Power Triangle

Volt-Amps (Apparent Power) can be determined if you know the Watts (True Power) and the Vars (Reactive Power).

Likewise Watts can be determined if Vars and Volt-Amps are known.

And Vars can be found when the Apparent and True Powers are known.


This can be done with the power triangle.

Assume Watts represents the horizontal side of a right triangle.

Vars would represent the vertical side of this right triangle.

To solve for the Apparent Power (Volt-Amps) you must simply solve for the hypotenuse of the right triangle.

If you know the values of any two sides then you can find the value of the third side.

Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two remaining sides of that right triangle.

That is:

(C x C) = (A x A) + (B x B)

or in the specific case of finding Apparent Power:

(Apparent Power x Apparent Power) = (Watts x Watts) + (Vars x Vars)

Some easy algebraic manipulation will allow for finding the third side if any two sides are given.


The Load Angle can easily be found by using Trigonometric functions to find the "Angle Theta".

(Angle Theta is the angle above the horizontal.)

Sine, Cosine or Tangent functions are easily applied depending on which sides you desire to work with.

The load angle can be found using the Arc Tangent function of the ratio of the Vars/Watts to find the angle Theta.

Load Angle = arc tan (Vars/Watts)