RLC Phase Angle Calculator

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.

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.