Three-Phase Power Calculator

Three-Phase Power Guide

Three-phase power is the standard for commercial, industrial, and utility electrical systems worldwide, including Australia and New Zealand. It delivers power using three conductors carrying alternating current waveforms that are offset by 120 degrees from each other. Compared to single-phase, three-phase supply provides approximately 73 percent more power using the same conductor cross section, produces a constant power output (no pulsating torque in motors), and enables more efficient transmission over long distances. The standard Australian three-phase supply is 400 V line-to-line and 230 V phase-to-neutral at 50 Hz. This calculator converts between voltage, current, real power, apparent power, and reactive power for both star and delta connected loads.

Key concepts

• Real power (P). The active power that performs useful work, measured in watts (W) or kilowatts (kW). In a balanced three-phase system, P = 1.732 x V_line x I_line x cos(phi). This is the power that appears on the electricity bill and converts to heat, motion, or light.
• Apparent power (S). The total power in the circuit, combining both real and reactive components. Measured in volt-amperes (VA) or kilovolt-amperes (kVA). Cables, transformers, and generators are all rated in kVA because their thermal limits depend on the total current they carry, regardless of power factor.
• Power factor (cos phi). The ratio of real power to apparent power, ranging from 0 to 1. A power factor of 1.0 means all current is doing useful work. Low power factor (below 0.90) means the supply is carrying more current than necessary, increasing cable losses, transformer loading, and supply authority demand charges. Most Australian supply authorities penalise consumers with power factor below 0.90.
• Star (Y) vs delta (triangle) connection. In a star connected system, each load is connected between a phase and the neutral point. Line voltage is 1.732 times phase voltage, and line current equals phase current. In a delta connected system, each load is connected between two phases directly. Line voltage equals phase voltage, and line current is 1.732 times phase current. Star connection provides a neutral for single-phase loads. Delta connection is common for motors and transformers.

Common scenarios

1. Sizing a three-phase cable for a motor. A 30 kW three-phase motor with a power factor of 0.85 on a 400 V supply draws approximately 51 A per phase. The cable must be sized to carry this current continuously, with allowances for installation conditions (grouping, ambient temperature, insulation type) per AS/NZS 3008.1.1. The calculator gives the line current directly from the kW rating, voltage, and power factor.
2. Checking transformer loading. A 500 kVA distribution transformer supplies a mixed load of motors and lighting. The total real power demand is 380 kW at 0.82 power factor. The apparent power is 380 / 0.82 = 463 kVA, which is within the transformer rating. If additional load is added, the power factor must be improved (capacitor bank) or a larger transformer specified.
3. Balancing single-phase loads across three phases. A commercial kitchen has twelve 2.4 kW single-phase ovens to distribute across a three-phase supply. Placing four ovens on each phase gives a balanced load of 9.6 kW per phase. The calculator can verify the per-phase and total current draw, helping identify whether the existing supply can handle the connected load before additional circuits are installed.