# Three-Phase Power Calculator Calculate active, reactive, and apparent power for a balanced three-phase system: S=√3·U·I, P=√3·U·I·cosφ, Q=√3·U·I·sinφ. Also returns the power-factor angle φ and verifies the power triangle. > Canonical page: https://elysiatools.com/en/tools/three-phase-power-calculator - **Category:** Math & Numbers - **Keywords:** three phase power, P=√3UIcosφ, active power, reactive power, apparent power, power triangle, balanced load, AC power, electrical engineering ## Overview The Three-Phase Power Calculator computes active, reactive, and apparent power for balanced AC electrical systems. By entering the line-to-line RMS voltage, line RMS current, and power factor, you can instantly determine the power-factor angle and verify the power triangle relationship. ## Inputs - **Line Voltage U (V)** (number): Line-to-line RMS voltage. - **Line Current I (A)** (number): Line RMS current per phase. - **Power Factor cosφ** (number): Power factor (0 < cosφ ≤ 1). Lagging by convention. - **Decimal Places** (number) ## When to use - When designing or auditing balanced three-phase electrical installations to determine total load requirements. - When calculating the reactive power compensation needed to improve the power factor of industrial machinery. - When verifying electrical measurements from field meters against theoretical power triangle calculations. ## How it works - Enter the line-to-line RMS voltage (U) in volts and the line RMS current (I) in amperes. - Input the system's power factor (cosφ) as a value between 0 and 1, and optionally set the desired decimal precision. - The calculator computes apparent power (S = √3·U·I), active power (P = S·cosφ), reactive power (Q = S·sinφ), and the phase angle (φ). - The tool verifies the calculations by confirming that the hypotenuse of the power triangle matches the apparent power (S = √(P² + Q²)). ## Use cases - Sizing electrical cables and switchgear based on the calculated apparent power (kVA) of a three-phase motor. - Estimating the active power consumption (kW) of industrial equipment to calculate energy costs. - Determining the reactive power (kvar) load to specify capacitor banks for power factor correction. ## Frequently asked questions ### What is the difference between active, reactive, and apparent power? Active power (P, in watts) does real work; reactive power (Q, in vars) sustains electromagnetic fields; apparent power (S, in volt-amperes) is the total power flowing in the circuit. ### Does this calculator work for unbalanced three-phase systems? No, this calculator assumes a balanced three-phase system where voltages and currents are equal across all three phases. ### How is the power-factor angle φ calculated? The angle φ is calculated as the arccosine of the power factor (cosφ), representing the phase shift between voltage and current. ### Why is the power triangle verification included? It mathematically confirms that the calculated active and reactive powers satisfy the Pythagorean relationship with the apparent power. ### What unit should I use for the line voltage? 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