Three-Phase AC Electrical Power Calculator
In a balanced three-phase AC distribution system, real active power P equals √3 (≈ 1.73205) multiplied by line-to-line RMS voltage V_L, line current I_L, and power factor cos(φ).
Active power delivered in Watts (switch inline unit to kW or hp)
Phase-to-phase RMS voltage in Volts (e.g., 208V, 400V, 480V)
RMS current per phase conductor in Amperes
Ratio of real power kW to apparent power kVA (0.1 to 1.0)
Step-by-Step Calculation
In a balanced three-phase AC distribution system, real active power P equals √3 (≈ 1.73205) multiplied by line-to-line RMS voltage V_L, line current I_L, and power factor cos(φ).
Real-World Reference Values
Standard North American motor & data center feed
50 Hz harmonized industrial three-phase grid
Set PF = 1.00 to solve directly for Apparent Power (VA / kVA)
20-Row Comparison Table
Three-Phase Real Power (P) · Line-to-Line Voltage (V_L)
| # | Line-to-Line Voltage (V) | Three-Phase Real Power (W) | Δ % |
|---|---|---|---|
| 01 | 10 V | 736.1216 W | -97.50% |
| 02 | 400 VCurrent | 29,444.86 W | 0.00% |
| 03 | 1,498.28 V | 110,291.35 W | +274.57% |
| 04 | 2,242.41 V | 165,068.97 W | +460.60% |
| 05 | 2,986.55 V | 219,846.59 W | +646.64% |
| 06 | 3,730.69 V | 274,624.20 W | +832.67% |
| 07 | 4,474.83 V | 329,401.82 W | +1018.71% |
| 08 | 5,218.97 V | 384,179.44 W | +1204.74% |
| 09 | 5,963.11 V | 438,957.05 W | +1390.78% |
| 10 | 6,707.24 V | 493,734.67 W | +1576.81% |
| 11 | 7,451.38 V | 548,512.29 W | +1762.85% |
| 12 | 8,195.52 V | 603,289.90 W | +1948.88% |
| 13 | 8,939.66 V | 658,067.52 W | +2134.91% |
| 14 | 9,683.80 V | 712,845.14 W | +2320.95% |
| 15 | 10,427.93 V | 767,622.75 W | +2506.98% |
| 16 | 11,172.07 V | 822,400.37 W | +2693.02% |
| 17 | 11,916.21 V | 877,177.99 W | +2879.05% |
| 18 | 12,660.35 V | 931,955.60 W | +3065.09% |
| 19 | 13,404.49 V | 986,733.22 W | +3251.12% |
| 20 | 14,148.63 V | 1,041,510.84 W | +3437.16% |
Frequently Asked Questions
How do I find the line current I_L for a 50 kW motor on a 480V 3-phase supply?+
Click SOLVE FOR on I_L, switch P unit to kW and enter 50, set V_L = 480, and enter the motor nameplate power factor PF.
Where does the √3 factor come from in three-phase power?+
In a Wye system, V_L = √3 × V_phase while I_L = I_phase; in Delta, I_L = √3 × I_phase. In both configurations, 3 × V_phase × I_phase simplifies to √3 × V_L × I_L.
How do I calculate Apparent Power (kVA) with this tool?+
Set Power Factor PF = 1.00; the resulting power P equals total Apparent Power S in VA (or kVA when kW is selected).