Complex Power Calculator

✖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.ⓘ Real Power [P]			+10% -10%
✖Reactive Power is a measure of the energy exchange between the source and the reactive part of the load.ⓘ Reactive Power [Q]			+10% -10%

✖Complex Power is basically the representation of electrical power in the form of complex numbers.ⓘ Complex Power [S]

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Formula

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Complex Power

Formula

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

Example

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

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Complex Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Complex Power = sqrt(Real Power^2+Reactive Power^2)
S = sqrt(P^2+Q^2)
This formula uses 1 Functions, 3 Variables

Functions Used

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., sqrt(Number)

Variables Used

Complex Power - (Measured in Watt) - Complex Power is basically the representation of electrical power in the form of complex numbers.
Real Power - (Measured in Watt) - 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.
Reactive Power - (Measured in Watt) - Reactive Power is a measure of the energy exchange between the source and the reactive part of the load.

STEP 1: Convert Input(s) to Base Unit

Real Power: 235 Watt --> 235 Watt No Conversion Required
Reactive Power: 134 Volt Ampere Reactive --> 134 Watt (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = sqrt(P^2+Q^2) --> sqrt(235^2+134^2)

Evaluating ... ...

S = 270.519869880199

STEP 3: Convert Result to Output's Unit

270.519869880199 Watt -->270.519869880199 Volt Ampere (Check conversion here)

FINAL ANSWER

270.519869880199 ≈ 270.5199 Volt Ampere <-- Complex Power

(Calculation completed in 00.004 seconds)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has created this Calculator and 1500+ more calculators!

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< AC Power Calculators

Power in Single-Phase AC Circuits using Voltage

Go Real Power = (Voltage^2*cos(Phase Difference))/Resistance

Power in Single-Phase AC Circuits using Current

Go Real Power = Current^2*Resistance*cos(Phase Difference)

Power in Single-Phase AC Circuits

Go Real Power = Voltage*Current*cos(Phase Difference)

Complex Power

Go Complex Power = sqrt(Real Power^2+Reactive Power^2)

< AC Circuit Design Calculators

Capacitance for Parallel RLC Circuit using Q Factor

Go Capacitance = (Inductance*Parallel RLC Quality Factor^2)/Resistance^2

Capacitance for Series RLC Circuit given Q Factor

Go Capacitance = Inductance/(Series RLC Quality Factor^2*Resistance^2)

Capacitance given Cut off Frequency

Go Capacitance = 1/(2*Resistance*pi*Cut-off Frequency)

Capacitance using Time Constant

Go Capacitance = Time Constant/Resistance

Complex Power Formula

Complex Power = sqrt(Real Power^2+Reactive Power^2)
S = sqrt(P^2+Q^2)

What is the difference between single phase and three phase power supply?

In a single-phase supply, the power flows through one conductor whereas the three-phase supply consists of three conductors for power supply. The single-phase supply requires two wires (one phase and one neutral) for completing the circuit. The three phase requires three-phase wires and one neutral wire for completing the circuit.

How to Calculate Complex Power?

Complex Power calculator uses Complex Power = sqrt(Real Power^2+Reactive Power^2) to calculate 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 calculate Complex Power using this online calculator? To use this online calculator for Complex Power, enter Real Power (P) & Reactive Power (Q) and hit the calculate button. Here is how the Complex Power calculation can be explained with given input values -> 270.5199 = sqrt(235^2+134^2).

FAQ

What is 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 and is represented as S = sqrt(P^2+Q^2) or Complex Power = sqrt(Real Power^2+Reactive Power^2). 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 & Reactive Power is a measure of the energy exchange between the source and the reactive part of the load.

How to calculate 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 is calculated using Complex Power = sqrt(Real Power^2+Reactive Power^2). To calculate Complex Power, you need Real Power (P) & Reactive Power (Q). With our tool, you need to enter the respective value for Real Power & Reactive Power and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Complex Power?

In this formula, Complex Power uses Real Power & Reactive Power. We can use 2 other way(s) to calculate the same, which is/are as follows -

Complex Power = Real Power/cos(Phase Difference)
Complex Power = Real Power/cos(Phase Difference)

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