RLC Series Circuit Impedance Calculator
Calculate total impedance, reactance, and phase angle for a series RLC circuit at any operating frequency.
🔌 What is a Series RLC Circuit's Impedance?
A series RLC circuit combines a resistor (R), an inductor (L), and a capacitor (C) in a single loop. Because the inductor and capacitor react to alternating current very differently, the circuit's total opposition to current flow, its impedance, depends on frequency in a way plain resistance never does. Impedance is a complex quantity with a magnitude Z (in ohms) and a phase angle that describes the timing relationship between current and voltage.
This calculation shows up constantly in real electronics work. Filter designers use it to find where a band-pass or notch circuit peaks and rolls off. RF engineers use it to match antenna and transmission-line impedances at a target operating frequency. Audio crossover networks rely on the same math to split signals between woofers and tweeters at the right frequency, and power-electronics engineers use it to check resonant tank behaviour in converters.
A common point of confusion is that impedance is not simply R + X_L + X_C added together. Inductive and capacitive reactance point in opposite directions on the phasor diagram, so they partially cancel: the formula uses (X_L minus X_C), not their sum. That is also why impedance can be lower than you might expect near resonance, where X_L and X_C nearly cancel and the circuit becomes almost purely resistive.
This calculator takes your resistance, inductance, capacitance, and operating frequency, and returns the inductive and capacitive reactance, the total impedance magnitude, the phase angle, whether the circuit is currently behaving as inductive or capacitive, and a chart showing how impedance changes as frequency sweeps through resonance.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Near Resonance, Slightly Capacitive
R = 10 Ω, L = 100 mH, C = 1 µF, evaluated at 500 Hz
Example 2 — Well Above Resonance, Strongly Inductive
Same R = 10 Ω, L = 100 mH, C = 1 µF, evaluated at 2,000 Hz
Example 3 — Well Below Resonance, Strongly Capacitive
Same R = 10 Ω, L = 100 mH, C = 1 µF, evaluated at 150 Hz
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the impedance of a series RLC circuit?
Total impedance magnitude is Z = sqrt(R^2 + (X_L - X_C)^2), where X_L = 2*pi*f*L is inductive reactance and X_C = 1/(2*pi*f*C) is capacitive reactance. For R = 10 ohms, X_L = 314.16 ohms, and X_C = 318.31 ohms, Z = sqrt(100 + 17.2) = 10.83 ohms.
What is the phase angle in an RLC circuit?
The phase angle phi = arctan((X_L - X_C) / R) tells you how far the current lags or leads the source voltage. A positive angle means inductive (lagging current), a negative angle means capacitive (leading current), and zero means the circuit is purely resistive at resonance.
What is inductive reactance?
Inductive reactance X_L = 2*pi*f*L (in ohms) is the opposition an inductor presents to alternating current. It rises linearly with frequency, so a 100 mH inductor has X_L = 314.16 ohms at 500 Hz but 1,256.64 ohms at 2,000 Hz.
What is capacitive reactance?
Capacitive reactance X_C = 1/(2*pi*f*C) (in ohms) is the opposition a capacitor presents to alternating current. It falls as frequency rises, so a 1 microfarad capacitor has X_C = 318.31 ohms at 500 Hz but only 79.58 ohms at 2,000 Hz.
When is impedance at its minimum in a series RLC circuit?
Impedance is minimum exactly at the resonant frequency f0 = 1/(2*pi*sqrt(LC)), where X_L equals X_C so they cancel and Z reduces to just R. Away from resonance in either direction, the (X_L - X_C) term grows and Z increases.
How does frequency affect a series RLC circuit's behaviour?
Below the resonant frequency, X_C exceeds X_L and the circuit behaves as capacitive with a negative phase angle. Above resonance, X_L exceeds X_C and the circuit behaves as inductive with a positive phase angle. Exactly at resonance, the circuit is purely resistive.
What units does this calculator use for L and C?
Inductance is entered in millihenries (mH) and internally converted to henries by dividing by 1,000. Capacitance is entered in microfarads (uF) and internally converted to farads by dividing by 1,000,000. Resistance is in ohms and frequency is in hertz.
Why is my phase angle close to zero but not exactly zero?
A phase angle near zero means your chosen frequency is close to, but not exactly at, the resonant frequency f0 = 1/(2*pi*sqrt(LC)) for your L and C values. Use the Resonant Frequency Calculator to find the exact f0 for your components.
Does resistance affect the resonant frequency of an RLC circuit?
No. The resonant frequency f0 = 1/(2*pi*sqrt(LC)) depends only on inductance and capacitance. Resistance R does not shift where the impedance minimum occurs, but it does control how sharp that minimum is (see the Quality Factor Calculator).
What does a negative phase angle mean physically?
A negative phase angle means the circuit's current waveform leads the source voltage waveform in time, which is the signature of capacitive behaviour. This happens whenever X_C is larger than X_L, typically at frequencies below resonance.
Can total impedance ever be less than the resistance R?
No. Since Z = sqrt(R^2 + (X_L - X_C)^2), the impedance magnitude is always greater than or equal to R, with equality only when X_L exactly equals X_C at resonance. Impedance can never fall below the circuit's resistance.