How do you calculate Phasor Angle (Rect → Polar)?

Use the formula θ = atan(X / R). The phase angle of a complex impedance is the arctangent of its reactance over its resistance. Enter the values you know in the calculator above and it solves for the remaining variable.

What is the formula for Phasor Angle (Rect → Polar)?

The Phasor Angle (Rect → Polar) formula is θ = atan(X / R), where θ—Phase angle (degrees); R—Resistance / real part (Ω); X—Reactance / imaginary part (Ω).

Phasor Angle (Rect → Polar)

θ = atan(X / R)

Calculator

Phase Angle

Real Part

Imaginary Part

Result

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Formula

θ = atan(X / R)

Description

The phase angle of a complex impedance is the arctangent of its reactance over its resistance. A positive angle means the impedance is inductive (current lags voltage); a negative angle means capacitive (current leads). Together with the magnitude it fully describes the impedance and tells you the phase relationship between voltage and current in the circuit.

Variables

θ — Phase angle (degrees)
R — Resistance / real part (Ω)
X — Reactance / imaginary part (Ω)

Practical Notes

A purely resistive load has θ = 0°; a pure inductor +90°; a pure capacitor −90°. The power factor is cos(θ).

Related Concepts

All AC Circuits formulas →

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