Reactive power, cos φ and compensation
Work out reactive and apparent power, see the current a load really draws, and calculate the theoretical capacitance needed for a stated cos φ correction.
How the calculation works
The calculator treats active power P and cos φ as values for a linear load with sinusoidal waveforms. It first calculates apparent power as S = P / cos φ. It then uses the power triangle to calculate reactive power as Q = √(S² − P²). The result describes one operating point; it is not a power-quality measurement or a capacitor-bank design.
S (VA) = P (W) / cos φ
Q (var) = √(S² − P²)
For a three-phase system, line current I (A) = P / (√3 × line-to-line voltage × cos φ)
What the calculator does not include: harmonics and total PF for non-linear loads; starting current, inrush and their duration; resonance and the effects of installing capacitor banks; manufacturer requirements for an inverter, UPS, capacitor or motor; local reactive-energy thresholds, rates and billing rules.
Worked examples with inputs
1 kW motor
Inputs: P = 1000 W, cos φ = 0.80. Result: S = 1250 VA and Q = 750 var. Open this example in the calculatorSmall motor with low cos φ
Inputs: P = 600 W, cos φ = 0.45. Result: S = 1333 VA and Q = 1191 var. Open this example in the calculator5.5 kW three-phase motor
Inputs: P = 5500 W, cos φ = 0.90. Result: S = 6111 VA and Q = 2664 var. At 400 V line-to-line, line current is approximately 8.82 A. Open this example in the calculator2 kW transformer
Inputs: P = 2000 W, cos φ = 0.70. Result: S = 2857 VA and Q = 2040 var. Open this example in the calculatorFrequently asked questions
What is the difference between cos φ and power factor (PF)?
cos φ describes the phase displacement of the fundamental voltage and current waveforms. For a linear load it equals power factor. PF is broader: it is P/S and includes current distortion in non-linear loads.
Can I enter cos φ for a computer power supply or LED lamp?
Do not treat the result as a complete description of that load. Power supplies and LED drivers can draw distorted current; look for total PF in the manufacturer documentation or measure it with a power-quality instrument.
Why do inverters and UPS units list both VA and W?
Current is one of their limits, so manufacturers list apparent power in VA. Compare the load VA separately with the unit continuous and surge limits in both VA and W.
Can this calculator size a power-factor-correction capacitor?
No. Q can help explain the scale of the issue, but capacitor-bank design needs voltage, frequency, connection method, harmonic data, network conditions and the manufacturer requirements.
Will power-factor correction always lower my bill?
No. Reactive-energy charges come from the contract, tariff and utility rules. Check the bill and connection terms first; do not assume thresholds or rates from a general calculator.
Does the result apply to single-phase and three-phase systems?
The relation S² = P² + Q² applies to the complete load in both cases. Current needs the correct voltage and formula; a three-phase calculation uses line-to-line voltage and √3.
Why can a lightly loaded motor have a low cos φ?
A motor still needs magnetising current even when it delivers little mechanical output. P falls while the magnetic-field component does not fall in the same proportion.