Three Phase Calculator
Real, apparent, and reactive power
Required Parameters
Waiting for input data...
Quick Answer
Total Real Power (W) in a balanced 3-phase system is P = √3 × Line Voltage × Line Current × Power Factor.
Three-Phase Power Calculator
Calculate line voltage, phase voltage, line current, phase current, and power in three-phase electrical systems.
Star (Y) Connection
- Vline = sqrt(3) x Vphase
- Iline = Iphase
- P = sqrt(3) x Vline x Iline x cos(phi)
Delta Connection
- Vline = Vphase
- Iline = sqrt(3) x Iphase
- P = sqrt(3) x Vline x Iline x cos(phi)
Power Factor
- Apparent Power: S = sqrt(3) x V x I (VA)
- Real Power: P = S x cos(phi) (W)
- Reactive Power: Q = S x sin(phi) (VAR)
Related Tools
- Ohm's Law Calculator
- Wire Size Calculator
- Energy Conversion Calculator
Design Notes
Three-phase systems are standard in industrial motor drives and high-power distribution because they provide constant power transfer (zero torque ripple on motors) and require less copper wire than equivalent single-phase systems. When switching between Wye (Star) and Delta configurations, remember that in Wye, Line Current = Phase Current but Line Voltage = √3 × Phase Voltage. In Delta, it's reversed. Always ensure your power factor (PF) is as close to 1.0 as possible to minimize reactive power losses.
Common Mistakes
- 1
Using Phase Voltage instead of Line-to-Line Voltage when applying the √3 factor.
- 2
Forgetting to multiply by the Power Factor, yielding Apparent Power (VA) instead of True Power (Watts).
- 3
Assuming an unbalanced load calculation can use this simple balanced formula.
Engineering Handbox
1. Identify variables: VL = 480, IL = 25, PF = 0.85 2. Multiply: 1.732 × 480 × 25 × 0.85 3. Result: 17,666.4 Watts
Knowledge Base
What is the three-phase power formula?
For a balanced three-phase system: P = √3 × V_line × I_line × PF, where P is real power in watts, V_line is line-to-line voltage, I_line is line current, and PF is the power factor. This single formula works for both Wye (Star) and Delta configurations when using line values.
What is the difference between Wye and Delta?
In Wye (Star): V_line = √3 × V_phase, I_line = I_phase. Loads share a neutral point; each phase sees V_line/√3. In Delta: V_line = V_phase, I_line = √3 × I_phase. Loads connect directly between line pairs. Wye is more common for distribution (provides neutral); Delta is common for motors and transformers.
What is power factor?
Power factor (PF) is the ratio of real power (W) to apparent power (VA): PF = P/S = cos(θ), where θ is the phase angle between voltage and current. PF = 1.0 means all power does useful work. PF < 1.0 means reactive power circulates in the circuit (inductive loads like motors typically have PF = 0.75-0.90). Low PF wastes capacity and increases utility bills.
What is apparent power vs real power vs reactive power?
Real Power (P, watts): does actual work — heat, motion, light. Reactive Power (Q, VAR): oscillates between source and load in inductive/capacitive circuits — does no work but occupies capacity. Apparent Power (S, VA): the vector sum S = √(P² + Q²). Your utility meter charges for real power, but your electrical system must be sized for apparent power.
Why is three-phase more efficient than single-phase?
Three-phase delivers constant instantaneous power (no zero-crossings), while single-phase power pulsates at 2× line frequency. This means: (1) motors run smoother with no torque ripple, (2) 3-phase needs ~25% less copper for the same power, (3) 3-phase allows higher power in the same wire gauge, (4) 3-phase transformers are smaller and cheaper per kVA.
What is 480V three-phase?
480V 3-phase is the standard industrial power in North America (460V nominal motor voltage). It provides 277V phase-to-neutral in Wye configuration (used for commercial lighting). A 480V/25A 3-phase circuit delivers √3 × 480 × 25 × 0.85 PF ≈ 17.7 kW of real power. In Europe/Asia, the equivalent is 400V 3-phase (230V phase-to-neutral).
How do I measure three-phase power?
Use two wattmeters for 3-wire systems (Blondel's theorem) or three wattmeters for 4-wire systems. A single clamp meter on one phase only gives accurate total power if the system is perfectly balanced. For accuracy, use a dedicated three-phase power analyzer that measures all three phases simultaneously and computes total P, Q, S, and PF.
What happens if the three phases are unbalanced?
The simple √3 × VL × IL × PF formula is only valid for balanced loads. With unbalanced loads: (1) Neutral current increases (can overload the neutral conductor). (2) Voltage distortion occurs. (3) Total power must be calculated per-phase: P_total = P_A + P_B + P_C. Maximum phase imbalance should be kept below 5-10% for motor applications.
How do I size a three-phase circuit breaker?
Calculate line current: I_line = P / (√3 × V_line × PF). For a 20kW load at 480V, PF=0.85: I_line = 20000 / (1.732 × 480 × 0.85) = 28.3A. Choose the next standard breaker size: 30A or 40A. Apply NEC derating factors for continuous loads (125%): 28.3 × 1.25 = 35.4A → use 40A breaker.
What is a VFD and how does it relate to three-phase?
A Variable Frequency Drive (VFD) converts single or three-phase AC to variable-frequency three-phase AC to control motor speed. VFDs improve energy efficiency by 20-50% in pump/fan applications by matching motor speed to load. Input side can be single-phase (small motors) or three-phase (large motors). Output is always three-phase.