# Power Factor Calculator

> Calculate power factor, real power, reactive power, and apparent power for AC electrical circuits.

**Category:** Conversion
**Keywords:** power factor, real power, reactive power, apparent power, kW, kVAR, kVA, phase angle, AC circuits, electrical, leading, lagging, power triangle
**URL:** https://complete.tools/power-factor-calculator

## How it calculates

The calculations involve several key formulas. The apparent power (S) is calculated using the formula S = V × I, where V is voltage in volts (V) and I is current in amperes (A). Real power (P) is given by P = S × PF, where PF is the power factor. The power factor itself can be calculated using PF = P ÷ S. Reactive power (Q) can be determined using the formula Q = √(S² - P²). In these equations, S represents the total power, P is the real power consumed, and Q is the reactive power that does not perform any actual work but is necessary for maintaining the voltage levels in the circuit. The relationships among these quantities help in analyzing the efficiency and stability of electrical systems.

## Who should use this

Electrical engineers conducting load analysis for power distribution systems, HVAC technicians assessing power quality in climate control systems, and renewable energy specialists evaluating the performance of solar inverters in power generation.

## Worked examples

Example 1: An electrical engineer measures a circuit with a voltage of 230 V and a current of 10 A. First, calculate apparent power: S = V × I = 230 V × 10 A = 2300 VA. If the power factor is 0.8, then real power is P = S × PF = 2300 VA × 0.8 = 1840 W. Reactive power is calculated as Q = √(S² - P²) = √(2300² - 1840²) = √(5290000 - 3385600) = √1904400 ≈ 1380 VAR. 

Example 2: A factory has a circuit with a power factor of 0.9, real power of 5000 W, and needs to find apparent power. Using P = S × PF, rearranging gives S = P ÷ PF = 5000 W ÷ 0.9 ≈ 5555.56 VA. To find reactive power, Q = √(S² - P²) = √(5555.56² - 5000²) = √(30864117.77 - 25000000) = √5864117.77 ≈ 2420.52 VAR.

## Limitations

This tool assumes that the circuit operates under sinusoidal conditions, which may not hold for non-linear loads. It also assumes pure resistive and inductive loads, potentially leading to inaccuracies in circuits with significant capacitance or harmonics. The tool may have precision limits based on floating-point calculations, which can affect results for very high or low values of voltage and current. Additionally, the tool does not take into account power losses due to resistance in the wires, which could yield an overestimation of real power.

## FAQs

**Q:** How does power factor affect electrical efficiency?


**A:** Power factor indicates how effectively electrical power is being converted into useful work output. A low power factor signifies poor efficiency, leading to higher energy costs and potential penalties from utility companies.


**Q:** Can the power factor be improved?


**A:** Yes, power factor can be improved using power factor correction devices such as capacitors or synchronous condensers that offset the inductive effects of motors and transformers.


**Q:** What is the significance of reactive power in a circuit?


**A:** Reactive power is crucial for maintaining voltage levels necessary for the operation of inductive loads like motors and transformers. It does not perform work but is essential for the stability of the electrical system.


**Q:** How is the power factor related to voltage drop in transmission lines?


**A:** A low power factor can lead to increased current flow, which results in higher voltage drops across transmission lines due to the resistance and reactance of the lines, affecting overall system efficiency.

---

*Generated from [complete.tools/power-factor-calculator](https://complete.tools/power-factor-calculator)*