3 phase power, formula and calculator

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, two phases, and the other three phase system. Single phase system contains two wires. One is neutral and the other is phase wire.

In two phase system, we divide the system into two parts. Each section of the alternating current is out of phase by half cycle. However, this two phase system is not much common. While in the three phases there are three wires. We will discuss 3 phase power system in detail.

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.

3 phase power formula

As we discussed in our previous topics that the power of an electrical circuit is the product of differential voltage and current. But here in three phase power system, we have another factor which is the power factor in the equation of power. The power factor is the ratio of real power to apparent power.

Most of the electrical engineering students do not distinguish between real power and apparent power. Real power is the amount of power that performs useful work. While Apparent power is the power supplied to the circuit. So the 3 phase formula is given below.

The formula states that power is equal to the square root of 3, power factor, voltage, and current.

P = √3 * V * I * cosΦ


P : electrical three phase power

I : the current of the 3 phase load

V : phase to phase voltage of the power source

cosΦ : is the power factor of the load.

Three phase power calculator

Our electrical4uonline design engineer designed the below three 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 VLL, 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 VLN=VLL / √3


I  = S(1ph) / VLL

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

I = (√3 *  P) / (3 * pf  * VLL )

We simplify the 3 = √3 x √3 we get

I = P / (√3 * VLL * pf)

Or we can write the equation of power in the form

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

Where “P” is three phase power

“Pf” is the power factor of three phase system

“I” is the current and

VLL” is line to line voltage