In AC circuits, the power factor is the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit.

The power factor can get values in the range from 0 to 1.

When all the power is reactive power with no real power (usually inductive load) - the power factor is 0.

When all the power is real power with no reactive power (resistive load) - the power factor is 1.

### Power factor definition

The power factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA):

*PF* = *P*_{(W)}* */* |S*_{(VA)}|

*PF *- power factor.

*P - *real power in watts (W).

*|S| - *apparent power - the magnitude of the complex power in volt⋅amps (VA).

### Power factor calculations

For sinusuidal current, the power factor PF is equal to the absolute value of the cosine of the apparent power phase angle *φ *(which is also is impedance phase angle):

*PF* = |cos* φ|*

*PF *is the power factor.

*φ *is the apprent power phase angle.

The real power P in watts (W) is equal to the apparent power |S| in volt-ampere (VA) times the power factor PF:

*P*_{(W)} = *|S*_{(VA)}| × *PF* = *|S*_{(VA)}| × |cos *φ|*

When the circuit has a resistive impedance load, the real power P is equal to the apparent power |S| and the power factor PF is equal to 1:

*PF*_{(resistive load)} = *P* / *|S|* = 1

The reactive power Q in volt-amps reactive (VAR) is equal to the apparent power |S| in volt-ampere (VA) times the sine of the phase angle *φ*:

*Q*_{(VAR)} = *|S*_{(VA)}| × |sin *φ|*

Single phase circuit calculation from real power meter reading P in kilowatts (kW), voltage V in volts (V) and current I in amps (A):

*PF* = |cos *φ|* = 1000 × *P*_{(kW)} / (*V*_{(V)} ×
*I*_{(A)})

Three phase circuit calculation from real power meter reading P in kilowatts (kW), line to line voltage *
V*_{L-L} in volts (V) and current I in amps (A):

*PF* = |cos* φ|* = 1000 ×
*P*_{(kW)} / (* √*3

*× V*

_{L-L(V)}×

*I*

_{(A)})

Three phase circuit calculation from real power meter reading P in kilowatts (kW), line to line neutral *
V*_{L-N} in volts (V) and current I in amps (A):

*PF* = |cos* φ|* = 1000 ×
*P*_{(kW)} / (3* × V*_{L-N(V)} × *I*_{(A)})

### Power factor correction

Power factor correction is an adjustment of the electrical circuit in order to change the power factor near 1.

Power factor near 1 will reduce the reactive power in the circuit and most of the power in the circuit will be real power. This will also reduce power lines losses.

The power factor correction is usually done by adding capacitors to the load circuit, when the circuit has inductive components, like an electric motor.

#### Power factor correction calculation

The apparent power |S| in volt-amps (VA) is equal to the voltage V in volts (V) times the current I in amps (A):

*|S*_{(VA)}| = *V*_{(V)} × *I*_{(A)}

The reactive power Q in volt-amps reactive (VAR) is equal to the square root of the square of the apparent power |S| in volt-ampere (VA) minus the square of the real power P in watts (W) (pythagorean theorem):

*Q*_{(VAR)} = √(*|S*_{(VA)}|^{2}
- * P*

_{(W)}

^{2})

*Q*_{c (kVAR)} = *Q*_{(kVAR)} - *Q*_{corrected (kVAR)}

The reactive power Q in volt-amps reactive (VAR) is equal to the square of voltage V in volts (V) divided by the reactance Xc:

*Q*_{c (VAR)} = *V*_{(V)}^{2}
/ *X*_{c} = *V*_{(V)}^{2}
/ (1 / (2π*f*_{(Hz)}*×C*_{(F)}))
= 2π*f*_{(Hz)}*×C*_{(F)}*×V*_{(V)}^{2}

So the power factor correction capacitor in Farad (F) that should be added to the circuit in parallel is equal to the reactive power Q in volt-amps reactive (VAR) divided by 2π times the frequency f in Hertz (Hz) times the squared voltage V in volts (V):

*C*_{(F)} = *Q*_{c (VAR)} / (2π*f*_{(Hz)}*·**V*_{(V)}^{2})

Currently, we have around 5612 calculators, conversion tables and usefull online tools and software features for students, teaching and teachers, designers and simply for everyone.

You can find at this page financial calculators, mortgage calculators, calculators for loans, calculators for auto loan and lease calculators, interest calculators, payment calculators, retirement calculators, amortization calculators, investment calculators, inflation calculators, finance calculators, income tax calculators, compound interest calculators, salary calculator, interest rate calculator, sales tax calculator, fitness & health calculators, bmi calculator, calorie calculators, body fat calculator, bmr calculator, ideal weight calculator, pace calculator, pregnancy calculator, pregnancy conception calculator, due date calculator, math calculators, scientific calculator, fraction calculator, percentage calculators, random number generator, triangle calculator, standard deviation calculator, other calculators, age calculator, date calculator, time calculator, hours calculator, gpa calculator, grade calculator, concrete calculator, subnet calculator, password generator conversion calculator and many other tools and for text editing and formating, downloading videos from Facebok (we built one of the most famous Facebook video downloader online tools). We also provide you online downloanders for YouTube, Linkedin, Instagram, Twitter, Snapchat, TikTok and other social media sites (please note we does not host any videos on its servers. All videos that you download are downloaded from Facebook's, YouTube's, Linkedin's, Instagram's, Twitter's, Snapchat's, TikTok's CDNs. We also specialise on keyboard shortcuts, ALT codes for Mac, Windows and Linux and other usefull hints and tools (how to write emoji online etc.)

There are many very usefull online free tools and we would be happy if you share our page to others or send us any suggestions for other tools which will come on your mind. Also in case you find any of our tools that it does not work properly or need a better translation - please let us know. Our tools will make your life easier or simply help you to do your work or duties faster and in more effective way.

These below are the most commonly used by many users all over the world.

- Free online calculators and tools
- Time zones/Clocks/Dates calculators
- Free Online Units Conversion Calculators
- Free online web design tools
- Free online electricity & electronics tools
- Mathematics
- Online Tools
- Text Tools
- PDF Tools
- Code
- Ecology
- Others
- Free online downloaders for social media
- Basic Electrical Terms
- Electrical & Electronic Units
- Electronic Components
- Electrical & Electronic Symbols
- Electronic Circuit Laws
- Electric charge
- Electric current
- Electric power
- Electric power efficiency
- Electrical resistance
- Electrical voltage
- Power factor

And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.

Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.