Three-Phase Power Calculator
Enter voltage, power factor and one known value (amps, kW or kVA) to get the full power triangle.
Step-by-step
- Enter valid values to begin.
Balanced, sinusoidal load assumed. Voltage is line-to-line (the nameplate voltage). For unbalanced or heavily distorted loads, use the unbalance and neutral-current calculators and a true-RMS power-quality meter.
Three-Phase Power: kW, kVA, kVAR and Why You Pay for All Three
Core Engineering Principles
Three coils spaced 120° apart on a stator, or three sinusoidal voltages 120° apart on a bus, give you something single-phase can’t: power that never drops to zero. At any instant one phase is peaking while the others are in the middle of a swing, so the sum of the instantaneous power is constant. That’s the reason a three-phase motor doesn’t pulse and doesn’t need a start winding, and it’s why the plant runs on it.
The √3 is geometry, nothing mystical. A line-to-line voltage is the difference between two phase voltages that are 120° apart, so its magnitude is 1.732 times a phase voltage. Multiply line voltage by line current and by 1.732 and you have apparent power in kVA. Multiply by the power factor and you have the real work, kW. What’s left over, kVAR, is the current sloshing back and forth to build magnetic fields in motors and transformers. It does no work, but it loads the cables, transformers and generators just the same, which is why the utility bills you for it.
Wye: Vph = VL / √3 • Delta: Iph = IL / √3
NEC & Standard References
IEEE Std 1459 defines active, reactive and apparent power for three-phase systems, including the unbalanced and distorted cases. This calculator assumes a balanced, sinusoidal load, which is a fair starting point on a motor control center but not on a panel full of drives. NEC 430.6(A) says to size motor conductors and protection from the Table 430.250 current rather than the nameplate, and NEC 215.2 and 220.5(A) have you size feeders in amps, so converting kW to amps correctly matters. For billing, most utilities meter kW demand and a power-factor penalty below 0.90–0.95; the real tariff is in your contract.1. Apparent power: S = 1.732 × 480 × 120 / 1000 = 99.8 kVA.
2. Real power: P = 99.8 × 0.85 = 84.8 kW.
3. Reactive: Q = √(99.8² − 84.8²) = 52.6 kVAR.
The utility bills on the 84.8 kW but the 99.8 kVA is what your transformer and cables carry. Bring the power factor to 0.95 and the same work needs only 89 kVA, about 11% less current on everything upstream.
- Don’t apply this to an unbalanced load blindly. If the three legs read 120, 100 and 140 A, average them for a rough answer, but use the unbalance calculator before you trust it for a motor.
- Power factor meters lie on drives. A VFD input shows high displacement PF but high harmonic current. True RMS and a power-quality analyzer give the real picture.
- Line voltage, not phase. Nameplates say 480 V, which is line-to-line. Plugging 277 V into the formula is the classic mistake.
- Leave margin on breakers. Continuous loads belong at 80% of the breaker rating, and a transformer at 100% load all day runs hot.