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RLC Phase Angle Calculator

Enter resistance, inductance, capacitance and frequency to find the RLC phase angle.

How it is calculated

For a series RLC circuit the tool first finds the two reactances: XL = 2π·f·L and XC = 1 ÷ (2π·f·C). The phase angle is φ = atan2(XL − XC, R) in degrees, and the impedance is Z = √(R² + (XL − XC)²). Units are ohms (R), henries (L), farads (C) and hertz (f); the net reactance and impedance are given in ohms with two decimals.

A positive angle means the circuit is inductive and the current lags the voltage; a negative angle means it is capacitive and the current leads. Near zero, the circuit is close to resonance, which lies at f = 1 ÷ (2π√(LC)). R, C and f must be greater than zero; L can be zero. Because R is in the denominator of the angle and L, C are in base units, the result is sensitive to unit mistakes.

Worked example

R = 50 Ω, L = 0.01 H (10 mH), C = 0.00001 F (10 µF), f = 1000 Hz. Inductive reactance: 2π × 1000 × 0.01 = 62.83 Ω. Capacitive reactance: 1 ÷ (2π × 1000 × 0.00001) = 15.92 Ω. Net reactance: 62.83 − 15.92 = 46.92 Ω. Phase angle: atan(46.92 ÷ 50) = atan(0.938) = 43.18 ° (inductive, current lags). Impedance: √(50² + 46.92²) = √4701.5 = 68.56 Ω.

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Common mistakes

  • Entering L in millihenries or C in microfarads. The fields are henries and farads, so 10 mH is 0.01 and 10 µF is 0.00001; a unit slip moves the angle by tens of degrees.
  • Entering the angular frequency ω (rad/s) instead of f in hertz. The tool multiplies by 2π itself, so the reactances would be 6.28 times too large.
  • Reading a negative angle as an error. It is correct for a capacitive circuit; for example 500 Hz with the same parts gives −0.48 °, very near resonance at about 503 Hz.
  • Using this for a parallel RLC circuit. The formulas here are for R, L and C in series; a parallel network has different phase relations.
  • Forgetting that a coil or capacitor also has its own resistance. Only the R you type is used, so real-world parts may need their series resistance added to R.

About this calculator

In a series RLC circuit driven by an AC source, current lags or leads voltage depending on the balance between inductive and capacitive reactance. The phase angle is φ = arctan((X_L − X_C) / R), where X_L = 2πfL is the inductive reactance, X_C = 1/(2πfC) is the capacitive reactance, and R is the resistance. When X_L exceeds X_C the circuit is inductive and current lags voltage; when X_C dominates the circuit is capacitive and current leads.

This calculator takes R, L, C and frequency to compute that phase angle directly. Electrical engineers use it in AC circuit analysis and when designing power-factor correction, since the phase angle determines how much of the apparent power is actually useful real power, while electronics technicians use it when tuning filter and resonance circuits, where the phase angle passes through zero exactly at resonance.

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Comments (1)

  • Editorial team

    For a series circuit the power factor is cosine of the phase angle, which equals R divided by the impedance. With the default values the impedance is 184.46 ohms and R is 100, so the power factor is about 0.542. That gives you a direct number to take into a power-factor correction decision. Are you tuning a filter or correcting power factor? Share your R, L, C and frequency.

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