This RLC calculator helps you analyze a series RLC circuit using standard AC circuit equations. Enter resistance, inductance, capacitance, and frequency to instantly compute impedance, phase angle, resonance, Q factor, and (optionally) current and power values.
Series RLC Circuit Calculator
Tip: You can use scientific notation like 1e-6 for 1 µF.
What is an RLC circuit?
An RLC circuit is an electrical network containing a resistor (R), inductor (L), and capacitor (C). In AC systems, these components interact in frequency-dependent ways, which is why RLC analysis is essential in filter design, tuning circuits, power electronics, and communication systems.
In a series RLC circuit, all three components carry the same current. The voltage drops across each element combine vectorially, not just arithmetically, because inductor and capacitor voltages are phase-shifted relative to current.
Core formulas used by this calculator
Reactance and impedance
- Angular frequency: ω = 2πf
- Inductive reactance: XL = ωL
- Capacitive reactance: XC = 1 / (ωC)
- Net reactance (series): X = XL - XC
- Impedance magnitude: |Z| = √(R² + X²)
- Phase angle: φ = tan-1(X/R)
Resonance and quality factor
- Resonant frequency: fr = 1 / (2π√(LC))
- Series quality factor: Q = (1/R)√(L/C)
- Bandwidth (series approximation): BW = fr/Q
How to use the calculator effectively
- Enter R in ohms, L in henries, and C in farads.
- Enter the operating frequency in hertz if you want behavior at that point.
- Click Use Resonant Frequency to automatically set the frequency to fr and evaluate the circuit at resonance.
- Optionally enter RMS voltage to compute current, real power, apparent power, and reactive power.
Interpreting results
Inductive vs capacitive behavior
If X > 0, the circuit is net inductive and current lags voltage. If X < 0, the circuit is net capacitive and current leads voltage. If X ≈ 0, you are at (or very close to) resonance.
Why resonance matters
At resonance in a series RLC circuit, inductive and capacitive reactances cancel each other. The impedance drops to approximately R, current reaches a maximum for a given source voltage, and power factor approaches 1. This is foundational in radio tuning and narrowband filter design.
Practical engineering notes
- Real components have tolerances, parasitics, and ESR, so measured values may differ from ideal calculations.
- At high frequencies, lead length and PCB layout can significantly alter circuit behavior.
- Very high-Q designs are sensitive to component drift and temperature changes.
- Always verify calculated RMS currents against component power ratings.
Example scenario
Suppose R = 10 Ω, L = 50 mH, and C = 1 µF. The resonant frequency is around 712 Hz. If you test at 1000 Hz, XL is larger than XC, so the circuit is net inductive and has a positive phase angle. If you then switch to resonant frequency, reactances cancel and impedance drops close to 10 Ω.
Frequently asked questions
Can I use this for parallel RLC?
This page is configured for series RLC calculations. Parallel RLC uses admittance-based equations and yields different current/voltage relationships.
What units should I enter?
Use SI base units: ohms (Ω), henries (H), farads (F), hertz (Hz), and volts (V). For microfarads, enter values like 1e-6.
What does negative reactive power mean?
Negative reactive power indicates capacitive behavior (current leading). Positive reactive power indicates inductive behavior (current lagging).