AC Phase Angle
φ = arctan((XL − XC) / R)
Quick answer
This calculator solves φ = arctan((X_L − X_C) / R) [degrees] for φ. With Inductive Reactance 0.47 kΩ, Capacitive Reactance 1.03 kΩ, Resistance 2.21 kΩ, the result is -14.22.
Calculator
Formula
Description
The phase angle between voltage and current in an AC circuit depends on the ratio of net reactance to resistance. When XL > XC (inductive), the phase angle is positive (voltage leads current). When XC > XL (capacitive), the phase angle is negative (current leads voltage). At resonance (XL = XC), the phase angle is zero and the circuit is purely resistive. The power factor equals cos(φ), so the phase angle directly determines how efficiently the circuit converts apparent power to real power.
Variables
- X_L — Inductive reactance, ωL (Ω)
- X_C — Capacitive reactance, 1/(ωC) (Ω)
- R — Resistance (Ω)
Practical Notes
Result is in degrees. A phase angle of 90° means purely reactive (no real power consumed). A phase angle of 0° means purely resistive (maximum power factor). Most utility loads are inductive (motors, transformers) with phase angles of 20-40°, corresponding to power factors of 0.77-0.94. Power factor correction aims to reduce this angle toward zero.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| XL | Inductive Reactance | Ω | mΩ, Ω, kΩ, MΩ |
| XC | Capacitive Reactance | Ω | mΩ, Ω, kΩ, MΩ |
| R | Resistance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Inductive Reactance 0.47 kΩ, Capacitive Reactance 1.03 kΩ, Resistance 2.21 kΩ
- 2. The relation: φ = arctan((X_L − X_C) / R) [degrees]
- 3. Substitute: XL = 0.47 kΩ, XC = 1.03 kΩ, R = 2.21 kΩ
- 4. Result: φ = -14.22
Worked examples
Minimum range
Given: Inductive Reactance 1 Ω, Capacitive Reactance 2.2 Ω, Resistance 4.7 Ω
Result: φ = -14.32
Low range
Given: Inductive Reactance 10 Ω, Capacitive Reactance 22 Ω, Resistance 47 Ω
Result: φ = -14.32
Typical
Given: Inductive Reactance 0.47 kΩ, Capacitive Reactance 1.03 kΩ, Resistance 2.21 kΩ
Result: φ = -14.22
High range
Given: Inductive Reactance 4.7 kΩ, Capacitive Reactance 10.3 kΩ, Resistance 22.1 kΩ
Result: φ = -14.22
Maximum range
Given: Inductive Reactance 47 kΩ, Capacitive Reactance 103 kΩ, Resistance 0.221 MΩ
Result: φ = -14.22
How φ changes with Inductive Reactance
| Inductive Reactance (input) | φ (result) |
|---|---|
| 47 Ω | -23.98 |
| 117.5 Ω | -22.44 |
| 0.235 kΩ | -19.79 |
| 0.3525 kΩ | -17.04 |
| 0.47 kΩ | -14.22 |
| 0.705 kΩ | -8.366 |
| 0.94 kΩ | -2.332 |
| 1.88 kΩ | 21.04 |
| 3.29 kΩ | 45.64 |
| 4.7 kΩ | 58.94 |
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<p><a href="https://vbatpower.com/formulas/ac-phase-angle/">AC Phase Angle</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate AC Phase Angle?
Use φ = arctan((X_L − X_C) / R) [degrees]. With Inductive Reactance 0.47 kΩ, Capacitive Reactance 1.03 kΩ, Resistance 2.21 kΩ, φ works out to -14.22.
How do you calculate ac capacitive phase angle?
Rearrange for φ: with Inductive Reactance 10 Ω, Capacitive Reactance 22 Ω, Resistance 47 Ω, φ is -14.32.
What is the formula for AC Phase Angle?
The formula is φ = arctan((X_L − X_C) / R) [degrees]. The phase angle between voltage and current in an AC circuit depends on the ratio of net reactance to resistance.
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