Calculate active, reactive or apparent power from any two values, and find power factor from active and apparent power in W, VA, kW, kVA and MW.

Sinusoidal AC power triangle. Active power is the consumed-power magnitude; reactive power may be signed (+ inductive, − capacitive). Solving an unknown power returns its nonnegative magnitude.

Positive for inductive and negative for capacitive loads; the magnitude enters the power triangle.

Active Power Formula

For sinusoidal AC, select Active power from S and Q and use the following power-triangle formula. Unknown active and reactive powers are nonnegative magnitudes; signed reactive inputs are accepted. Power-factor modes use PF = P/S and do not infer reactive power under harmonic distortion. 

Pa = SQRT (AP² - RP²)
  • Where Pa is the Active Power (watts)
  • AP is the apparent power (VA) 
  • RP is the reactive power (var) 

How to Calculate Active Power?

The following two example problems outline how to calculate the Active Power.

Example Problem #1:

  1. First, determine the apparent power (VA). In this example, the apparent power (VA) is measured to be 40.
  2. Next, determine the reactive power (var). For this problem, the reactive power (var) is calculated to be 20.
  3. Finally, calculate the Active Power using the formula above: 

Pa = SQRT ( AP^2 – RP^2)

Inserting the values from above and solving the equation with the imputed values gives: 

Pa = SQRT (40^2 – 20^2) = 34.64 (watts)

Example Problem #2: 

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

apparent power (VA) = 70

reactive power (var) = 20

Entering these values into the formula or calculator above gives us: Pa = SQRT ( 70^2 – 20^2) = 67.08 (watts)