How this calculator works
For sinusoidal steady-state loads, real and reactive power form perpendicular components of complex power. The apparent power is their magnitude, and power factor is the real fraction. Series resistance and reactance produce the same triangle when multiplied by current squared. This model gives displacement power factor; nonlinear loads with harmonic distortion require measured true power factor rather than this simple triangle.
Formula
S = sqrt(P² + Q²), PF = P/S = cos(phi), phi = atan2(Q,P). For Z = R + jX, P = I²R, Q = I²X and |Z| = sqrt(R²+X²).
Worked example
Real power 3 W and reactive power 4 var give 5 VA apparent power and power factor 0.6. A series impedance 3 - j4 ohm carrying 2 A uses 12 W, -16 var and 20 VA, again with power factor 0.6.
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Frequently asked questions
Does the sign belong on power factor?
This page reports a nonnegative magnitude and states leading or lagging separately. Meter sign conventions can differ.
Can I use this for an LED driver with distorted current?
Only if a sinusoidal equivalent is appropriate. True power factor includes distortion and should be measured for nonlinear loads.
Why is apparent power never less than real power?
Its magnitude includes both real and reactive components, so it must be at least as large as the real component.