Apparent Power

In AC circuits, real power P is the part that does useful work, while reactive power Q represents energy that sloshes back and forth between the source and fields in inductors or capacitors. These two components are perpendicular in the complex-power plane, so the total apparent power S is the magnitude of the vector formed by P and Q, which is why Pythagoras gives S = √(P² + Q²). This tells you the overall power a source, transformer, or cable must be able to handle even though not all of it becomes useful output.

Use this when you know real power and reactive power and need the total power demand seen by the supply, such as sizing generators, transformers, UPS systems, or conductors. It is also useful for power-factor analysis and checking whether equipment ratings in volt-amperes are adequate.

• Adding P and Q directly instead of using the square-root of the sum of squares
• Mixing units: P should be in watts and Q in vars, with S reported in volt-amperes
• Using this formula for DC circuits or purely resistive AC loads where Q is zero