Power Factor Calculator — Calculate PF & Phase Angle Instantly

Compute power factor, phase angle, and reactive power from real power and apparent power. Free online power factor calculator with step-by-step formula breakdown, copy & share support, and educational explanations for electrical engineers.

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Power Factor Calculator

Enter real power and apparent power, or a phase angle, to calculate the power factor of an AC circuit.

Enter values and click Calculate Power Factor to see the result.

Power Factor Formula Explained

The power factor (PF) is the ratio of real power to apparent power in an AC electrical system. It indicates how efficiently electrical power is converted into useful work.

PF = P / S   |   PF = cos(θ)
S² = P² + Q²   |   Q = S × sin(θ) = S × √(1 − PF²)

Variable Definitions

  • PF — Power Factor (dimensionless, between 0 and 1, or expressed as a percentage)
  • P — Real Power (measured in kW or W), the actual work-producing power
  • S — Apparent Power (measured in kVA or VA), the total power supplied
  • Q — Reactive Power (measured in kVAR or VAR), power that oscillates between source and load
  • θ — Phase Angle (in degrees or radians), the angular difference between voltage and current waveforms

A power factor of 1.0 (unity) means all supplied power is converted to useful work. Lower values indicate reactive power is present, reducing system efficiency.

How to Calculate Power Factor

Power factor can be calculated using either the power triangle method or the phase angle method. Follow these steps:

  1. Identify known values — Determine whether you have real power (P) and apparent power (S), or the phase angle (θ).
  2. Apply the power factor formula — If using P and S: PF = P / S. If using phase angle: PF = cos(θ).
  3. Calculate reactive power — Use Q = S × sin(arccos(PF)) or Q = √(S² − P²) to find the reactive component.
  4. Express the result — Power factor is typically written as a decimal (e.g., 0.85) or percentage (85%).
  5. Determine leading or lagging — Inductive loads cause lagging PF (current lags voltage); capacitive loads cause leading PF.

For example, with 80 kW real power and 100 kVA apparent power: PF = 80/100 = 0.80 (80%). The phase angle is arccos(0.80) ≈ 36.87°.

Power Factor Calculator Examples

Example 1: Industrial Motor Load

A 3-phase induction motor draws 80 kW of real power with 100 kVA apparent power. Find the power factor and phase angle.

PF = 80 kW / 100 kVA = 0.80 (80%)
θ = arccos(0.80) ≈ 36.87°
Q = 100 × sin(36.87°) ≈ 60 kVAR

Example 2: Near-Unity Power Factor

A facility operates with 250 kW real power and 260 kVA apparent power.

PF = 250 / 260 ≈ 0.962 (96.2%)
θ = arccos(0.962) ≈ 15.9°
This is considered an excellent power factor.

Example 3: From Phase Angle

A circuit has a measured phase angle of 25° between voltage and current.

PF = cos(25°) ≈ 0.906 (90.6%)
This represents a lagging power factor typical of lightly loaded motors.

Real-World Power Factor Applications

  • Industrial Power Systems: Monitoring PF in factories with large motor loads to avoid utility penalties and optimize energy costs.
  • Power Factor Correction: Sizing capacitor banks to improve PF from 0.70–0.85 up to 0.95+, reducing line currents and I²R losses.
  • Transformer Sizing: Using PF to determine the correct kVA rating for transformers serving mixed inductive and resistive loads.
  • Generator Selection: Matching generator kVA capacity to actual load requirements based on the expected power factor.
  • HVAC & Refrigeration: Evaluating compressor and fan motor efficiency in commercial building systems.
  • Renewable Energy: Assessing inverter PF performance in solar PV and wind turbine grid interconnections.
  • Utility Billing Analysis: Calculating potential savings from PF correction by comparing kVA demand charges before and after improvement.

