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Complex Power Formula

GoComplex Power given Power Factor Formula

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Complex Power is basically the representation of electrical power in the form of complex numbers. Check FAQs

S = \sqrt{P^{2} + Q^{2}}

S - Complex Power?P - Real Power?Q - Reactive Power?

Complex Power Example

With values

With units

Only example

Here is how the Complex Power equation looks like with Values.

Here is how the Complex Power equation looks like with Units.

Here is how the Complex Power equation looks like.

270.5199 = \sqrt{235^{2} + 134^{2}}

270.5199VA = \sqrt{{235W}^{2} + {134VAR}^{2}}

270.5199 = \sqrt{235^{2} + 134^{2}}

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Complex Power Solution

Follow our step by step solution on how to calculate Complex Power?

FIRST Step Consider the formula

S = \sqrt{P^{2} + Q^{2}}

Next Step Substitute values of Variables

∴

S = \sqrt{{235W}^{2} + {134VAR}^{2}}

Next Step Convert Units

∴

S = \sqrt{{235W}^{2} + {134W}^{2}}

Next Step Prepare to Evaluate

∴

S = \sqrt{235^{2} + 134^{2}}

Next Step Evaluate

∴

S = 270.519869880199W

Next Step Convert to Output's Unit

∴

S = 270.519869880199VA

LAST Step Rounding Answer

∴

S = 270.5199VA

Complex Power Formula Elements

Variables

Functions

Complex Power

Complex Power is basically the representation of electrical power in the form of complex numbers.

Symbol: S

Measurement: PowerUnit: VA

Note: Value can be positive or negative.

Formulas to find Complex Power

Real Power

The Real Power P is the average power in watts delivered to a load. It is the only useful power. It is the actual power dissipated by the load.

Symbol: P

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Real Power

Reactive Power

Reactive Power is a measure of the energy exchange between the source and the reactive part of the load.

Symbol: Q

Measurement: PowerUnit: VAR

Note: Value can be positive or negative.

Formulas to find Reactive Power

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Complex Power

Go Complex Power given Power Factor

S = \frac{P}{\cos (Φ)}

Other formulas in AC Power category

Go Capacitance for Parallel RLC Circuit using Q Factor

C = \frac{L \cdot {Q ||}^{2}}{R^{2}}

Go Capacitance for Series RLC Circuit given Q Factor

C = \frac{L}{{Q se}^{2} \cdot R^{2}}

Go Capacitance given Cut off Frequency

C = \frac{1}{2 \cdot R \cdot π \cdot f c}

Go Capacitance using Time Constant

C = \frac{τ}{R}

How to Evaluate Complex Power?

Complex Power evaluator uses Complex Power = sqrt(Real Power^2+Reactive Power^2) to evaluate the Complex Power, Complex Power is basically the representation of electrical power in the form of complex number. Like a complex number, it consists of real and imaginary part. Real part represents the active power whereas the imaginary part represents the reactive power. It is generally represented by symbol S. Complex Power is denoted by S symbol.

How to evaluate Complex Power using this online evaluator? To use this online evaluator for Complex Power, enter Real Power (P) & Reactive Power (Q) and hit the calculate button.

FAQs on Complex Power

What is the formula to find Complex Power?

The formula of Complex Power is expressed as Complex Power = sqrt(Real Power^2+Reactive Power^2). Here is an example- 270.5199 = sqrt(235^2+134^2).

How to calculate Complex Power?

With Real Power (P) & Reactive Power (Q) we can find Complex Power using the formula - Complex Power = sqrt(Real Power^2+Reactive Power^2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Complex Power?

Here are the different ways to Calculate Complex Power-

Complex Power=Real Power/cos(Phase Difference)

Can the Complex Power be negative?

Yes, the Complex Power, measured in Power can be negative.

Which unit is used to measure Complex Power?

Complex Power is usually measured using the Volt Ampere[VA] for Power. Watt[VA], Kilowatt[VA], Milliwatt[VA] are the few other units in which Complex Power can be measured.

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