Three-Phase Industrial Power
Calculations for heavy-duty industrial systems. Handle complex √3 vector math for motors and plant distribution panels.
Industrial Config
Current result accounts for the line-voltage multiplier (√3 ≈ 1.732) and system efficiency losses. Suitable for motor FLA verification.
Three-Phase Power Formulas
Three-phase power delivers 73% more power than single-phase at the same voltage and current — using only one extra conductor.
Real Power (kW)
P = √3 × V × I × PF The √3 (1.732) factor accounts for the 120° phase offset between the three current waveforms, which produces consistent instantaneous power delivery.
Apparent Power (kVA)
S = √3 × V × I Apparent power is the total capacity the supply must provide, regardless of power factor. Used to size transformers and generators.
Understanding Three-Phase AC Power
Three-phase power is the standard for industrial and commercial electrical distribution. It consists of three sinusoidal voltages, each offset by 120°, that together produce a constant, smooth power delivery. This makes three-phase motors smoother and more efficient than single-phase equivalents — and allows a given amount of power to be transmitted with less conductor material.
Why √3 (1.732)?
The three-phase power formula uses the square root of 3 because of the vector relationship between line voltage and phase voltage. In a balanced three-phase system, line-to-line voltage (V_LL) equals √3 times the line-to-neutral phase voltage (V_LN). For example, 208V line-to-line corresponds to 120V phase voltage (208 ÷ 1.732 ≈ 120).
Three-Phase Advantages
- Constant Power Delivery: The three phases sum to a constant total at every instant — unlike single-phase which pulses at twice the supply frequency. This makes motors run smoother with less vibration.
- Higher Power Density: A three-phase system delivers 73% more power than single-phase at the same conductor size and voltage, making it far more economical for large loads.
- Simpler Large Motor Design: Three-phase induction motors have no starting capacitors or split-phase windings — the rotating magnetic field forms naturally from the three phases.
- Lower Neutral Current: In a balanced three-phase system, the neutral conductor carries zero current, saving conductor material in distribution systems.
Common Three-Phase Voltages
- 208V / 120V: US commercial — line-to-line / line-to-neutral. Common in office buildings and light industrial.
- 480V / 277V: US industrial standard. Used for large motors, HVAC, and industrial equipment.
- 400V / 230V: International (IEC) standard across most of Europe, Asia, and Australia.