You are about to start calculating Power Factor Correction. This allows you to calculate the apparent power, the real power, the reactive power and its phase angle. Consider the equation of a right triangle. So to calculate the angle, you need to know the laws of cosine, sine and tangent. You will also need to know the Pythagorean Theorem (c² = √(a² + b²)) to calculate the magnitudes of the sides of the triangle. You will also need to know which unit the power is in. Apparent power is measured in Volt-Ampère (VA). Real power is measured in Watts and reactive power is measured in units called Volt-Ampere-Reactive (VAR). There are several equations to calculate these values, all of which will be referenced in this article. Now you have the basis of what you are trying to calculate.

## Steps

#### Step 1. Calculate the impedance

Pretend the impedance is in the same place as the apparent power in the photo above. Then, to find the impedance, use the Pythagorean theorem c² = √ (a² + b²).

#### Step 2. Therefore, Total Impedance (represented by a Z) is equal to Real Power squared plus Reactive Power squared and then square root of answer

### (Z = √(60² + 60²)). If you put it on your scientific calculator, you will get the response of 84.85Ω. (Z = 84.85Ω.)

#### Step 3. Find your phase angle

Now you have the hypotenuse, which is your impedance. You also have your adjacent side, which is the real power, and the opposite side, which is the reactive power. To find the angle, you must use any of the above laws. For example, we use the Law of Tangent, which is the opposite side divided by the adjacent side (Reactive/Real).

### You should have an equation that looks like this: (60/60 = 1)

#### Step 4. Take the inverse of the tangent and get the Phase Angle

The inverse of the tangent is a button on your calculator. Now, you have the inverse of the tangent of the equation in the previous step and this will give you the phase angle. Your equation should look like this: tan ‾ ¹ (1) = Phase Angle. Your answer should be 45°.

#### Step 5. Calculate your total Current (Amperes)

Its current is in amps, also represented as an “A”. The formula used to calculate current is Voltage divided by Impedance, which numerically becomes 120V/84.85Ω. Now, you have an answer of approximately 1141 A. (120V/84.84Ω = 1141 A).

#### Step 6. Now you must calculate your apparent power which is represented by an “S”

For that, you don't need to calculate the Pythagorean theorem, because your hypotenuse was considered your impedance. Remembering that the apparent power is in the unit of Volt-amperes, we can calculate it using the following formula: voltage squared divided by its total impedance. Your equation should be: 120V²/84.85Ω. You should have the answer of 169.71 VA. (120²/84.85 = 169.71).

#### Step 7. Now you should calculate the real power, represented as “P”

To calculate the real power, you should have found the current, which you calculated in Step four. The real power, which is in Watt, is calculated by multiplying the current squared (1.141²) by the resistance (60Ω) in your circuit. You should have a response of 78, 11 watts. Your equation should look like this: 1,141² x 60 = 78, 11.

#### Step 8. Calculate your Power Factor

To do this, you will need the following information: Watts and Volt-amps. You have already calculated this information in the previous steps. Its Watt is equal to 78, 11 W and its Volt-amperes is equal to 169. 71 VA. The formula for the power factor, also represented by Fp, is Watts divided by Volt-amperes. You should have an equation like this: 78, 11/169, 71 =.460.

### This can also be expressed as a percentage, so you multiply.460 by 100, giving a power factor of 46%

## Notices

- This is just a basic example of how to calculate a phase angle and power factor. There are many more complicated circuits, including capacitive power and higher resistances and reactance.
- When calculating your impedance, use the inverse tangent function and not just the regular tangent function. This will give you an incorrect phase angle.