3-Phase Watt Calculator
Calculate active power (W), apparent power (VA), reactive power (VAR), and line current in 3-phase Wye and Delta AC systems.
Calculate 3-Phase Power
Enter line-to-line voltage, current, and power factor to compute 3-phase power.
How to Calculate 3-Phase Power
To calculate 3-phase power, multiply the square root of 3 (≈ 1.732) by line-to-line voltage, line current, and power factor: P = √3 × VLL × IL × PF. This formula applies to both balanced Wye (Star) and Delta three-phase configurations.
Where:
- P = active power in watts (W)
- V = line-to-line voltage in volts (V)
- I = line current in amperes (A)
- PF = power factor (cosine of phase angle θ)
- √3 = 1.732 (accounts for phase displacement in 3-phase systems)
Scenario: A 480V 3-phase motor draws 20A with a power factor of 0.85
P = 1.732 × 480 × 20 × 0.85
P = 14,117 W (14.12 kW)
The motor consumes 14.12 kilowatts of active power.
Wye vs Delta Configuration
Three-phase power systems use two winding configurations that affect the relationship between line and phase quantities:
| Property | Wye (Star) ⭐ | Delta (Triangle) △ |
|---|---|---|
| Phase Voltage | Vphase = VLL ÷ √3 | Vphase = VLL |
| Phase Current | Iphase = Iline | Iphase = Iline ÷ √3 |
| Common Use | Distribution, long-distance transmission | Industrial motors, heavy loads |
| Neutral Wire | Available (center point) | Not available |
Both configurations deliver the same total power when balanced: Ptotal = 3 × Vphase × Iphase × PF. The √3 multiplier in the standard formula accounts for the 120° phase displacement between the three phases.
3-Phase Power Reference Table
Common 3-phase power calculations at standard voltages (power factor = 0.85):
| Voltage (V) | Current (A) | PF | Active Power | Apparent Power |
|---|---|---|---|---|
| 208 V | 10 A | 0.85 | 3,060 W | 3,601 VA |
| 208 V | 30 A | 0.85 | 9,181 W | 10,801 VA |
| 480 V | 20 A | 0.85 | 14,117 W | 16,609 VA |
| 480 V | 50 A | 0.85 | 35,293 W | 41,522 VA |
| 600 V | 30 A | 0.85 | 26,470 W | 31,141 VA |
| 600 V | 100 A | 0.85 | 88,234 W | 103,805 VA |
Frequently Asked Questions About 3-Phase Power
What is 3-phase power?
3-phase power is an AC electrical system that uses three alternating currents, each offset by 120 degrees. Three-phase power delivers more power per conductor than single-phase and provides constant power delivery, making it standard for industrial motors, commercial buildings, and power distribution systems. The three phases are typically labeled A, B, and C (or L1, L2, L3).
How do you calculate watts in a 3-phase system?
To calculate watts in a 3-phase system, use P = √3 × V × I × PF, where V is line-to-line voltage, I is line current, and PF is power factor. For a 480V system drawing 25A at 0.85 PF: P = 1.732 × 480 × 25 × 0.85 = 17,647 W (17.65 kW).
Why is √3 (1.732) used in 3-phase calculations?
The √3 factor accounts for the 120° phase angle between the three phases. In a balanced 3-phase system, line-to-line voltage is √3 times the phase voltage (in Wye configuration). This geometric relationship means total 3-phase power equals √3 × V_LL × I_L × PF rather than simply 3 × V × I × PF.
What is the difference between Wye and Delta connections?
In a Wye (Star) connection, one end of each winding connects to a common neutral point, so phase voltage = line voltage ÷ √3 and phase current = line current. In a Delta connection, windings form a triangle with no neutral, so phase voltage = line voltage and phase current = line current ÷ √3. Both deliver the same total power.
What is power factor in 3-phase systems?
Power factor (PF) is the ratio of real power (W) to apparent power (VA) in an AC circuit. PF = cos(θ), where θ is the phase angle between voltage and current. A PF of 1.0 means all power is real (resistive loads). Typical motor PF ranges from 0.80–0.90. Low PF means more current is needed for the same real power, increasing cable size and energy losses.
How do I convert 3-phase power to amps?
To find amps from 3-phase power: I = P ÷ (√3 × V × PF). For example, a 15 kW load at 480V with PF 0.85: I = 15,000 ÷ (1.732 × 480 × 0.85) = 15,000 ÷ 706.7 = 21.2 A. This gives the line current drawn by the load.