Power factor formula: PF = kW ÷ kVA. For this calculator, PF is expressed as a magnitude from 0 to 1 — a power factor of 0.8 means that real power is 80% of the apparent-power magnitude for the given AC load condition; it does not mean that 20% of the electrical energy is simply wasted. Power Factor (PF) is one of the most important concepts in electrical engineering — it is the ratio of real power to apparent power, and is not the same as equipment efficiency. Industrial plants, factories, commercial buildings, and large electrical loads often run inductive equipment such as motors, transformers, welding machines, and compressors, and these loads consume both useful power and reactive power at the same time. Understanding how kW, kVAR, and kVA relate to each other is what lets engineers reduce current and losses, and manage electricity costs where tariffs include demand, power-factor, or reactive-energy charges.
1. What is kW (Real Power)?
kW (kilowatt) is the actual useful power that performs work — it runs motors, lights lamps, heats heaters, and powers equipment. This is the power that produces useful output. Electricity tariffs commonly charge for energy consumption in kWh, and some commercial or industrial tariffs also include demand, power factor, or reactive-energy charges.
2. What is kVAR (Reactive Power)?
kVAR (kilovolt-ampere reactive) is the power required to establish the magnetic fields inside inductive equipment. Motors, transformers, reactors, and other inductive loads need reactive power simply to operate. kVAR doesn't perform useful work directly, but it's still necessary for many electrical devices to function.
3. What is kVA (Apparent Power)?
kVA (kilovolt-ampere) is the total power supplied by the source — it combines both real power (kW) and reactive power (kVAR). Generators, transformers, UPS systems, and distribution equipment are usually rated in kVA precisely because they have to carry both the useful and the reactive components of the load.
4. The Power Triangle
The relationship between kW, kVAR, and kVA is best visualized as a right-angled power triangle, with kVA as the hypotenuse.
Using the Pythagorean theorem:
This same triangle is what the APFC Calculator uses to work out exactly how many capacitor kVAr you need to shrink it.
5. What is Power Factor?
Power Factor is the ratio of real power (kW) to apparent power (kVA). A lower power factor means the electrical system requires more current to deliver the same real power. For this calculator, power factor is represented as a magnitude from 0 to 1 — in AC systems, power factor may also be described as leading or lagging depending on the reactive behavior of the load.
Typical Practical Interpretation
These ranges are general engineering guidance, not universal utility limits — actual thresholds vary by utility, tariff, and contract.
| PF | Condition |
|---|---|
| 1.0 | Excellent |
| 0.95 | Very Good |
| 0.85 | Acceptable |
| Below 0.80 | Poor |
6. Voltage, Current & Phase Angle: Where Power Factor Really Comes From
In an AC circuit, voltage and current don't necessarily peak at the same instant. For an inductive load such as a motor, current lags behind voltage by a phase angle φ (phi). This single angle is the physical root of everything covered above — it sets the power factor directly:
A power factor of 0.70, for example, corresponds to a phase angle of about 45.6° — current is lagging voltage by 45.6° on every cycle. The waveforms and phasor diagrams below show what that lag actually looks like at a few common phase angles, all at the same frequency and amplitude so only the angle changes.
AC Voltage & Current Waveforms at Different Phase Angles
0° — In Phase (PF = 1.00)
- Voltage and current peak at the same instant.
- PF = 1.00 — a purely resistive load.
30° Lagging (PF = 0.866)
- Current lags voltage by 30°.
- Moderate reactive power.
45° Lagging (PF = 0.707)
- Current lags voltage by 45°.
- Reactive power now equals real power.
60° Lagging (PF = 0.500)
- Current lags voltage by 60°.
- Very high reactive power relative to real power.
Phasor Diagrams
The same relationship drawn as rotating phasors: voltage (V) fixed along the real axis, current (I) lagging behind it by φ.
0° — In Phase
30° Lagging
45° Lagging
60° Lagging
Key Values by Phase Angle
For a fixed real power P, this shows how reactive power, apparent power, and current all scale as the phase angle grows.
| Phase angle (φ) | Power factor (cos φ) | Relative current | kVAR (Q) | kVA (S) |
|---|---|---|---|---|
| 0° | 1.000 | 1.000 | 0 | 1.000P |
| 30° | 0.866 | 1.155 | 0.577P | 1.155P |
| 45° | 0.707 | 1.414 | 1.000P | 1.414P |
| 60° | 0.500 | 2.000 | 1.732P | 2.000P |
The Power Triangle, in Terms of φ
Worked Example: 100 kW Before vs After Correction
Take a 100 kW motor load running at a poor 0.70 power factor, corrected up to 0.95 with capacitors:
| Parameter | PF 0.70 (before) | PF 0.95 (after) |
|---|---|---|
| Real power (P) | 100 kW | 100 kW |
| Phase angle (φ) | 45.6° | 18.2° |
| Reactive power (Q) | 102.02 kVAR | 32.87 kVAR |
| Apparent power (S) | 142.86 kVA | 105.26 kVA |
Real power (P) doesn't change — the motor still does exactly the same work. But reactive power drops from about 102 kVAR to 33 kVAR, a reduction of roughly 69 kVAR, which is the size of capacitor bank a correction panel would need to supply. At a three-phase 415 V supply, the current for this load falls from about 198.7 A to 146.4 A — a drop of roughly 26%, all from correcting the phase angle rather than reducing the actual work being done. Use the "kW, V & I" mode in the calculator above to run this kind of before/after comparison on your own numbers.
