Phase Angle Calculator — RL, RC, and RLC Circuits
Calculate impedance and phase angle for RL, RC, and RLC circuits at any frequency.
Returns total impedance Z, phase angle φ, and power factor cos(φ) in degrees and radians.
In AC circuits, voltage and current are not necessarily in phase. The phase angle phi tells you how far ahead or behind the current lags the voltage (or vice versa).
For a series RLC circuit with resistance R, inductance L, and capacitance C at angular frequency omega = 2pif:
Inductive reactance: XL = omega * L = 2pifL (ohms) Capacitive reactance: XC = 1 / (omega * C) = 1 / (2pifC) (ohms) Net reactance: X = XL - XC Impedance magnitude: Z = sqrt(R^2 + X^2) Phase angle: phi = arctan(X / R)
When phi > 0 (XL > XC), the circuit is inductive – voltage leads current. When phi < 0 (XC > XL), the circuit is capacitive – current leads voltage. At resonance (XL = XC, phi = 0), impedance is minimized to just R and the power factor is 1.
Power factor: cos(phi). This is the fraction of apparent power (VA) that does real work (watts). A power factor of 1 means all power is useful. A power factor of 0.7 means 30% of delivered VA is reactive – wasted as magnetic and electric field oscillations. Industrial facilities pay penalties for low power factor.
For RL only (no capacitor): set C to zero or very large. For RC only: set L to zero.