Three-Phase Power Calculator
Three-phase alternating current power is the standard for commercial and industrial electrical systems in the United States and worldwide. This calculator computes real power (kW), apparent power (kVA), and reactive power (kVAR) from the line-to-line voltage, line current, and power factor of a balanced three-phase load. Real power (kW) is the power that does useful work and is what your electricity meter measures. Apparent power (kVA) is the total power drawn from the supply, including reactive power, and is the basis for sizing generators and transformers. Reactive power (kVAR) is the power that cycles between the source and inductive or capacitive loads without doing work, but still flows through conductors and must be accounted for in system design. Enter the line-to-line voltage in volts, the line current in amps, and the power factor (default 0.85, typical for an industrial motor load). The single-phase equivalent current is also shown for comparison.
Three-phase power formulas
For a balanced three-phase AC system using line-to-line voltage and line current:
Real power: P (kW) = VLL × I × 1.732 × PF / 1,000
Apparent power: S (kVA) = VLL × I × 1.732 / 1,000
Reactive power: Q (kVAR) = VLL × I × 1.732 × sin(arccos(PF)) / 1,000
Single-phase equiv. current: I1ph = P × 1,000 / VLL
Worked example: 480V, 50 A per phase, PF 0.85
- S (kVA) = 480 × 50 × 1.732 / 1,000 = 41.57 kVA
- P (kW) = 41.57 × 0.85 = 35.33 kW
- sin(arccos(0.85)) = 0.5268; Q (kVAR) = 41.57 × 0.5268 = 21.89 kVAR
- Single-phase equiv. current = 35,330 / 480 = 73.60 A
The power triangle
Real power (kW), apparent power (kVA), and reactive power (kVAR) form a right triangle known as the power triangle. kVA is the hypotenuse, kW is the adjacent side, and kVAR is the opposite side. Power factor = kW / kVA = cos(angle), and kVAR = kVA × sin(angle).
Frequently asked questions
What is three-phase power?
Three-phase power is a method of electrical power transmission using three alternating current conductors, each carrying a current wave offset by 120 degrees from the others. It is the standard for commercial and industrial electricity distribution because it delivers more power per conductor than single-phase, produces a smooth constant power delivery (rather than the pulsing of single-phase), and enables the use of simpler, more efficient three-phase induction motors. Most residential service in the US is single-phase 120/240V split-phase; three-phase is found in commercial buildings, factories, and large HVAC systems.
Why does industry use three-phase power?
Three-phase power offers several engineering advantages: (1) for the same amount of real power, three-phase requires less conductor material than single-phase because current is shared across three wires; (2) three-phase induction motors are self-starting and simpler than single-phase motors of the same size; (3) the combined power in a balanced three-phase system is constant over time, reducing vibration and mechanical stress in motors; (4) three-phase transformers are smaller and more efficient than equivalent single-phase transformers.
What is the difference between line-to-line and line-to-neutral voltage?
In a three-phase wye (Y) system, the line-to-neutral voltage (V_LN) is the voltage between any one phase conductor and the neutral. The line-to-line voltage (V_LL) is the voltage between any two phase conductors. The two are related by V_LL = V_LN times sqrt(3). For example, in a 120/208V wye system, V_LN = 120V and V_LL = 208V. In a 277/480V wye system, V_LN = 277V and V_LL = 480V. This calculator uses line-to-line voltage in its formula.
What does kVA mean and how does it differ from kW?
kVA (kilovolt-amperes) is apparent power, the product of voltage and current without regard to phase angle. kW (kilowatts) is real power, the portion of apparent power that does actual work. The ratio of kW to kVA is the power factor. For example, a motor drawing 100 kVA at PF 0.85 produces 85 kW of real work; the remaining 15 kVA is reactive power that cycles back and forth between the source and the load. Generators and transformers are rated in kVA (or MVA) because they must handle the full apparent power regardless of power factor.
How do I calculate three-phase power from nameplate data?
Most three-phase motor nameplates show rated voltage (V), full-load amperes (FLA), power factor (PF), and output horsepower (HP). To find input real power in kW: kW = V_LL x FLA x 1.732 x PF / 1,000. To find apparent power in kVA: kVA = V_LL x FLA x 1.732 / 1,000. To convert output horsepower to input kW, also account for efficiency: input kW = (HP x 0.746) / efficiency. Enter the nameplate V and FLA into this calculator (with the stated PF) to get the power drawn from the supply.
Sources
- IEEE Standard 141-1993 (Red Book), Electric Power Distribution for Industrial Plants: standards.ieee.org.
- NFPA 70: National Electrical Code 2023, Article 430 (Motors): nfpa.org.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.