Power factor formula
Power factor is the ratio of real power to apparent power. For the basic power triangle, it can be calculated from kW and kVA.
For example, 8 kW of real power and 10 kVA of apparent power produce a power factor of 0.8, or 80%.
kW to kVA formula
If real power and power factor are known, apparent power is:
A 100 kW load at a power factor of 0.8 therefore corresponds to 125 kVA.
kVA to kW formula
If apparent power and power factor are known, real power is:
A 10 kVA load at 0.8 power factor has 8 kW of real power.
Reactive power formula
Real, reactive and apparent power form a right triangle.
Reactive power can therefore be calculated as:
With 8 kW and 10 kVA, reactive power is 6 kVAR.
Phase angle
In the ideal sinusoidal power triangle, power factor equals the cosine of the phase angle.
The phase angle can therefore be found using the inverse cosine of the power factor.
A power factor of 0.8 corresponds to a phase angle of approximately 36.87°.
Real, reactive and apparent power
Real power, measured in kW, is the portion associated with useful energy transfer. Apparent power, measured in kVA, represents the magnitude associated with voltage and current in the AC system.
Reactive power, measured in kVAR, is the perpendicular component of the ideal power triangle. Together, the three quantities describe the basic relationship used by this calculator.
Why can kVA be larger than kW?
Since power factor is no greater than 1 in this model, real power cannot exceed apparent power. At a power factor of 1, kW and kVA have the same numerical value.
As power factor decreases, apparent power becomes larger relative to the same real power.
Power factor as a percentage
Power factor is normally written as a decimal between 0 and 1. Multiplying by 100 expresses the same value as a percentage.
For example, 0.85 equals an 85% power factor.
Power factor vs. efficiency
Power factor and efficiency describe different relationships. Power factor compares real power with apparent power, while efficiency compares useful output with input energy or power.
A device can therefore have both an efficiency value and a power factor value, and the two should not be treated as interchangeable.
Related electrical calculations
For basic voltage, current and resistance calculations, use the Ohm's Law Calculator.
For converting between current and real power, use the Amps to Watts Calculator or Watts to Amps Calculator.
For resistor networks, use the Series & Parallel Resistor Calculator.
This calculator uses the standard ideal AC power triangle. It reports power factor magnitude and does not distinguish between leading and lagging power factor. Harmonics and non-sinusoidal waveform effects are not modeled.
Frequently asked questions
How do I calculate power factor from kW and kVA?
Divide real power in kW by apparent power in kVA. For example, 8 kW divided by 10 kVA gives 0.8.
How do I convert kW to kVA?
Divide kW by power factor. For example, 100 kW at 0.8 power factor equals 125 kVA.
How do I convert kVA to kW?
Multiply kVA by power factor. For example, 10 kVA at 0.8 power factor equals 8 kW.
What is kVAR?
kVAR is the unit used for reactive power in the AC power triangle.
Can power factor be greater than 1?
Not in the standard power factor magnitude used by this calculator. Valid entries must be greater than 0 and no more than 1.
Using this calculator effectively
The Power Factor Calculator uses the ideal AC power triangle to solve power factor, real power in kW, apparent power in kVA, reactive power in kVAR and phase angle.
Common uses
- Finding power factor when real power and apparent power are known.
- Converting between kW and kVA when power factor is known.
- Calculating reactive power and phase angle from power-triangle values.
Tips for a better estimate
- Use power values from the same operating condition rather than mixing nameplate and measured values.
- Remember that this calculator uses power factor magnitude and does not identify leading or lagging conditions.
- For distorted or non-sinusoidal waveforms, the simple displacement power triangle may not describe total power factor completely.
Related calculations
Power Factor Correction Calculator · Amps to Watts Calculator · Ohm's Law Calculator