People Also Ask

The power factor formula is PF = P / S, where P is real power in watts (or kW) and S is apparent power in volt-amperes (or kVA). Alternatively, PF = cos(θ), where θ is the phase angle between voltage and current waveforms in an AC circuit.
Simply divide the real power (kW) by the apparent power (kVA). For example, if your equipment uses 80 kW and the apparent power is 100 kVA, the power factor is 80 ÷ 100 = 0.80 or 80%. The closer this ratio is to 1.0, the more efficient your power usage.
Lagging power factor occurs when current lags behind voltage, typical of inductive loads like motors and transformers. Leading power factor occurs when current leads voltage, typical of capacitive loads. Most industrial facilities have lagging PF, which is corrected using capacitor banks.
Take the cosine of the phase angle in degrees. For example, a phase angle of 30° gives PF = cos(30°) ≈ 0.866. Most scientific calculators and this online tool can perform the conversion instantly. Remember to ensure your calculator is in degree mode, not radians.
Reactive power (measured in kVAR) is the power that oscillates between the source and inductive/capacitive loads without performing useful work. It is related to power factor by the equation Q = S × √(1 − PF²). Higher reactive power means lower power factor and reduced system efficiency.

Frequently Asked Questions

A power factor of 0.95 or higher is generally considered good. Unity (1.0) is ideal. Most utilities charge penalties when PF drops below 0.85–0.90. Improving PF from 0.70 to 0.95 can reduce line current by over 25%, lowering both energy losses and demand charges.
No. Power factor cannot exceed 1.0 (or 100%) because real power can never be greater than apparent power in a passive circuit. If your calculation yields PF > 1, check your measurements — apparent power should always be equal to or larger than real power.
Power factor correction adds capacitors in parallel with inductive loads. Capacitors supply reactive power locally, reducing the reactive power drawn from the utility. This improves the power factor, reduces line current, and can eliminate utility PF penalties.
Power factor and efficiency are related but distinct concepts. PF measures how effectively current is converted into useful work. Efficiency measures output power versus input power. A system can have high efficiency but poor power factor, or vice versa. Both should be optimized for best overall performance.
Yes. The power factor formula PF = P/S is the same for single-phase and 3-phase systems. For 3-phase calculations, use the total 3-phase real power (kW) and total 3-phase apparent power (kVA). The relationship S = √3 × V_L × I_L can be used to find apparent power from line measurements.
Low power factor means higher current is required for the same real power output. This increases I²R losses in transmission lines and requires larger transformers, switchgear, and conductors. Utilities pass these infrastructure costs to customers through PF penalties or kVA-based demand charges.

Power Factor Glossary

Power Factor (PF)

The ratio of real power to apparent power in an AC circuit, measuring electrical efficiency. Ranges from 0 to 1.

Real Power (P)

The actual work-producing power measured in watts (W) or kilowatts (kW). This is the useful power consumed by resistive loads.

Apparent Power (S)

The total power supplied to a circuit, measured in volt-amperes (VA) or kVA. It is the vector sum of real and reactive power.

Reactive Power (Q)

Power that oscillates between source and reactive components (inductors/capacitors), measured in VAR or kVAR. It performs no useful work.

Phase Angle (θ)

The angular displacement between voltage and current waveforms in an AC circuit. PF = cos(θ). Measured in degrees or radians.

Power Triangle

A right-triangle representation where S is the hypotenuse, P is the adjacent side, Q is the opposite side, and θ is the angle between S and P.

Lagging PF

When current lags behind voltage, typical of inductive loads. Most common in industrial settings due to motors and transformers.

PF Correction

The process of improving power factor by adding capacitors or synchronous condensers to supply reactive power locally.

Editorial Review & Methodology

This power factor calculator was built and reviewed by the NumbrWiz Editorial Team. The power factor formula is a fundamental concept in AC electrical engineering, verified against IEEE standards, NEC guidelines, and standard electrical engineering textbooks including the IEEE Std 1459-2010 power definitions.

  • Formula verification: Cross-checked against IEEE power definitions and multiple authoritative electrical engineering sources.
  • Edge case testing: Tested with unity PF, very low PF values, negative phase angles, and boundary conditions.
  • UX review: Designed for intuitive input with clear error messaging and comprehensive step-by-step breakdowns.

Transparency note: All calculations run client-side in your browser. No data is ever collected, stored, or transmitted. Results are for educational and reference purposes; always verify critical electrical design calculations independently with a qualified engineer.

Page last reviewed: May 2026 · NumbrWiz Editorial Team