Three-Phase Current Calculator
In a balanced three-phase AC system, the line current drawn by a load is I = P / (sqrt(3) * VL * pf), where P is total three-phase real power in watts, VL is the line-to-line voltage in volts, and pf is the power factor. This formula is essential for sizing conductors, circuit breakers, and motor starters for three-phase equipment. Apparent power is S = sqrt(3) * VL * I. Enter the power, voltage, and power factor to find line current and apparent power.
Three-phase power formulas
I = P / (sqrt(3) * VL * pf)
S = sqrt(3) * VL * I (apparent power, VA)
sqrt(3) = 1.7321
Example: P = 15,000 W, VL = 480 V, pf = 0.90. I = 15,000 / (1.7321 * 480 * 0.90) = 15,000 / 748.27 = 20.05 A. S = 1.7321 * 480 * 20.05 = 16,667 VA.
Three-phase current in practice
- Motor nameplates list full-load amps (FLA) at rated voltage and power factor. Use this calculator to verify sizing or to convert kW to amps for unlabeled equipment.
- NEC Article 430 requires conductors sized at 125% of motor FLA for branch circuit protection. Calculate FLA first, then multiply by 1.25.
- Three-phase 480 V systems deliver the same power as 240 V with half the current, significantly reducing conductor cost for long runs.
- Variable frequency drives (VFDs) may have non-unity power factor on the input; use the VFD's rated input kVA for sizing, not the motor's rated kW output.
Frequently asked questions
What is the three-phase current formula?
For a balanced three-phase system, line current I = P / (sqrt(3) * VL * pf), where P is real power in watts, VL is line-to-line voltage in volts, and pf is power factor. Apparent power S = sqrt(3) * VL * I.
What is the difference between line voltage and phase voltage?
In a three-phase system, line voltage (VL) is the voltage between any two line conductors. Phase voltage (Vphase) is the voltage between one line conductor and neutral. For a balanced star (wye) system, VL = sqrt(3) * Vphase. In the US, 208 V three-phase has 120 V phase-to-neutral.
What is sqrt(3) in the three-phase formula?
The sqrt(3) factor (approximately 1.732) accounts for the 120-degree phase offset between the three phases. When you add three phasors separated by 120 degrees, the result is sqrt(3) times the individual phasor magnitude.
What are common three-phase voltages in the US?
Common US three-phase voltages include 208/120 V (commercial buildings), 240 V (delta, industrial), 480/277 V (large commercial/industrial), and 4,160 V or higher (utility distribution). Industrial motor nameplate voltages are 200, 230, 460, and 575 V.
How does three-phase compare to single-phase for the same power?
Three-phase delivers the same power as single-phase but with lower current per conductor by a factor of sqrt(3) at the same line voltage, reducing conductor losses. It also provides smoother power delivery and is more efficient for large motors.
Official sources
- NFPA 70 (NEC): NEC Article 430, Motors and Motor Circuits.
- IEEE: IEEE Standards Association.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.