Phasor Magnitude (Rect → Polar)

Formula

Description

Converting a complex impedance from rectangular form (real resistance plus imaginary reactance) to polar form gives its magnitude as the Pythagorean sum of the two parts. The magnitude is what an AC ohmmeter reads—the ratio of voltage to current amplitudes—while the angle (computed separately) gives the phase. This is the everyday tool for combining resistive and reactive components.

Variables

• |Z| — Impedance magnitude (Ω)
• R — Resistance / real part (Ω)
• X — Reactance / imaginary part (Ω)

Practical Notes

Pair with the phasor angle θ = atan(X/R) for the full polar form. The same Pythagorean rule converts any rectangular phasor (voltage, current) to its amplitude.