Power Factor Calculator Formula
Understand the math behind the power factor calculator. Each variable explained with a worked example.
Formulas Used
Power Factor
pf = real_power / apparent_powerReactive Power (Q)
reactive = sqrt(pow(apparent_power, 2) - pow(real_power, 2))Phase Angle
phase_angle = (180 / pi) * sqrt(1 - pow(real_power / apparent_power, 2)) / (real_power / apparent_power)Variables
| Variable | Description | Default |
|---|---|---|
real_power | Real Power (P)(kW) | 25 |
apparent_power | Apparent Power (S)(kVA) | 30 |
How It Works
Power Factor
Power factor indicates how effectively electrical power is being converted to useful work.
Formulas
PF = P / S = kW / kVA
Q = sqrt(S^2 - P^2)
A power factor of 1.0 means all power is real (useful). Low power factor means more current flows than needed, increasing losses. Industrial facilities typically aim for PF > 0.95 to avoid utility penalties.
Worked Example
A facility drawing 30 kVA with 25 kW real power.
- 01PF = 25 / 30 = 0.833
- 02Q = sqrt(30^2 - 25^2) = sqrt(900 - 625) = sqrt(275) = 16.58 kVAR
- 03Phase angle = arccos(0.833) = 33.6 degrees
Frequently Asked Questions
What causes low power factor?
Induction motors (especially when lightly loaded), transformers, fluorescent lighting ballasts, and welding equipment all draw reactive current that lowers power factor. Heavily loaded motors have better PF than lightly loaded ones.
How do I improve power factor?
Install capacitor banks to offset reactive power, use synchronous condensers, replace lightly loaded motors with properly sized ones, or use active power factor correction (PFC) on electronic loads.
What is the penalty for low power factor?
Most utilities penalise facilities with PF below 0.9 or 0.85. Penalties can range from 1% to 15% of the electrical bill. Additionally, poor PF wastes energy in conductors due to higher I^2R losses.
Learn More
Guide
Understanding Electrical Circuits: Fundamentals for Engineers
Learn the fundamentals of electrical circuits including Ohm's law, Kirchhoff's laws, series and parallel circuits, AC vs DC, power calculations, and three-phase systems.
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