Power Formula And Calculations (Step By Step Examples)

Electrical power formula is considered one of the basic electrical formulas we use in our work every day life.

Every day around the world, power formula is being used to calculate power of various load types like, motors, lighting and much more.

This is why I have designed an easy electrical power calculator and an android electrical calculator 100% FREE, you can find them later in this article.

However, I always recommend all my followers, on YouTube, to understand how exactly the power is calculated step by step, and understand the formulas.

In this article I will share with you how we calculate power.

Table of Contents

Power formulas, AC and DC Circuits

Power (1 phase), P = V * I * pf
Power (3 phase), P=√3* V * I * pf
P_DC = V² ÷ R = I² x R

Where:

P power
V voltage
I current
pf power factor

Let’s dive into some examples and details!

3 phase Power

Power generation uses 3 phase power system as the default power system around the world.

In an electrical system, the phase system is used for the distribution of load. There are three different types of phase systems in use.

The first one is a single phase and the other three phase system. Single phase system contains two wires, one is the neutral and the other is phase wire.

While in the three phases there are three wires, in sometimes we use three wires and the neutral, 4 wires system.

A 3 phase power is a poly phase system which is used to transfer three time more power from electrical grids to other destinations.

Similarly, we use three phase system to power up heavy loads like large power three phase induction motors. The three phase system uses the same principle as two phase system but here all three parts of the current are out of phase by one-third of each.

For more information about three and single phase power read my article, Three phase vs single phase power.

Power formula for AC loads

For inductive loads, such as induction motors, electrical power formula is given as follows:

Power (1 phase), P = V * I * pf
Power (3 phase), P=√3* V * I * pf

Where:

P is the power
V is the operating voltage of the load or the source
I the current of the load
pf is the power factor, some times is referred to as, cos ø

You should understand the following:

Resistive electrical loads, like lighting loads and heaters, the current and voltage match and no phase shift or angle between them, and hence no power factor needed in the power formula of resistive loads. Resistive loads have a Unity Power Factor.
While in inductive loads like single and three phase induction motors, the voltage is a head of current, then a power factor is taken into account in the formula.

AC power calculation step by step example

I have built an android calculator app for you, it has all these calculations like, but not limited to:

KW to HP converter
KW/HP to Amp converter
Amp to KW/HP converter

And some more calculations, Its 100% Free on Google Play Store, Install it now from here.

Single phase power calculation example

A single phase motor, power rating 90 A, operating voltage 110V, 0.8 power factor, What is the motor power?

From the single phase power formula above,

P = V*I*pf = 110*90*0.8 = 7.9 Kilo Watt

We can convert the motor power from KW to HP, P = 7.9/0.746 = 10.59 HP

Three phase power calculation example

In instance, we have the same motor, 90A motor, but its a three phase motor, operating voltage is 400V with the same power factor!

From the three phase power formula above,

P =√3* V*I*pf = √3*110*90*0.8 = 49.88 Kilo Watt = 66.8 HP

Use the below electrical power calculator to calculate single and three phases power, I built it to be easy to use and helpful for you.

Three phase power online calculator

I have designed the below three phase and single phase power calculator for you:

Derivation of 3 Phase power formula

To derive the formula for three phase power, consider three phase system having total power P (W), a line to line voltage V_LL, and power factor pf.

According to the single phase power equation

P = V * I

For three phase system, we divide the P by 3 to obtain a single phase value.

P(1ph) = P/3

Apparent power for a single phase

S(1ph) = P(1ph)/pf

Putting the value of p(1ph) we get

S(1ph) = P(1ph)/ (3* pf)

To find the value of phase current we divide the apparent power of a single phase by phase to neutral voltage.

We know that V_LN=V_LL / √3

Hence

I = S(1ph) / V_LL

Putting the value of and we get the value of “I”

I = (√3 * P) / (3 * pf * V_LL )

We simplify the 3 = √3 x √3 we get

I = P / (√3 * V_LL * pf)

Or we can write the equation of power in the form

3 phase power (P) = √3 * V_LL * I * pf

Where “P” is three phase power

“Pf” is the power factor of three phase system

“I” is the current and

“V_LL” is line to line voltage

Power formula for DC circuits

For DC circuits, Power = current * voltage, or P = I * V , the resulted power is in watt.

Power equation also has three forms,

P = V² ÷ R
P = I² x R
P = I x V

Where,

P is the power, V is the operating voltage, I is the current and R is the resistance of the load.

DC power calculation, step by step example

In instance , we have a DC motor, its voltage is 24VDC and its current is 19A, the motor Power will be,

P = I*V = 24*19 =456 Watt

Best FREE Electrical Apps

I was a fresh graduate, from the electrical engineering faculty, when I realized that I needed many electrical formulas, tables, and calculations in my work.

I never like memorizing this stuff and carrying cable catalogs everywhere.

So I created my own simple custom android apps to help myself. It feels great that I have my solution!

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Cables tables cables most used tables, I use this one all the time.
Fast Electrical Calculator App, the one I use for electrical calculations, I always count on this baby the most.
Motor Calculator App is a simple app for electrical motor calculations.
Cables Ampacity Tables App we need cable ampacity almost every day, in this app, I made it easy for you to check cable ampacity.
Circuit breaker Selection App This one is a fast way to determine circuit breaker sizing.

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