# Amps (A) to Kilowatts (kW) Calculator

Convert Amps (A) to kilowatts (kW) using our conversion calculator. Also, learn more about relations between Amps (A), Voltage (V), Watts (W), and other units often used not only in Electrical Engineering but in many other walks of life.

Published: February 7, 2024.

## Amps to Kilowatts Watts Conversion Calculator

In order to convert Amps (A) to kilowatts (kW), feel free to use this conversion calculator - write your values and click 'Calculate' to convert them.

 Amps (A) to Kilowatts (kW) Amps (A): Volts (V): Phase Shift (default 1):

Note: Phase shift must be ≤1. If you are unsure, leave the default value (1).

To convert Kilowatts to Amps, feel free to check our Kilowatts (kW) to Amps (A) Calculator article.

## How to Convert Amps to Kilowatts, and Other Formulas

Before diving into math and physics, it is important to know which unit is used for what:

• 'I': current strength, measured in Amps (A),
• 'P': power, measured in Watts (W),
• 'U': potential difference, measured in Volts (V),

In order to convert Amps (A) to kilowatts (kW), one must use two different (although similar) formulas (based on Ohm's Law Wheel), one for Direct Current (DC) and another for Alternate Current (AC):

DC:

P (W) = I (A)  *  U (V)

AC:

P (W) = I (A) * U (V) * cos α

Note: α is the phase angle between voltage and current - in DC electric systems α=0° (cos 0°=1), while in AC electric systems α depends on the type of load (inductive or capacitive) - this is the Effective Power of AC electric system and is expressed by Watts.

The Apparent Power of AC systems is expressed in Volt-Amps (never in watts) and is obtained by multiplying Volts and Amps.

So, to convert Amps to kilowatts, we will use the following formula:

P (kW) = [I(A) * U (V) * cos α] / 1000

Note: cos α is also known as the "Power Factor," and if it is below 0.9, the system is usually considered inefficient. But, there are various applications, so it may vary... If unsure, the Power Factor should be 1. The Power Factor or Phase Shift is often represented with φ.

## Amps to Kilowatts Conversion Example

Imagine that we have an AC system that requires 100 Amps at 120V, with a power factor of 0.95. What is the power of such a system, given in kilowatts (kW)?

In this example, the power is:

P(kW) = [100A * 120V * 0.95] / 1000 = 11.4 kW

## Apparent Power (Complex Power) vs. Real Power (True or Working Power) vs. Reactive Power

Understanding the differences between apparent power, real power, and reactive power is fundamental for the efficient design, operation, and optimization of electrical systems.

These concepts are crucial when dealing with AC (alternating current) circuits, where the power consumed by loads is not always as straightforward as in DC (direct current) circuits. This comprehensive guide aims to elucidate these three types of power, highlighting their definitions, significance, and interrelationships.

### Real Power (True or Working Power)

Real power, also known as true power or working power, is the actual power consumed by electrical equipment to perform useful work. It is measured in watts (W) and represents the capacity of the circuit for performing work at a particular time. Real power is the product of the voltage, current, and the cosine of the phase angle (cos φ) between them in circuits where the voltage and current are out of phase. The formula for real power (P) can be expressed as:

P = U * I * cos(φ)

where "U" is the voltage across the load (potential difference), "I" is the current flowing through the load, and "φ" is the phase angle between the voltage and current.

Real power is what powers devices and performs useful work, such as turning a motor or lighting a bulb. It is the "effective" part of the power that actually contributes to the energy consumption of the system.

### Reactive Power

Reactive power, measured in volt-amperes reactive (VAR), is the power that oscillates between the source and the reactive components of the load, such as inductors and capacitors. It does not perform any work but is necessary to establish the electric and magnetic fields required for the operation of inductive and capacitive components. The formula for reactive power (Q) is:

Q = U * I * sin(φ)

where sin(φ) is the sine of the phase angle between the current and voltage. Reactive power contributes to the total power flow in the system but does not result in energy consumption by the load. It is crucial for the proper functioning of AC systems, affecting voltage levels and the ability to deliver real power efficiently.

### Apparent Power (Complex Power)

Apparent power is the combination of real power and reactive power in a circuit. It represents the total power supplied from the source to the circuit. Apparent power is measured in volt-amperes (VA) and is calculated using the formula:

S = U * I

The apparent power "S" is the vector sum of real power "P" and reactive power "Q", and it can be represented as a complex number or as a magnitude and angle.

The relationship among apparent power, real power, and reactive power can be represented in a power triangle, where:

• The horizontal side represents real power (P),
• The vertical side represents reactive power (Q),
• The hypotenuse represents apparent power (S).

The power factor, a key concept in understanding these types of power, is the ratio of real power to apparent power and indicates the efficiency with which electrical power is converted into useful work output. It is a measure of how effectively electrical power is being used.

### Significance and Application

Understanding the distinctions and relationships between real power, reactive power, and apparent power is crucial for the design, analysis, and optimization of electrical systems.

Engineers use these concepts to ensure that electrical systems are efficient, safe, and capable of meeting the required performance specifications. For instance, improving the power factor of a system can lead to reduced power losses, lower electricity costs, and improved voltage regulation.