EngineeringFormulaElectrical Engineering
Power Factor Calculator
Calculate power factor, apparent power, reactive power, and phase angle from the AC power triangle, or estimate the capacitor kVAR needed to improve power factor to a target value.
Power factor describes how effectively an AC electrical system turns supplied apparent power into useful real power. A low power factor means the same real work requires more current, more kVA capacity, and usually more losses in conductors and equipment. This calculator covers both the basic power triangle relationships and a practical correction case: sizing the capacitor reactive power needed to raise an installation from its current power factor to a target value.
P · Useful working power delivered to the load.
S · The total VA demand seen by the source.
Power-triangle mode uses the classic sinusoidal AC relationships between real power, apparent power, reactive power, and phase angle. It is best for PF checks, kVA sizing, and general power-quality interpretation.
Solution
Enter the required values to calculate power factor.
PF = P / S
Formula Sheet
- PReal Power
- SApparent Power
- QReactive Power
- PFPower Factor
- PF₂Target Power Factor
- φPhase Angle
- QcCorrection Reactive Power
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| P | Real Power | Useful working power actually converted into heat, light, motion, or other productive work. | mW, W, kW, MW, hp |
| S | Apparent Power | Voltage-current demand seen by the source, without removing the effect of phase displacement. | VA, kVA, MVA |
| Q | Reactive Power | Power exchanged with inductive or capacitive fields rather than converted into net useful work. | kVAR |
| PF | Power Factor | Ratio of real power to apparent power, equal to cos φ in sinusoidal steady-state conditions. | |
| PF₂ | Target Power Factor | Desired corrected power factor after capacitor compensation, in power factor correction mode. | |
| φ | Phase Angle | Angle between voltage and current waveforms in the sinusoidal power-triangle model. | deg, rad |
| Qc | Correction Reactive Power | Capacitive reactive power that must be added to move from the initial power factor to the target power factor. | kVAR |
How to Use This Calculator
- 01Choose the calculation type first. Use Power Triangle for PF, kVA, kVAR, or phase-angle questions. Use Power Factor Correction when you want the capacitor-bank kVAR required to improve an existing lagging power factor.
- 02Select which variable to solve for. The calculator will show only the inputs required for that relationship.
- 03Enter power factor values as decimals between 0 and 1, not percentages. For example, enter 0.95 instead of 95%.
- 04Enter the required real power, apparent power, and/or target power-factor inputs in the correct engineering units, then select Calculate to see the result, active formula, and derived supporting values.
How the Formula Works
In sinusoidal AC systems, real power P, reactive power Q, and apparent power S form the power triangle, where S² = P² + Q² and power factor PF = P / S = cos φ. Once PF is known, the phase angle is φ = cos⁻¹(PF), and reactive power follows from Q = P tan φ. This means any improvement in power factor reduces the apparent power and current required to deliver the same real power.
Power factor correction usually adds capacitors to offset part of an inductive load's reactive demand. If the starting phase angle is φ₁ and the target phase angle is φ₂, the capacitor reactive power required is Qc = P (tan φ₁ − tan φ₂). This calculator reports that correction kVAR along with the before-and-after reactive and apparent power values so you can see what the correction is actually changing.
Worked Example 01
Power factor from real and apparent power
Known
- Real Power (P): 80 kW
- Apparent Power (S): 100 kVA
Formula
PF = P / S
Substitution
PF = 80 / 100
Result
PF = 0.8 (Q = 60 kVAR, φ ≈ 36.87°)
An 80 kW load drawing 100 kVA has a power factor of 0.8, with 60 kVAR of reactive power in the simplified sinusoidal power triangle.
Worked Example 02
Apparent power from real power and PF
Known
- Real Power (P): 48 kW
- Power Factor (PF): 0.6
Formula
S = P / PF
Substitution
S = 48 / 0.6
Result
S = 80 kVA
A 48 kW load at 0.6 power factor requires 80 kVA of apparent power, which means it draws more current than a higher-PF load delivering the same real power.
Worked Example 03
Reactive power from real power and PF
Known
- Real Power (P): 75 kW
- Power Factor (PF): 0.8
Formula
Q = P × tan(cos⁻¹ PF)
Substitution
Q = 75 × tan(cos⁻¹ 0.8)
Result
Q ≈ 56.25 kVAR
At 0.8 PF, a 75 kW load carries significant reactive demand, even though only 75 kW is doing net useful work.
Worked Example 04
Phase angle from power factor
Known
- Power Factor (PF): 0.85
Formula
φ = cos⁻¹(PF)
Substitution
φ = cos⁻¹(0.85)
Result
φ ≈ 31.79°
A power factor of 0.85 corresponds to a phase angle of about 31.79° in the sinusoidal power-triangle model.
Worked Example 05
Correction kVAR to improve a lagging PF
Known
- Real Power (P): 100 kW
- Current Power Factor (PF₁): 0.75
- Target Power Factor (PF₂): 0.95
Formula
Qc = P × (tan φ₁ − tan φ₂)
Substitution
Qc = 100 × (tan(cos⁻¹ 0.75) − tan(cos⁻¹ 0.95))
Result
Qc ≈ 55.32 kVAR
Improving a 100 kW installation from 0.75 to 0.95 PF requires about 55.32 kVAR of capacitive correction in the idealized steady-state model.
Applications
- 01Checking whether a measured kW and kVA pair implies an acceptable power factor
- 02Estimating reactive demand and phase angle for motors, transformers, and other inductive loads
- 03Sizing the approximate capacitor-bank kVAR needed to improve an installation's lagging power factor
Assumptions
- 01The relationships on this page assume sinusoidal steady-state AC operation.
- 02Power factor is treated as a magnitude only; this calculator does not distinguish lead versus lag sign in the result itself.
- 03Correction mode assumes the real power stays constant while the power factor is improved.
Where This Model Stops
- 01Does not model harmonic distortion, so true power factor and displacement power factor are treated as the same simplified quantity.
- 02Correction mode estimates required capacitive kVAR only; it does not size specific capacitor stages, switching steps, or detuning reactors.
- 03Not a substitute for a full utility or plant power-quality study when resonance, harmonics, or changing load profiles are important.
References
- [1]Power Factor: What it is and How to Calculate it
Fluke
Explains PF as real power divided by apparent power and summarizes why low PF increases system current and demand.
- [2]Power factor (PF)
Schneider Electric PowerLogic ION9000 Help
Defines PF as the ratio of real power to apparent power and distinguishes power factor from more detailed harmonic-aware measurements.
- [3]How to Improve Power Factor
Fluke
Discusses practical PF improvement and capacitor-based correction; the correction formula used here is inferred from the cited PF and power-triangle relationships.
Frequently Asked Questions
How is this different from the Single-Phase Power Calculator?
Single-Phase Power Calculator starts from voltage, current, and power factor to solve AC load power. This page focuses on the power triangle itself - PF, kVA, kVAR, phase angle, and correction kVAR - which makes it better for utility-billing, capacitor-bank, and general power-quality questions.
Why does a low power factor matter?
For the same real power, a lower power factor means higher apparent power and higher current. That increases conductor losses, uses more equipment capacity, and can trigger utility penalties or demand-related costs.
Does this calculator handle harmonics?
No. It uses the classic sinusoidal power-triangle model. In heavily distorted systems, true power factor and displacement power factor can differ, so a power-quality analyzer or a more detailed study is needed.