Power Factor Calculator
Calculate the AC power triangle for single-phase supplies, UPS systems, motors, inverters, and industrial loads. Solve power factor, real power, apparent power, reactive power, and phase angle with consistent engineering units.
Engineering tool
Power Factor Calculator
Solve real, reactive, and apparent AC power with power factor and phase angle.
Result console
- Real power (P)
- 800W
- Reactive power (Q)
- 600VAR
- Apparent power (S)
- 1kVA
- Power factor
- 0.8PF
- Phase angle
- 36.869898°
Power factor status
Fair
Formula: PF = P / S; θ = arccos(PF)
Reactive current is material. Review cable, switchgear, UPS, and correction requirements.
Formula reference
AC Power Triangle Formulas
These relationships describe sinusoidal AC power using the magnitude of the power triangle.
Power factor: PF = P / SPhase angle: θ = arccos(PF)Real power: P = S × PFApparent power: S = P / PFReactive power: Q = √(S² - P²)Power triangle: S² = P² + Q²Variable definitions
- P
- real power in watts
- Q
- reactive power in VAR
- S
- apparent power in VA
- θ
- phase angle in degrees
Worked Example
For 800 W of real power and 1000 VA of apparent power:
PF = 800 / 1000 = 0.8. Q = √(1000² - 800²) = 600 VAR. θ = arccos(0.8) ≈ 36.87°.
The resulting power factor status is Fair.
Engineering Notes
- Power factor indicates how effectively electrical power is used.
- Low power factor increases current and cable losses.
- Capacitor banks are commonly used for power factor correction.
- Industrial loads such as motors often have lagging power factor.
- Utilities may impose penalties for low power factor.
Support reference
FAQ
What is power factor?
Power factor is real power divided by apparent power. It indicates how effectively AC current is converted into useful work.
How do you calculate power factor?
Divide real power in watts by apparent power in volt-amperes: PF = P / S. For sinusoidal systems, the phase angle is arccos(PF).
Why is low power factor bad?
Low power factor requires more current for the same real power, increasing cable loss, voltage drop, equipment loading, and potentially utility charges.
What is reactive power?
Reactive power in VAR represents energy exchanged with inductive or capacitive fields rather than converted into net useful work.
How do capacitors improve power factor?
Capacitors supply leading reactive power that offsets lagging reactive demand from inductive loads, reducing source current and apparent power.
Documentation
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