Three Phase Power Calculator
Compute the total real power delivered by a three-phase AC system from line voltage, line current, and power factor. Essential for engineers sizing motors, generators, and industrial electrical panels.
About this calculator
Three-phase power is the standard for industrial and commercial electricity distribution because it delivers more power with less conductor material than single-phase systems. The real (active) power formula for a balanced three-phase system is: P = √3 × V_line × I_line × PF, where V_line is the line-to-line voltage in volts, I_line is the line current in amperes, and PF is the power factor (a dimensionless value between 0 and 1). The factor √3 (≈ 1.732) arises from the 120° phase relationship between the three voltage phases. Power factor represents the ratio of real power to apparent power, accounting for reactive loads such as motors and transformers. A power factor of 1.0 means purely resistive load; lower values indicate reactive energy that does not perform useful work. The result P is in watts (W) and can be converted to kilowatts by dividing by 1,000.
How to use
A three-phase motor operates at a line voltage of 400 V, draws a line current of 25 A, and has a power factor of 0.85. Step 1 — Enter 400 as line voltage. Step 2 — Enter 25 as line current. Step 3 — Enter 0.85 as power factor. Step 4 — The calculator computes: P = √3 × 400 × 25 × 0.85 = 1.7321 × 400 × 25 × 0.85 ≈ 14,722 W ≈ 14.7 kW. This is the real power consumed by the motor. The apparent power would be √3 × 400 × 25 ≈ 17,321 VA, confirming PF = 14,722 / 17,321 ≈ 0.85.
Frequently asked questions
What is the difference between real power, apparent power, and reactive power in a three-phase system?
Real power (P, measured in watts) is the actual power consumed and converted to useful work such as heat, light, or mechanical motion. Apparent power (S, measured in volt-amperes, VA) is the product of RMS voltage and RMS current without regard to phase angle. Reactive power (Q, measured in VAR) is energy stored and released by inductive or capacitive elements each cycle without performing net work. The three are related by the power triangle: S² = P² + Q², and the power factor PF = P / S. Only real power is billed by utilities and does productive work.
Why is a power factor less than 1 a problem for industrial electrical systems?
A low power factor means a system draws more current from the supply than is strictly needed to deliver the required real power, increasing resistive losses in cables, transformers, and switchgear. Utilities often impose penalty charges on commercial and industrial customers whose average power factor falls below a threshold such as 0.90 or 0.95. Equipment must also be rated for the higher apparent power, increasing capital costs. Power factor correction — typically using capacitor banks — compensates for inductive loads like motors and brings the power factor closer to unity, reducing current draw and energy costs.
How does three-phase power differ from single-phase power and when should I use each?
Single-phase power uses one alternating voltage waveform and is standard for residential lighting and small appliances, typically up to a few kilowatts. Three-phase power uses three waveforms offset by 120°, providing smoother power delivery and significantly higher power capacity from the same conductor size. Three-phase is preferred for motors above about 1 kW, large HVAC systems, industrial machinery, and data centres because it is more efficient and motors run more smoothly. The three-phase formula P = √3 × V × I × PF delivers roughly 1.73 times more power than the equivalent single-phase formula (P = V × I × PF) at the same voltage and current.