kW kVA kVAR formula, Relation with Power Factor

kW kVA kVAR formula:

kW is nothing but a kilowatt and it is the unit of real power in kilo rating. kVA is a unit of apparent power in kilo rating. kVAR is the unit of reactive power in kilo rating.

Look at the power triangle, kW kVA kVAR formula can be written as below,

kVA² = kW² + kVAR²

kVA = √ (kW² + kVAR²)

Look at the above formula, the kVA is equal to the square root of the sum of the square of the kW and KVAR.

From that formula, we can easily find out the kW and KVAR,

kW² = kVA² – kVAR²

kW = √ (kVA² – kVAR²)

Like that, kVAR can be calculated from kW and kVA,

kVAR² = kVA² – kW²

kVAR = √ (kVA² – kW²)

Also if you know the power factor, then we can relate them

KW, KVA and power factor formula,

kW is equal to power factor times of kVA, the formula can be written as

kW = kVA * power factor

or

kW = kVA * cos (φ)

or

The real power in kW = apparent power in kVA * power factor.

Hence,

kVA = KW / cos(φ)

kVAR kVA, power factor formula:

kVAR is equal to the sin of power angle times of kVA.

kVAR = kVA * sin(φ)

or

Reactive power = apparent power * sin of power angle.

The power angle φ can be calculated by the cosine inverse of power factor.

From that,

kVA = KVAR / Sin(φ)

kW, kVAR and power factor formula:

kVAR is equal to the tan of kW. Hence the formula can be

kVAR = kW * tan (φ)

Reactive power in kilo volt-ampere reactive = kW * tan (power angle)

From that,

kW = kVAR / tan(φ)

Video for kW, KVAR, KW explanation