Three Phase Power Calculator
Calculate the real output power (kW) of a three-phase electrical system from line voltage, line current, power factor, and efficiency. Use it for motor sizing, generator selection, and load analysis.
About this calculator
Three-phase power systems deliver energy more efficiently than single-phase systems and are standard in industrial and commercial settings. Real output power depends on the connection type. For a wye (star) connection the formula is: P (kW) = V × I × PF × (η/100) / 1000, where V is line voltage and I is line current. For a delta connection an additional √3 factor applies because line current and phase current differ: P (kW) = √3 × V × I × PF × (η/100) / 1000. Power factor (PF) accounts for reactive loads (motors, transformers) that draw current out of phase with voltage. System efficiency η captures mechanical and electrical losses. Apparent power in kVA = √3 × V × I / 1000 for both configurations.
How to use
Example: delta-connected motor, line voltage 480 V, line current 20 A, power factor 0.85, efficiency 92%. Step 1 — connection factor for delta: √3 ≈ 1.732. Step 2 — multiply all terms: 1.732 × 480 × 20 × 0.85 × (92/100) = 1.732 × 480 × 20 × 0.85 × 0.92. Step 3 — compute: 1.732 × 480 = 831.4; × 20 = 16,627; × 0.85 = 14,133; × 0.92 = 13,002 W. Step 4 — convert to kW: 13,002 / 1000 ≈ 13.0 kW. The motor delivers approximately 13 kW of real output power.
Frequently asked questions
What is the difference between wye and delta connection in three-phase power calculations?
In a wye (star) connection, each phase connects between a line and a neutral point, so phase voltage equals line voltage divided by √3, and phase current equals line current. In a delta connection, each phase spans two lines directly, so phase voltage equals line voltage but line current equals phase current multiplied by √3. This √3 factor appears in the delta power formula. The choice of connection affects starting torque, insulation requirements, and how voltage imbalances propagate through the system.
How does power factor affect three-phase power consumption and electricity bills?
Power factor is the ratio of real power (kW) to apparent power (kVA). A low power factor means the system draws more current than the actual work requires, increasing losses in cables and transformers. Utilities often charge commercial customers a penalty for power factors below 0.9 or 0.95. Improving power factor with capacitor banks reduces reactive current, lowers energy losses, and can eliminate utility surcharges — often paying back the investment within months.
Why is three-phase power more efficient than single-phase for industrial applications?
Three-phase systems deliver power continuously through three overlapping voltage waveforms, producing smoother torque in motors and allowing smaller conductors to carry the same power compared to single-phase. For the same apparent power, a three-phase system uses about 75% of the conductor material of an equivalent single-phase system. Three-phase motors are also simpler, more reliable, and more efficient than single-phase motors of comparable size, making them the preferred choice for pumps, compressors, and CNC machinery.