150A to a distribution panel 250 feet away. The conductors are 1/0 AWG copper THHN in steel conduit.

Step 1: Find Z effective from NEC Chapter 9, Table 9. For 1/0 AWG copper in steel conduit at 0.85 PF: Z = 0.12 ohms per 1000 ft.

Step 2: Apply the formula. Vd = 1.732 x 250 x 150 x 0.12 / 1000 = 7.79V

Step 3: Calculate the percentage. Vd% = 7.79 / 480 x 100 = 1.62%

Under 3%, so this feeder meets the NEC recommendation. Voltage at the panel will be approximately 472V.

Worked Example: Long Single-Phase Branch Circuit

A single-phase, 120V branch circuit feeds a 16A load through 12 AWG copper conductors in PVC conduit, with a 175-foot run.

Step 1: Find Z effective. For 12 AWG copper in PVC conduit at 0.85 PF: Z = 2.0 ohms per 1000 ft.

Step 2: Apply the formula. Vd = 2 x 175 x 16 x 2.0 / 1000 = 11.2V

Step 3: Calculate the percentage. Vd% = 11.2 / 120 x 100 = 9.33%

Well above 3%. You'd need to upsize the conductors — switching to 8 AWG (Z = 0.78 ohms per 1000 ft in PVC) brings the drop to about 4.4V or 3.6%. For a comfortable margin, 6 AWG may be warranted.

When Voltage Drop Is Critical

Voltage drop matters most in three situations:

Long cable runs. Feeders over 100 feet start to accumulate meaningful drop, especially at higher currents. Facilities with remote buildings, long parking structures, or outdoor equipment often hit voltage drop limits before ampacity limits.

Motor loads. Motors are sensitive to voltage. A 10% voltage reduction increases motor current by roughly 11% and reduces available torque by about 19%. During starting — when inrush current is 6 to 8 times full-load current — voltage drop can prevent the motor from accelerating to full speed.

Sensitive electronics. Data centers, medical equipment, and process control systems may need voltage regulation tighter than the NEC 5% guideline.

A voltage drop check should be part of every cable sizing exercise. A conductor that passes the ampacity check (NEC 310.16) may still be undersized for voltage drop on a long run. See our guide on cable sizing per NEC for the complete process, or use the ekx voltage drop calculator to check system-wide drop automatically as part of a load flow study.

Key Takeaways

• Voltage drop formula: Vd = 2 x L x I x Z / 1000 (single-phase) or 1.732 x L x I x Z / 1000 (three-phase)
• NEC recommends 3% max on branch circuits, 5% total from service to outlet
• Use NEC Chapter 9, Table 9 for AC impedance values — more accurate than DC resistance for longer runs
• Always check voltage drop in addition to ampacity, especially for runs over 100 feet
• Motor loads are particularly sensitive to voltage drop during starting and running