Formula and input convention
For the site's resistance-based model, Vd = √3 × K × I × L ÷ CM. Use line-to-line system voltage, line current and one-way distance for a balanced three-phase circuit.
Do not add the three line currents together. Do not double the one-way distance before entry. The √3 multiplier already represents the simplified balanced circuit geometry.
How do you calculate voltage drop?
Every metallic conductor has internal electrical resistance. As current flows through a run of copper or aluminum wire, part of the source voltage is lost as heat along the cable path. Using Ohm's law (V = I × R) and circular-mil resistivity at 75°C, the voltage lost across a two-wire circuit is:
where:
- VD – Total voltage drop between the supply panel and the load terminals, measured in volts (need a target gauge instead? Use the wire size calculator);
- K – Conductor resistance constant at 75°C (K = 12.9 for copper and K = 21.2 for aluminum in Ω·CM/ft);
- I – Load current flowing through the circuit in amps (estimate from wattage with our watts to amps calculator);
- L – One-way wire distance in feet (the multiplier of 2 already accounts for the return conductor); and
- CM – Conductor cross-sectional area in circular mils from NEC Chapter 9, Table 8.
Three-phase AC voltage drop equation
In a balanced three-phase system, the return currents cancel in phase opposition, so the round-trip factor of 2 is replaced by √3:
Subtract VD from the source voltage (V_load = V_source − VD) to find the actual voltage delivered to the equipment terminals. Explore all related tools in our electrical calculators hub.
Worked example: 480 V, 50 A, 200 ft
| AWG | Estimated volts lost | Estimated percentage | Estimated load voltage |
|---|---|---|---|
| 8 | 13.53 V | 2.82% | 466.5 V |
| 6 | 8.52 V | 1.77% | 471.5 V |
| 4 | 5.35 V | 1.12% | 474.6 V |
Second example: 208 V, 60 A, 150 ft
At a 3% target, the simplified circular-mil requirement is about 32,226. The calculator list moves to 4 AWG at 41,740 circular mils. Estimated drop with that candidate is about 4.82 V, or 2.32%.
This is a voltage-drop candidate only. The professional must check load type, ampacity, motor rules, protection, terminals and actual AC impedance.
Stop conditions for the simple formula
- Materially unbalanced phase loads
- Motor-starting performance controls design
- Power factor or reactance is significant
- Parallel conductors or multiple taps
- Harmonic current or nonlinear loads
- Unknown line-to-line voltage or circuit arrangement
When to use the calculator instead
Use this formula guide to audit the method and input convention. Use the 3-phase voltage drop calculator when you need to compare actual conductor sizes and see volts lost, percentage drop and estimated load voltage together.
The calculator and this guide serve different intent: the calculator produces an interactive estimate, while this page explains how the balanced three-phase equation works and when it stops being suitable.
Frequently asked questions
What is the 3-phase voltage drop formula?
For the simplified resistance model used here, voltage drop equals square root of 3 multiplied by K, line current and one-way distance, divided by conductor circular-mil area.
Do I double distance in a 3-phase voltage drop calculation?
No. Enter one-way distance. The balanced three-phase formula uses the square-root-of-three multiplier rather than doubling the path.
Should I use line-to-line or line-to-neutral voltage?
This site's balanced three-phase method uses line-to-line system voltage when converting volts lost to percentage drop.
When is the simplified formula not enough?
Use a fuller professional method for unbalanced loads, important power-factor or reactance effects, motors, harmonics, parallel conductors or complex distribution.