35,333.84
W
35.3338
kW
41,569.22
VA
41.5692
kVA
21,897.95
VAR
—
V
—
A
—
°
35,333.84
W
35.3338
kW
41,569.22
VA
41.5692
kVA
21,897.95
VAR
—
V
—
A
—
°
The Three Phase Calculator computes the total power, per-phase values, and power triangle for balanced three-phase AC systems. Three-phase power is the backbone of modern electrical power distribution, used in virtually all industrial, commercial, and utility-scale applications because it delivers power more efficiently and with less conductor material than single-phase systems.
A three-phase system uses three sinusoidal voltages of equal amplitude and frequency, offset by 120° from each other. This arrangement provides constant instantaneous power delivery (unlike single-phase, which pulsates) and enables efficient operation of large motors and industrial equipment. The total real power in a balanced three-phase system is P = √3 · Vₗ · Iₗ · cos(φ).
Three-phase systems can be configured in two ways: Wye (Y or Star) and Delta (Δ or Triangle). In a Wye configuration, each phase is connected between a line conductor and a common neutral point. The line-to-line voltage is √3 times the phase voltage (Vₗ = √3 · Vₚ), while line current equals phase current (Iₗ = Iₚ). In a Delta configuration, each phase is connected between two line conductors. The line voltage equals the phase voltage (Vₗ = Vₚ), while line current is √3 times the phase current (Iₗ = √3 · Iₚ).
The total power equations are the same for both configurations when expressed in terms of line quantities, which makes the √3 factor particularly convenient for power calculations regardless of the internal winding arrangement. This calculator determines the total real, reactive, and apparent power from line voltage, line current, and power factor, while also computing the per-phase voltage and current for the selected configuration.
Three-phase power systems operate at standard voltages worldwide: 208V, 240V, 380V, 400V, 415V, 480V, and higher voltages for transmission. Industrial motors from fractional horsepower to thousands of horsepower run on three-phase power. Understanding three-phase calculations is essential for electrical engineers, electricians, and facility managers who design, install, and maintain electrical systems.
This calculator handles balanced loads, where all three phases carry equal current at equal power factor. For unbalanced loads, each phase must be analyzed separately, which requires more complex per-phase analysis.
The three-phase calculator uses the standard balanced three-phase power equations:
Total Real Power:
$$P = \sqrt{3} \cdot V_L \cdot I_L \cdot \cos(\varphi)$$
Total Apparent Power:
$$S = \sqrt{3} \cdot V_L \cdot I_L$$
Total Reactive Power:
$$Q = \sqrt{3} \cdot V_L \cdot I_L \cdot \sin(\varphi)$$
Wye (Star) Configuration:
$$V_{phase} = \frac{V_L}{\sqrt{3}}, \quad I_{phase} = I_L$$
Delta (Triangle) Configuration:
$$V_{phase} = V_L, \quad I_{phase} = \frac{I_L}{\sqrt{3}}$$
Phase Angle:
$$\varphi = \arccos(PF)$$
The total real power (kW) represents the actual useful power consumed by the load. The apparent power (kVA) determines the required capacity of transformers, generators, and switchgear. The reactive power (kVAR) indicates the reactive component that must be supplied. The per-phase values show the voltage across and current through each individual winding, which is essential for component sizing and protection coordination.
Inputs
Results
A three-phase motor on a 480V system drawing 60A per line at PF = 0.85 consumes 42.36 kW of real power. In Wye configuration, each phase sees 277 V. The system requires a transformer rated at least 50 kVA.
Inputs
Results
A resistive heating load in Delta draws 30A line current at unity power factor on 400V. Total power is 20.78 kW with zero reactive power. Each heating element carries 17.32 A at 400 V.
Three-phase power delivers constant instantaneous power (no pulsation), uses 25% less conductor material for the same power, and enables self-starting rotating magnetic fields for motors. Three-phase generators and motors are smaller, lighter, and more efficient than equivalent single-phase machines. This is why all utility-scale power generation and industrial distribution uses three-phase systems.
The √3 (approximately 1.732) factor arises from the 120° phase offset between the three phases. In a Wye system, the line-to-line voltage is the vector difference of two phase voltages separated by 120°, which gives Vₗ = 2·Vₚ·sin(60°) = √3·Vₚ. Similarly, in Delta, the line current is √3 times the phase current.
Wye is preferred when a neutral point is needed (for single-phase loads and grounding), and for higher voltage transmission (phase voltage is lower, reducing insulation requirements). Delta is used when no neutral is needed, for driving certain motors, and when higher phase voltage is acceptable. Many systems use Wye for distribution and Delta for motor windings.
A balanced three-phase load draws equal current at equal power factor on all three phases. Under balanced conditions, the neutral current in a Wye system is zero, and the simple √3 formulas apply. Unbalanced loads (different currents on each phase) require individual phase analysis and result in non-zero neutral current.
For Wye: Vₚ = Vₗ/√3 and Iₚ = Iₗ. For Delta: Vₚ = Vₗ and Iₚ = Iₗ/√3. These relationships hold for balanced conditions. Remember that line quantities are what you measure at the terminals, while phase quantities are across/through each individual winding.
This calculator assumes a balanced load with equal current and power factor on all three phases. For unbalanced loads, you would need to analyze each phase separately using single-phase power calculations and then sum the results. Unbalanced analysis also requires considering neutral current and sequence components.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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