**3 Phase Power Formula, P = √3* V * I * pf , While **

**1 Phase Power Formula, P = V * I * pf,**Every day , the power formula is being used to calculate the power of various load types like motors, lighting, and much more.

In this article, I will share with you how we calculate power step by step and below I provide a power calculator.

## Power formulas, AC and DC Circuits

**Power (1 phase), P = V * I * pf****Power (3 phase), P=***√3** V * I * pf**P**_{ DC}=**V**^{2}÷ R =**I**^{2}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 neutral and the other is a phase wire.

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

A 3-phase power is a poly-phase system that is used to transfer three times more power from electrical grids to other destinations.

Similarly, we use the three-phase system to power up heavy loads like large power three-phase induction motors. The three-phase system uses the same principle as the 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, the 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:

- In resistive electrical loads, like lighting loads and heaters, the current and voltage match, and no phase shift or angle between them, hence no power factor is 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 ahead of the current, then a power factor is taken into account in the formula.

**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, 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**

For instance, we have the same motor, a 90A motor, but it’s a three-phase motor, and an operating voltage is 400V with the same power factor!

From the three-phase power formula, P =** √3*** V*I*pf =

***110*90*0.8 =**

*√3***49.88 Kilo Watt = 66.8 HP**

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

### Three-phase power online calculator

I have designed online three-phase and single-phase power calculator for you:

### Derivation** of 3 Phase power formula **

To derive the formula for three-phase power, consider a 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 a 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*/ √3

_{LL}**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 a 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 resulting power is in watts.

Power equation also has three forms,

**P = V**^{2}÷ R**P = I**^{2}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

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

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

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