A series RLC circuit combines a resistor, inductor, and capacitor along a single current path, and how it responds depends heavily on the driving frequency.
Enter the series resistance (R), inductance (L), capacitance (C), and the AC source frequency (f). Each field has its own unit dropdown — L and C can be entered in H/mH/µH and F/µF/nF/pF, so you don't need to convert to base SI units by hand. All four values apply to every tab; the calculator recomputes instantly as you type.
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Read the impedance
The Impedance tab shows the total opposition to current flow, Z (in ohms), plus the inductive and capacitive reactances that combine to produce it. The detail line and stat grid also surface the resonant frequency and phase angle so you can see all three headline results at a glance without switching tabs.
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Check resonance and phase angle
Switch to the Resonance tab to see the frequency where this L and C combination resonates (impedance drops to just R), or the Phase Angle tab to see whether the current leads or lags the voltage and by how much. Try setting the frequency equal to the resonant frequency shown on the Resonance tab — impedance should drop to match the resistance exactly.
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Reference
Formula & Methodology
4 formulas▸
Reactances
X_L = 2πfL, X_C = 1 / (2πfC)
Inductive reactance X_L (ohms) grows with frequency and inductance — it's the opposition an inductor presents to changing current. Capacitive reactance X_C (ohms) shrinks with frequency and capacitance — it's the opposition a capacitor presents to changing voltage. They work in opposite directions as frequency rises, which is what makes resonance possible.
Impedance
Z = √(R² + (X_L − X_C)²)
Impedance Z (ohms) is the total opposition to current in the series circuit. Resistance R and the net reactance (X_L − X_C) act like the two legs of a right triangle, with Z as the hypotenuse — the same Pythagorean relationship used for the power triangle in AC circuit analysis.
Phase angle
φ = atan((X_L − X_C) / R)
The phase angle φ (degrees) is the angle by which the current waveform leads or lags the voltage waveform. A positive φ means the circuit is net inductive (current lags); a negative φ means it's net capacitive (current leads); φ = 0 means the circuit behaves as if it were purely resistive.
Resonant frequency
f₀ = 1 / (2π√(LC))
The resonant frequency f₀ (Hz) is the frequency at which X_L exactly equals X_C, so the reactances cancel and impedance drops to its minimum possible value, Z = R. It depends only on L and C — resistance sets how sharp or damped the resonance is, but not where it occurs.
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General reference
Trust, Methodology & Sources
Written by Calculover Editorial Team · Updated 2026-07-31▸
Editorial accountability
Author: Calculover Editorial Team - Editor
Owner: Calculover Editorial Team - Editorial owner
Last reviewed: 2026-07-31
Last verified: 2026-07-31
Methodology
Limitations & guidance
This calculator computes series and parallel RLC AC network behavior using fundamental Maxwellian electromagnetic field equations and phasor domain network analysis:
Professional guidance:
Primary sources
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Glossary
Key Terms Explained
7 terms▸
RLC circuit ↗An electrical circuit containing a resistor (R), inductor (L), and capacitor (C) connected together — in this calculator, in series with an AC source. The interaction of these three components determines how the circuit responds to different frequencies.
Impedance ↗The total opposition a circuit presents to alternating current, measured in ohms (Ω). Unlike plain resistance, impedance combines resistance and reactance and depends on the source frequency: Z = √(R² + (X_L − X_C)²).
Reactance ↗The frequency-dependent opposition to current caused by inductors and capacitors, measured in ohms. Inductive reactance (X_L) rises with frequency; capacitive reactance (X_C) falls with frequency. Unlike resistance, reactance doesn't dissipate energy — it stores and releases it each cycle.
Resonant frequency ↗The frequency (f₀) at which a circuit's inductive and capacitive reactances cancel exactly, minimizing impedance in a series RLC circuit. Calculated as f₀ = 1 / (2π√(LC)), it depends only on the inductance and capacitance values.
Phase angle ↗The angle, in degrees, by which the current waveform leads or lags the voltage waveform in an AC circuit. In a series RLC circuit, φ = atan((X_L − X_C)/R); a positive angle means the current lags (inductive), a negative angle means it leads (capacitive).
Series circuit ↗A circuit arrangement where components are connected end-to-end along a single path, so the same current flows through the resistor, inductor, and capacitor. This calculator models a series RLC circuit, as opposed to a parallel one where the components share the same voltage instead.
Resonance ↗The condition where a circuit's inductive and capacitive reactances are equal and cancel out, leaving impedance at its minimum (Z = R for a series circuit) and current at its maximum for a given voltage. Radio tuners and filters exploit resonance to select or reject specific frequencies.
