Voltage Drop Calculator: Single and Three Phase Runs
Voltage Drop Calculator
Voltage drop over a cable run, single or three phase, copper or aluminium, with the length in metres or feet. It reports the drop in volts and percent, judges it against the usual 3 percent branch circuit target, and suggests the size that would pass.
The estimate uses the standard K constants at operating temperature, 12.9 ohm circular mil per foot for copper and 21.2 for aluminium, with the single phase drop as 2 K I L over the circular mil area and the three phase drop as root 3 K I L over the same. Length is one way; the out and back is in the formula. The 3 percent figure is the usual branch circuit recommendation, with 5 percent for feeder plus branch combined.
How to use this tool
Pick single or three phase, copper or aluminium, the wire size, then enter the load current, the one way run length in metres or feet, and the system voltage. The tool returns the drop in volts and percent, the voltage actually arriving at the load, the power being lost in the cable, and, if the run fails the 3 percent target, the smallest size that would pass it.
Length is one way. The out and back of the circuit is already inside the formula, which is the first thing to check when someone elses numbers differ from yours by exactly a factor of two.
Why long runs quietly starve their loads
Every conductor is a resistor, and at 120 V there is not much headroom to spend on it. The estimating formula for single phase is Vd equals 2 K I L over the circular mil area, with K at 12.9 ohm circular mil per foot for copper and 21.2 for aluminium at operating temperature. Three phase replaces the 2 with root 3, which is why a balanced three phase run drops about 13 percent less than the same single phase run.
The percent targets are the usual recommendation rather than a hard code limit: 3 percent on a branch circuit, 5 percent for feeder and branch combined. Past that, lights dim, heaters underperform by the square of the voltage shortfall, and motors draw extra current trying to hold their output, which heats them.
A worked check you can repeat on paper
The classic trap: a 20 A load at the end of 100 ft of 12 AWG copper on a 120 V circuit. Twelve gauge is 6530 circular mils, so the drop is 2 times 12.9 times 20 times 100 over 6530, which is 7.90 V, and 7.90 over 120 is 6.6 percent, more than double the target, on a wire size that is perfectly legal for 20 A ampacity. The load sees 112 V, and 158 W is heating the cable run instead of the tool at the end of it.
This is the whole lesson of voltage drop: ampacity says the wire will not overheat, and says nothing about whether the load gets its voltage. On this run, meeting 3 percent takes 8 AWG.
Mistakes that catch people out
Sizing by ampacity alone on long runs. As above: legal and inadequate are different things. Fix: check drop on anything past roughly 50 ft, and always on well pumps, gate motors and outbuildings.
Doubling the length yourself. The formula already contains the return path. Fix: enter the one way distance.
Forgetting aluminium is different. The same size in aluminium drops 64 percent more. Fix: the material selector is not decorative.
Measuring the run on the drawing. Cable routes up walls, across ceilings and around obstructions. Fix: estimate the routed length, not the straight line.
How this was checked
The worked example above was verified to full precision against the K constant formula. The three phase factor was confirmed as exactly root 3 over 2 of the single phase result, the aluminium to copper ratio as exactly the ratio of the K constants, and the AWG areas come from the exact gauge formula, matching the published 6530 circular mils for 12 AWG to within a tenth of a percent. Metric lengths convert at exactly 0.3048 m per foot.
Related Calculators and Reference
Whether the conductor can carry the current at all is the separate question handled by the Cable Size and Ampacity Estimator. The V equals I R behind all of this is the Ohm Law Calculator. Three phase currents for a given load come from the Three Phase Power Calculator, and run lengths convert between metres, feet and chains in the Length and Distance Converter. The resistance figures this calculator runs on, and the question of when voltage drop rather than ampacity is what sizes a conductor, are covered in the Wire Gauge Chart. Backup power for an outage is the Generator Size Calculator. Also see the Power Factor Correction Calculator: lower line current from a better power factor also lowers the drop in the feeder.