Why voltage drops
Every wire has some resistance, so current flowing through it loses a little voltage along the way. On a long run, or with a thin wire, the equipment at the far end gets noticeably less than the supply provides, and the lost energy heats the cable.
The formula
For DC and single-phase circuits the current flows out and back, so the length counts twice:
voltage drop = 2 × length × current × resistivity ÷ cross-section
For three-phase circuits, replace the 2 with √3, about 1.732. Copper has a resistivity of about 0.0172 Ω·mm²/m; aluminum about 0.0282.
Worked example
A 25 m single-phase run of 2.5 mm² copper carrying 16 A: 2 × 25 × 16 × 0.0172 ÷ 2.5 = 5.5 V. On 230 V that is 2.4%.
How much is acceptable
A common target is no more than 3% on a branch circuit and 5% in total from the supply to the load, which the US National Electrical Code recommends in an informational note. Local wiring rules set their own limits. If the drop is too high, use a thicker wire or a shorter run. The wire must also be rated for the current, which voltage drop alone does not check.
Calculator and chart
The Voltage Drop Calculator works in AWG or mm², copper or aluminum. The Wire Gauge Chart lists every AWG size with its diameter, area and resistance.
A worked example in AWG
A 120 V circuit runs 100 ft to a load drawing 15 A. 12 AWG copper has about 1.59 Ω per 1,000 ft at 20 °C.
- 12 AWG: 2 × 100 × 15 × 1.59 ÷ 1,000 = 4.8 V, which is 4.0% of 120 V. Over the 3% target.
- 10 AWG, at about 1.00 Ω per 1,000 ft: 3.0 V, which is 2.5%. Within the target.
Warm wires drop more
Copper's resistance rises about 0.4% for each degree Celsius. A wire running at 75 °C has about 22% more resistance than at 20 °C, and so about 22% more voltage drop. Tables for building wiring often list values at 75 °C for this reason.
Low-voltage circuits
A 1 V drop is under 1% on 120 or 230 V, but over 8% on a 12 V LED strip or a car accessory. Low-voltage runs need thicker wire for the same length. Long LED strips are often fed from both ends to keep the far end from dimming.