Three-phase power equations
For a balanced three-phase system, line-to-line voltage and line current define apparent power. Power factor then separates apparent power into active and reactive components.
where:
- S
- Apparent power[kVA]
- P
- Active power[kW]
- Q
- Reactive power; positive for lagging loads and negative for leading loads[kvar]
- VLL
- RMS line-to-line voltage[V]
- I
- RMS line current[A]
- PF
- Power factor, equal to cos φ
- φ
- Phase angle between voltage and current[°]
The factor 1000 converts VA to kVA or W to kW. These equations assume a balanced sinusoidal three-phase system; unbalanced or harmonic-rich loads require per-phase measurements and true-power analysis.
How to use the Three-Phase Power Calculator
Calculate balanced three-phase active power, apparent power, reactive power, current, phase angle, and power-factor improvement effects. Start by choosing the operating mode, then enter values from nameplates, measurements, or project documents in the units shown. The result updates immediately and keeps intermediate quantities visible for review.
- Confirm the system and calculation mode.
- Enter measured or manufacturer-rated values.
- Review the primary result and intermediate metrics.
- Continue with the related protection or equipment-selection checks.
Calculation method and validation
The equations and symbol definitions above show the complete calculation basis. Inputs are checked before calculation so zero, negative, incompatible, or physically impossible combinations are flagged instead of silently producing a misleading result.
How to interpret the result
Use the main result as a starting value and read every supporting metric. Balanced three-phase sinusoidal system Voltage is line-to-line RMS Current is line current RMS Power factor represents the total displacement/true PF used for the calculation A passing or recommended result means the entered mathematical conditions are satisfied; it does not certify the complete installation or a particular product combination.
- Balanced three-phase sinusoidal system
- Voltage is line-to-line RMS
- Current is line current RMS
- Power factor represents the total displacement/true PF used for the calculation
Selection limits and next checks
Unbalanced loads require per-phase measurement or calculation. Harmonics, waveform distortion, motor efficiency, transients, and neutral current are outside the basic power-triangle equations. Capacitor-bank selection requires harmonic, resonance, switching, voltage, and manufacturer checks. Compare the output with the current applicable standard, local rules, exact VIOX product datasheet, environmental conditions, protection coordination, and the engineer's project requirements before procurement or installation.
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Assumptions
- Balanced three-phase sinusoidal system
- Voltage is line-to-line RMS
- Current is line current RMS
- Power factor represents the total displacement/true PF used for the calculation
Important Warnings
- Unbalanced loads require per-phase measurement or calculation.
- Harmonics, waveform distortion, motor efficiency, transients, and neutral current are outside the basic power-triangle equations.
- Capacitor-bank selection requires harmonic, resonance, switching, voltage, and manufacturer checks.