PowerFactor
Calculate the AC power factor (cos φ) from real power and apparent power using PF = P/S. Free online calculator with reactive power, phase angle, and power triangle charts.
About This Calculator
The Power Factor Calculator computes the power factor (cos φ) of an alternating current (AC) electrical circuit from real power (P) and apparent power (S). Power factor is a critical metric in electrical engineering that measures how effectively electrical power is converted into useful work output. It is essential for electrical engineers, facility managers, electricians, and anyone designing or maintaining AC power systems.
This calculator uses the fundamental power factor formula PF = P / S = cos φ. It also calculates the reactive power (Q) using the Pythagorean relationship Q = √(S² − P²) and the phase angle φ in degrees. A power triangle chart visually represents the relationship between real, reactive, and apparent power. Results update instantly and can be shared via URL bookmarking.
Regional Notes
India (IN): Power factor penalties by state electricity boards typically apply below 0.85 lagging. Capacitor banks for PF correction are common in industrial installations across Maharashtra, Gujarat, Tamil Nadu, and other industrial states. BEE (Bureau of Energy Efficiency) mandates PF correction for large consumers.
United States (US): Utilities like PG&E, Duke Energy, and Southern Company impose power factor penalties below 0.85-0.90 for commercial and industrial customers. IEEE 519 standard provides harmonic and PF guidelines. Power factor correction capacitors are widely used in US manufacturing facilities.
United Kingdom (UK): UK distribution network operators (DNOs) charge reactive power penalties via the CCRC (Capacity Charging Reactive Power) mechanism when PF falls below 0.95. Ofgem regulations encourage PF correction for large consumers to reduce grid losses.
Frequently Asked Questions
What is power factor in an AC circuit?
Power factor (PF) is the ratio of real power (P) to apparent power (S) in an AC circuit, calculated as PF = P/S = cos φ. It measures how effectively electrical power is being used, with values ranging from 0 to 1. A power factor of 1.0 (unity) means all power is used for real work.
How do you calculate power factor from real and apparent power?
Power factor is calculated by dividing real power (P in watts) by apparent power (S in volt-amperes): PF = P / S = cos φ. For example, if real power is 10,000 W and apparent power is 12,500 VA, the power factor is 10,000 / 12,500 = 0.8 or 80%.
What is the difference between real, reactive, and apparent power?
Real power (P in watts) performs actual work in the circuit and is dissipated by resistors. Reactive power (Q in VAR) oscillates between source and reactive components (inductors, capacitors) without doing work. Apparent power (S in VA) is the vector sum of real and reactive power, calculated as S = √(P² + Q²).
What causes a low power factor?
Low power factor is primarily caused by inductive loads such as electric motors, transformers, fluorescent lighting ballasts, and induction furnaces. These loads draw reactive power to maintain magnetic fields, which increases the phase angle between voltage and current and reduces the power factor.
How can power factor be corrected?
Power factor correction is achieved by adding capacitors (or synchronous condensers) in parallel with the load. Capacitors supply leading reactive power that cancels the lagging reactive power from inductive loads. The required capacitance can be calculated from the reactive power Q and line voltage using C = Q / (2πfV²).
What is a good power factor value?
A power factor between 0.95 and 1.0 is considered excellent. Most utilities charge penalties for power factors below 0.85-0.90. A power factor of 1.0 (unity) is ideal but rarely achieved in practice due to the presence of inductive loads in all electrical systems.
Is power factor relevant for DC circuits?
No, power factor only applies to AC circuits. In DC circuits, voltage and current are in phase, so the power factor is always 1.0 (unity). Reactive power does not exist in DC systems since there is no phase difference between voltage and current.
How do utilities penalize low power factor?
Many utilities impose power factor penalties or demand charges when the power factor drops below a threshold (typically 0.85 to 0.90). These penalties reflect the additional current required to deliver the same real power, which increases line losses and reduces system capacity. Power factor correction can significantly reduce electricity bills.