How Three-Phase Power Is Calculated: Real Power, Apparent Power, and Current
Understand three-phase power calculations — how to find real power (kW), apparent power (kVA), reactive power (kVAR), and current from three-phase motor and generator specifications.
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What Is Three-Phase Power?
Three-phase power uses three conductors carrying alternating current waves offset by 120° from each other. It's the standard for industrial motors, commercial buildings, and power distribution because it delivers more power with less conductor material than single-phase and runs motors more smoothly.
Three-Phase Power Formulas
Real Power (P, in watts or kW): P = √3 × V_LL × I_L × PF
Where: - V_LL = line-to-line voltage (between any two phases) - I_L = line current (amps per conductor) - PF = power factor (0 to 1) - √3 ≈ 1.732
Apparent Power (S, in VA or kVA): S = √3 × V_LL × I_L (same formula without PF)
Reactive Power (Q, in VAR or kVAR): Q = √3 × V_LL × I_L × sin(θ)
Where θ = arccos(PF) (the power factor angle)
Power Factor: PF = P / S = cos(θ)
The Power Triangle
Real power (P), reactive power (Q), and apparent power (S) form a right triangle: S² = P² + Q² or: S = √(P² + Q²)
Worked Examples
Example 1: 20 HP electric motor at 480V, PF = 0.85 20 HP = 14,920 W
Find line current: I = P / (√3 × V × PF) = 14,920 / (1.732 × 480 × 0.85) = 14,920 / 707.5 = 21.1 amps per phase
Apparent power: S = √3 × 480 × 21.1 = 17,553 VA = 17.6 kVA Reactive power: Q = √(17.6² − 14.9²) = √(309.8 − 222.0) = √87.8 = 9.37 kVAR
Example 2: Find power from measured current Three-phase load at 208V, measuring 50 amps per phase, PF = 0.92
P = √3 × 208 × 50 × 0.92 = 1.732 × 208 × 46 = 1.732 × 9,568 = 16,572 W = 16.6 kW
Line vs. Phase Voltage
Three-phase systems have two voltage references: - Line-to-line (V_LL): Voltage between two phases (what's usually listed: 208V, 480V) - Line-to-neutral (V_LN): Voltage from one phase to neutral = V_LL / √3
Common Three-Phase Voltages and Motor Current Guide
Approximate full-load amps for three-phase motors:
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Frequently Asked Questions
- How do I calculate three-phase power?
- Real power: P = √3 × V_LL × I_L × PF (watts). Apparent power: S = √3 × V_LL × I_L (VA). Example: 480V three-phase, 25 amps, PF=0.90: P = 1.732 × 480 × 25 × 0.90 = 18,687 W ≈ 18.7 kW. Without PF (apparent): S = 1.732 × 480 × 25 = 20,764 VA = 20.8 kVA.
- What is the difference between kW and kVA in three-phase power?
- kW (kilowatts) is real power — the actual work done. kVA (kilovolt-amperes) is apparent power — what the source must supply including reactive components. kW = kVA × Power Factor. A 20 kVA transformer with PF=0.85 delivers 17 kW of real power. Equipment is rated in kVA because that's what determines transformer and conductor sizing regardless of load PF.
- Why does three-phase use √3 in power calculations?
- The √3 factor comes from the geometry of three-phase vectors offset by 120°. When you calculate power across the three phases, the line-to-line voltage (used in the formula) is √3 times the phase-to-neutral voltage. The √3 converts between these two reference voltages and appears in both current and power calculations for three-phase systems.
- How do I convert three-phase amps to kW?
- kW = √3 × V_LL (kV) × I_L (A) × PF. At 480V with 30A and PF=0.90: kW = 1.732 × 0.480 × 30 × 0.90 = 22.5 kW. If power factor is unknown, use 0.85 as a conservative estimate for motor loads, or 1.0 for resistive heating loads.
Last updated 7/28/2026