Engineering

Power Factor Calculator

Calculate power factor from kW and kVA, or from watts, volts, and amps. Also calculate kVA, kVAR, phase angle, and estimated power factor correction kVAR for AC single-phase and three-phase systems.

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Power factor
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Power factor percent—
Reactive power—
Phase angle—
Load interpretation—
Formula usedPF = kW ÷ kVA

Power factor formulas

Power factor is only used for AC circuits. It compares real power with apparent power and is shown as a decimal from 0 to 1, or as a percentage.

Power factor: PF = kW ÷ kVA PF = W ÷ VA Single-phase apparent power: kVA = V × A ÷ 1000 Three-phase apparent power using line-to-line voltage: kVA = √3 × V × A ÷ 1000 Reactive power: kVAR = √(kVA² − kW²) Phase angle: θ = cos⁻¹(PF) Power factor correction: kVAR required = kW × (tan(cos⁻¹ PF old) − tan(cos⁻¹ PF target))

Power factor interpretation table

Power factor Meaning Typical notes
0.98 – 1.00 Excellent Mostly resistive or well-corrected load
0.95 – 0.98 Very good Common target range for commercial correction
0.90 – 0.95 Good Usually acceptable for many systems
0.80 – 0.90 Moderate Common for motors without strong correction
Below 0.80 Poor Higher current, higher kVA, possible penalties

Worked examples

Example 1 — PF from kW and kVA Real power = 8 kW Apparent power = 10 kVA PF = 8 ÷ 10 = 0.80 Example 2 — PF from single-phase watts, volts, amps Watts = 4,000 W Voltage = 230 V Current = 20 A VA = 230 × 20 = 4,600 VA PF = 4,000 ÷ 4,600 = 0.87 Example 3 — Correction from PF 0.80 to PF 0.95 Load = 100 kW kVAR required = 100 × (tan(cos⁻¹ 0.80) − tan(cos⁻¹ 0.95)) kVAR required ≈ 42.1 kVAR

Why power factor matters

A low power factor means a system draws more current for the same useful kW. More current can increase voltage drop, cable heating, transformer loading, generator size, UPS size, and utility demand charges. Improving power factor does not normally reduce the main work done by the equipment, but it can reduce wasted capacity and losses in the electrical distribution system.

For small household loads, power factor is usually not something you need to correct manually. For industrial sites with motors, compressors, chillers, welders, pumps, and large transformers, power factor correction can be financially and technically important.

kW, kVA, and kVAR power triangle

The power triangle connects real, apparent, and reactive power. kW is the useful real power. kVAR is reactive power. kVA is the apparent power combining both. The relationship is kVA² = kW² + kVAR². Power factor is the cosine of the phase angle between real power and apparent power.

Common questions

  • Power factor is the ratio of real power to apparent power in an AC circuit. It shows how effectively electrical current is being converted into useful work. The formula is PF = kW ÷ kVA. A PF of 1 is ideal, while lower values mean more current is needed for the same useful power.
  • Use PF = kW ÷ kVA. For example, if a machine uses 8 kW and 10 kVA, the power factor is 8 ÷ 10 = 0.8. This means 80% of the apparent power is converted into real power.
  • First calculate apparent power. For single-phase, VA = V × A. For three-phase line-to-line voltage, VA = √3 × V × A. Then divide real watts by apparent VA: PF = W ÷ VA.
  • For balanced three-phase using line-to-line voltage, PF = W ÷ (√3 × V × A). If using kW and kVA, the formula is simply PF = kW ÷ kVA. If using line-to-neutral voltage, apparent power is 3 × V × A.
  • kVA is apparent power. It represents the total voltage-current capacity in an AC circuit before power factor is applied. The relationship is kW = kVA × PF. Generators, UPS systems, and transformers are often rated in kVA.
  • kVAR is reactive power. It is the part of apparent power that does not perform useful work but is exchanged between the source and reactive components such as motors, transformers, and inductors. The power triangle relationship is kVA² = kW² + kVAR².
  • A power factor close to 1.0 is excellent. Many commercial and industrial systems aim for 0.95 or higher. Values around 0.8 are common for motors without correction, while values below 0.8 can indicate poor power factor and may increase current, losses, or utility penalties.
  • No. In normal real-power calculations, power factor ranges from 0 to 1. If a calculation gives a value above 1, the input data is inconsistent, the voltage/current/power units are mixed, or the measured values were not taken at the same operating condition.
  • Lagging power factor happens when current lags voltage, usually because of inductive loads such as motors, pumps, compressors, transformers, and fluorescent ballasts. Most industrial poor power factor problems are lagging.
  • Leading power factor happens when current leads voltage, usually because of capacitive loads or over-correction from capacitor banks. Too much correction can create a leading power factor, which can also cause system problems.
  • Use kVA = kW ÷ PF. For example, 10 kW at PF 0.8 requires 12.5 kVA. This is useful for generator, UPS, transformer, and cable loading estimates.
  • First calculate the phase angle using arccos(PF), then use kVAR = kW × tan(angle). You can also calculate kVAR from kVA and kW using kVAR = √(kVA² − kW²).
  • For correction from an existing power factor to a target power factor, use kVAR required = kW × (tan(arccos(existing PF)) − tan(arccos(target PF))). This gives the approximate capacitor-bank reactive power needed for a lagging load.
  • Improving power factor usually does not greatly reduce the real kWh used by the load. It reduces current and kVA demand, which can reduce losses, voltage drop, transformer loading, generator size, and utility demand penalties.
  • It can estimate required correction kVAR, but capacitor bank design must also consider harmonics, switching steps, detuning reactors, voltage rating, load variation, and local utility requirements. A qualified electrical professional should verify final designs.
  • No. Power factor is an AC concept because it depends on phase difference and waveform behavior. In DC circuits, power is normally calculated as watts = volts × amps.