Phasor Angle (Rect → Polar)
θ = atan(X / R)
Quick answer
This calculator solves θ = atan(X / R) for Phase Angle. With Real Part 0.47 kΩ, Imaginary Part 1.03 kΩ, the result is 65.47 °. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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).
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| theta | Phase Angle | ° | ° |
| R | Real Part | Ω | mΩ, Ω, kΩ, MΩ |
| X | Imaginary Part | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Real Part 0.47 kΩ, Imaginary Part 1.03 kΩ
- 2. The relation: θ = atan(X / R)
- 3. Substitute: R = 0.47 kΩ, X = 1.03 kΩ
- 4. Result: Phase Angle = 65.47 °
Worked examples
Minimum range
Given: Real Part 1 Ω, Imaginary Part 2.2 Ω
Result: Phase Angle = 65.56 °
Low range
Given: Real Part 10 Ω, Imaginary Part 22 Ω
Result: Phase Angle = 65.56 °
Typical
Given: Real Part 0.47 kΩ, Imaginary Part 1.03 kΩ
Result: Phase Angle = 65.47 °
High range
Given: Real Part 4.7 kΩ, Imaginary Part 10.3 kΩ
Result: Phase Angle = 65.47 °
Maximum range
Given: Real Part 47 kΩ, Imaginary Part 103 kΩ
Result: Phase Angle = 65.47 °
Solving for each variable
Solve for Phase Angle
Real Part 1 Ω, Imaginary Part 2.2 Ω → 65.56 °
Solve for Real Part
Phase Angle 1.5 °, Imaginary Part 2.2 Ω → 84.01 Ω
Solve for Imaginary Part
Phase Angle 1.5 °, Real Part 1 Ω → 26.19 mΩ
How Phase Angle changes with Real Part
| Real Part (input) | Phase Angle (result) |
|---|---|
| 47 Ω | 87.39 ° |
| 117.5 Ω | 83.49 ° |
| 0.235 kΩ | 77.15 ° |
| 0.3525 kΩ | 71.11 ° |
| 0.47 kΩ | 65.47 ° |
| 0.705 kΩ | 55.61 ° |
| 0.94 kΩ | 47.62 ° |
| 1.88 kΩ | 28.72 ° |
| 3.29 kΩ | 17.38 ° |
| 4.7 kΩ | 12.36 ° |
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<p><a href="https://vbatpower.com/formulas/phasor-angle/">Phasor Angle (Rect → Polar)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Phasor Angle (Rect → Polar)?
Use θ = atan(X / R). With Real Part 0.47 kΩ, Imaginary Part 1.03 kΩ, Phase Angle works out to 65.47 °.
What is the formula for Phasor Angle (Rect → Polar)?
The formula is θ = atan(X / R). The phase angle of a complex impedance is the arctangent of its reactance over its resistance.
How do you find Real Part when you know the other values?
Rearrange for Real Part: with Phase Angle 1.5 °, Imaginary Part 2.2 Ω, Real Part is 84.01 Ω.
How do you find Imaginary Part when you know the other values?
Rearrange for Imaginary Part: with Phase Angle 1.5 °, Real Part 1 Ω, Imaginary Part is 26.19 mΩ.
Related Concepts
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