RLC Impedance Calculator
Enter the resistance, inductance, capacitance, and frequency of your RLC circuit to get the total impedance magnitude, phase angle, inductive and capacitive reactances, resonant frequency, quality factor, and bandwidth. Switch between series and parallel configurations and between SI unit prefixes instantly. The step-by-step panel shows every formula substituted with your actual values.
What is RLC circuit impedance?
An RLC circuit contains three passive components: a resistor (R), an inductor (L), and a capacitor (C). When driven by an alternating current signal, each component opposes current flow in a different way. The resistor produces a real, frequency-independent opposition called resistance. The inductor produces an inductive reactance X_L that grows with frequency, and the capacitor produces a capacitive reactance X_C that shrinks with frequency. Impedance (Z) is the combined opposition of all three, expressed as a complex number with a magnitude and a phase angle. The phase angle tells you whether the voltage leads or lags the current: a positive angle means the circuit is net inductive (voltage leads), while a negative angle means it is net capacitive (voltage lags).
Series vs. parallel RLC: formulas and key differences
In a series RLC circuit the same current flows through all three components, so their impedances add. The total impedance is |Z| = sqrt(R^2 + (X_L - X_C)^2), and the phase angle is phi = arctan((X_L - X_C) / R). At resonance the reactances cancel, leaving Z = R at its minimum, which maximises current. In a parallel RLC circuit the same voltage appears across all three components, so their admittances (1/Z) add instead. The magnitude is |Z| = 1 / sqrt((1/R)^2 + (1/X_L - 1/X_C)^2). At resonance the susceptances cancel, leaving Z = R at its maximum, which minimises current. This complementary behavior makes the two configurations useful in very different filter and tuning applications.
Resonant frequency, Q factor, and bandwidth
The resonant frequency f0 = 1 / (2 * pi * sqrt(L * C)) is the same for both configurations. At f0 the inductive and capacitive reactances are equal and opposite, so their combined effect is zero. The quality factor Q measures how sharply the circuit responds near resonance. For a series circuit Q = (1/R) * sqrt(L/C), and for a parallel circuit Q = R * sqrt(C/L). A high Q means a narrow, sharp resonance peak - the circuit is very selective. The half-power bandwidth BW = f0 / Q is the frequency range over which the circuit delivers at least half its maximum power. High-Q circuits are used in narrow-band filters and radio tuners; low-Q circuits suit broadband applications.
How to use this calculator
Select series or parallel configuration, then enter the resistance, inductance, capacitance, and driving frequency. Each value has a unit selector so you can enter millihenries, microfarads, or kilohertz without converting by hand. The calculator returns the total impedance magnitude, phase angle, individual reactances, resonant frequency, Q factor, and bandwidth. The step-by-step panel shows every formula substituted with your actual values so you can follow and check the math. The frequency-sweep chart plots |Z| vs frequency to show how impedance changes across the spectrum around the resonant point.
RLC circuit behavior at key frequencies
| Condition | Series |Z| | Series phase | Parallel |Z| | Parallel phase |
|---|---|---|---|---|
| f << f0 (very low) | High (cap. dominated) | Near -90 deg | High (ind. dominated) | Near +90 deg |
| f = f0 (resonance) | Minimum (= R) | 0 deg | Maximum (= R) | 0 deg |
| f >> f0 (very high) | High (ind. dominated) | Near +90 deg | High (cap. dominated) | Near -90 deg |
How impedance and phase behave for series and parallel RLC circuits relative to the resonant frequency.
Frequently asked questions
What does impedance mean in an RLC circuit?
Impedance is the total opposition to alternating current in a circuit. Unlike resistance, which is constant with frequency, impedance has a magnitude and a phase angle that both depend on frequency. The magnitude tells you how much the circuit restricts current for a given voltage (following Ohm's law in its AC form: V = I * Z), and the phase angle tells you the timing relationship between voltage and current. An impedance of 200 Ohm at +45 degrees means the circuit restricts current to V/200 amperes and that voltage peaks 45 degrees before current does.
What is the resonant frequency and why does it matter?
The resonant frequency f0 = 1 / (2 * pi * sqrt(L * C)) is the frequency at which the inductive reactance X_L equals the capacitive reactance X_C. At this point they cancel, and the circuit behaves as if only the resistor were present. In a series RLC circuit this means minimum impedance and maximum current. In a parallel RLC circuit it means maximum impedance and minimum current. Resonance is used in radio tuners, oscillators, and bandpass filters to select a specific frequency from a mix.
What is the Q factor and what counts as a high or low Q?
The Q (quality) factor measures the sharpness of the resonance peak. A high Q (above roughly 10) means the circuit responds strongly to a narrow band of frequencies near f0 and rejects others - ideal for selective filters or radio receivers. A low Q (below 1) means heavy damping, a very broad resonance, and weak frequency selectivity. Values between 1 and 10 are moderately selective. Q is dimensionless and equals f0 divided by the -3 dB bandwidth.
Why does phase angle change with frequency?
At low frequencies the capacitor dominates because X_C = 1 / (omega * C) is large, so the circuit is capacitive and current leads voltage (negative phase angle). At high frequencies the inductor dominates because X_L = omega * L is large, so the circuit is inductive and current lags voltage (positive phase angle). At the resonant frequency the two effects cancel and the phase angle is zero. The phase angle therefore sweeps from about -90 degrees at low frequencies through 0 degrees at resonance to about +90 degrees at high frequencies.
How do series and parallel RLC circuits differ in practice?
In a series RLC circuit impedance reaches its minimum at resonance, so it passes the resonant frequency most easily - useful as a series bandpass element or a notch filter in shunt. In a parallel RLC circuit impedance reaches its maximum at resonance, so it blocks the resonant frequency - useful as a parallel bandpass (tank circuit) in power electronics, oscillators, and RF amplifiers. The resonant frequency formula is the same for both, but the Q factors differ: higher resistance raises Q in a parallel circuit but lowers it in a series circuit.