Key Takeaways
- Voltage and current have a phase angle (φ) between them in any AC circuit with reactive (inductive or capacitive) load.
- PF = cos φ — a higher power factor always means a smaller angle.
- As φ increases, kVAR and kVA increase for the same kW, and so does the current the source has to supply.
- A capacitor bank supplies leading reactive power that cancels part of the load's lagging reactive power, shrinking φ.
- The result of correction: lower current, lower kVA demand, reduced I²R losses, and better use of existing transformer and cable capacity.
Common Voltages by Region
The power factor formulas above (PF = cos φ = P ÷ S) are universal — only the supply voltage convention changes by region. The "kW, V & I" mode supports the common low-voltage figures used across India, the UK and Europe, North America, the Middle East, Australia, and South Africa, plus any custom voltage.
| Region | Common Low-Voltage Distribution Voltage |
|---|---|
| India | 415V three-phase / 230V single-phase |
| UK & Europe | 400V three-phase / 230V single-phase |
| USA | 480V or 208V three-phase (varies by facility) |
| Canada | 600V or 208V three-phase (varies by facility) |
| Australia | 400V three-phase / 230V single-phase |
| Middle East | 400V three-phase / 230V single-phase |
| South Africa | 400V three-phase / 230V single-phase |
7. Why Low Power Factor Is Bad
A low power factor means more current is required to deliver the same amount of useful power. This causes:
- Potentially higher electricity costs where tariffs include power-factor, kVA demand, maximum-demand, or reactive-energy charges
- Transformer overloading
- Cable overheating
- Higher power losses
- Reduced system capacity
For a deeper look at how these costs stack up, and the exact capacitor kVAr needed to fix them, see Why Power Factor Correction Matters on the APFC Calculator page.
8. How to Improve Power Factor
The most common fix is installing capacitor banks. Capacitors generate reactive power that opposes the reactive demand of inductive loads, which directly reduces the kVAR the utility has to supply.
Phasor Diagram — Power Factor Improvement with a Capacitor
- I₁ is the original (uncorrected) current, lagging V by φ₁.
- Adding the capacitor's leading current IⅨ shortens the reactive part of the current.
- I₂ (= I₁ + IⅨ) is the new, more in-phase current the utility actually sees — smaller in magnitude for the same real power.
Methods of PF Improvement
- Capacitor Banks (most common)
- Automatic Power Factor Correction Panels (APFC)
- Synchronous Condensers
- VFDs with suitable power-quality and harmonic mitigation
- Proper Motor Sizing
- Avoiding Idle Running Motors
9. Example Calculation
Suppose a workshop consumes:
Then:
If the PF is improved to 0.93:
Notice that apparent power drops by nearly 19 kVA, which reduces current and losses — that's the efficiency gain from power factor correction, and it lowers operating costs. Try your own numbers in the calculator above, or size the exact capacitor bank needed for this kind of correction with the APFC Calculator.
10. Resistance, Reactance & Impedance
Resistance (R), reactance (X), and impedance (Z) are the electrical properties behind kW, kVAR, and kVA — R and X combine into Z the same way real and reactive power combine into apparent power.
- Resistance (R), measured in ohms (Ω), opposes current flow and is directly linked to real power: P = I²R.
- Reactance (X), also measured in ohms (Ω), is the opposition produced by inductors and capacitors and is linked to reactive power: Q = I²X.
- Impedance (Z), measured in ohms (Ω), is the combined AC opposition of a circuit and is linked to apparent power: S = I²Z.
Just like the power triangle, resistance and reactance combine as a right triangle with impedance as the hypotenuse:
A purely resistive load (heaters, incandescent lighting) has reactance close to zero, so Z ≈ R and the power factor is close to 1. A purely inductive or capacitive component has resistance close to zero, so Z ≈ X — this is why motors, transformers, and other inductive equipment pull a power factor well below 1 unless corrected.
Conclusion
kW represents useful power, kVAR represents reactive power, and kVA represents total apparent power — power factor indicates how effectively the electrical system's apparent power is being utilized in terms of real power; it is not the same as equipment efficiency. A higher power factor reduces losses, decreases current, improves voltage regulation, and lowers electricity costs where demand, kVA, reactive-energy, or power-factor charges apply. Capacitor banks and APFC systems are among the most common methods used for industrial and commercial power-factor correction, and maintaining a power factor above 0.95 is generally considered good engineering practice.