Power ratio and sinusoidal power triangle
Power factor lies between zero and one for the entered consuming load. The reactive magnitude is shown without a sign. On nonlinear loads, true power factor includes distortion and the equivalent angle should not be treated as a measured displacement angle.
To value real electrical energy used over a schedule, the Appliance Electricity Cost Calculator uses watts, operating time, and an electricity rate.
The formula
The real-to-apparent ratio is the power factor. Reactive power and equivalent angle use the sinusoidal power-triangle model. They do not identify whether current leads or lags voltage because the inputs provide magnitudes only.
Worked example
With 8 kW of real power and 10 kVA of apparent power, power factor is 0.8. The sinusoidal triangle gives a reactive magnitude of 6 kvar and an equivalent angle of 36.8699 degrees.
How to use this calculator
- Enter real power, apparent power using the units shown.
- Check both measurements against their labels before calculating.
- Calculate and review power factor alongside the supporting quantities.
Keep the measurements from the same operating point
Real and apparent power should describe the same circuit, time interval, and loading condition. Mixing a rated kVA capacity with a measured kW draw does not necessarily give the operating power factor. Apparent power must be positive, and the real-power magnitude cannot be larger than it for this consuming-load calculation.
Distortion and direction are separate issues
The power triangle relates real, reactive, and apparent power for sinusoidal voltage and current. Harmonics can make the apparent-power difference include distortion rather than reactive power alone. Leading or lagging behavior also requires additional circuit information. This calculator reports the ratio and a clearly labeled sinusoidal interpretation without recommending capacitor correction or equipment sizing.
Assumptions & limitations
What this calculation assumes
- Reactive magnitude and phase angle assume sinusoidal voltage and current.
What to keep in mind
- Excludes harmonic decomposition, leading/lagging signs, and power-factor correction design.
Common questions
Does 0.8 power factor mean 80% efficiency?
No. Power factor compares real and apparent electrical power. Efficiency compares useful output with input energy or power.
Can this tell whether the load is inductive?
No. The magnitudes do not supply the reactive sign or current direction, so leading versus lagging remains unknown.
Why is real power limited to apparent power?
The power factor magnitude cannot exceed one. Entering a larger real-power value indicates incompatible inputs for this model.
Sources & further reading
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