#### Watt's Law - Three Phase

Three phase power is used primarily in commercial and industrial environments, providing power to motors and equipment. It is more economical to operate large equipment with three phase power. In order to calculate three-phase wattage, we multiply the average voltage of each phase times the average current of each phase, times the power factor, then multiply by the square root of 3. The square root of 3 is equal to 1.732, so the equation is written as shown:

Watt's Law: W = V avg. x A avg x p.f. x 1.732

Where:

W = wattage (watts)
Vavg = average voltage of the three separate phases (volts)
Aavg = average current of the three separate phases current (amps)
p.f. = average power factor or the three separate phases
1.732 = a constant necessary with 3 phase.

In a three phase circuit, the use of the constant 1.732 results from the fact that not all three phases are producing the same amount of power at the same time. Each phase's voltage and current move through zero at different times. Suffice it to say that the correct power from a three-phase system at any point in time is found by multiplying by the square root of 3.

The electrical power input in kilowatts for a three phase motor is calculated by multiplying the average voltage of all three phases measured at the motor times the average amperage of all three phases measured at the motor times the average power factor of all three phases measured at the motor times a constant of 1.732 and dividing the result by 1000.

An operating three phase motor has voltages measured with a voltmeter on each phase of 453, 458, and 461 volts, amperage measured on each phase with an ammeter are 14.1, 13.9, and 13.8 amps, power factor was measured as 0.82. The average voltage is 453 plus 458 plus 461 divided by 3 which equals 457 volts.

The average current is 14.1 plus 13.9 plus 13.8 divided by 3 which equals 13.9 amps.

The electrical power input to the motor equals 457 volts times 13.9 amps times 0.82 power factor divided by 1000 which equals 5.2 kilowatts.

(457V x 13.9A x .082pf x 1.732) / 1000 = 9.02 Kwatts