X_L = 2π(60)(0.5) ≈ 188.5 Ω and X_C = 1/(2π(60)(10×10⁻⁶)) ≈ 265.3 Ω, so Z = √(100² + (188.5−265.3)²) ≈ 126.1 Ω. Since X_C > X_L, the circuit is net capacitive at this frequency.
f₀ = 1/(2π√(0.1 × 100×10⁻⁶)) ≈ 50.33 Hz. Driven exactly at that frequency, X_L equals X_C, so they cancel and impedance drops to its minimum: Z = R = 20 Ω — the smallest impedance this circuit can have at any frequency.
X_L ≈ 125.7 Ω and X_C ≈ 795.8 Ω, so φ = atan((125.7 − 795.8)/30) ≈ −87.4°. With resistance small relative to the net reactance, the circuit behaves almost like a pure capacitor — current leads voltage by nearly a full 90°.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
A series RLC circuit combines a resistor, inductor, and capacitor along a single current path, and how it responds depends heavily on the driving frequency. This calculator computes the three quantities engineers and students check most often: impedance (the total opposition to current at a given frequency), resonant frequency (where impedance is at its minimum), and phase angle (whether current leads or lags voltage, and by how much).
How the RLC Circuit Calculator works
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The calculator first finds each reactive component's opposition to current: inductive reactance X_L = 2πfL grows with frequency, while capacitive reactance X_C = 1/(2πfC) shrinks with frequency. Because they move in opposite directions, the resistor's steady resistance R and this frequency-dependent net reactance (X_L − X_C) combine like the two legs of a right triangle to give the total impedance, Z = √(R² + (X_L − X_C)²) — the hypotenuse. The same three quantities determine the phase angle φ = atan((X_L − X_C)/R), the offset between the voltage and current waveforms. Separately, the resonant frequency f₀ = 1/(2π√(LC)) is the one frequency where X_L and X_C are exactly equal — at that point they cancel completely, φ drops to 0°, and impedance falls to its absolute minimum, Z = R.
Inputs and what they mean
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Resistance (R) is the circuit's real, frequency-independent opposition to current, in ohms. Inductance (L) sets how strongly a changing current induces an opposing voltage — measured in henries, but usually entered in millihenries (mH) or microhenries (µH) for real-world coils. Capacitance (C) sets how much charge a capacitor stores per volt — in farads, though practical capacitors are almost always specified in microfarads (µF), nanofarads (nF), or picofarads (pF). Frequency (f) is the AC source's driving frequency in hertz. Of the four, L and C together set where resonance occurs; R doesn't move the resonant frequency at all, but it does set the impedance floor at resonance and how sharply impedance rises as you move away from f₀.
Limits and edge cases
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This calculator models an ideal series RLC circuit with a single resistor, inductor, and capacitor — it does not account for parallel (tank) RLC topologies, parasitic resistance inside real-world inductors and capacitors, or multi-stage filter networks, all of which shift the effective resonance and damping. A resistance of exactly 0 Ω is accepted (an idealized LC circuit) and produces a phase angle of exactly ±90° rather than an undefined result. Extremely small resistances combined with a frequency very close to resonance can make the theoretical current spike sharply — in a real circuit, parasitic resistance in the wiring and components limits how far this actually goes, so treat results very near resonance with R ≈ 0 as a theoretical bound rather than a literal current reading.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for RLC circuit impedance?+
Impedance is Z = √(R² + (X_L − X_C)²), where R is resistance in ohms, X_L = 2πfL is inductive reactance, and X_C = 1/(2πfC) is capacitive reactance. All three combine to give the total opposition to current at a given frequency.
What happens at resonance?+
At the resonant frequency f₀ = 1/(2π√(LC)), inductive and capacitive reactance are equal (X_L = X_C), so they cancel out completely. Impedance drops to its minimum possible value, Z = R, and the phase angle goes to 0° — the circuit behaves as if it were purely resistive.
How is the phase angle calculated?+
The phase angle is φ = atan((X_L − X_C)/R), in degrees. A positive angle means the circuit is net inductive and current lags voltage; a negative angle means it's net capacitive and current leads voltage; 0° means the circuit is purely resistive (which happens exactly at resonance).
Does this calculator handle series or parallel RLC circuits?+
This calculator models a series RLC circuit, where the resistor, inductor, and capacitor share the same current path. A parallel (tank) RLC circuit uses different formulas for impedance and resonance and isn't covered here.
What units does the calculator use?+
Resistance is in ohms (Ω) or kilohms (kΩ); inductance in henries (H), millihenries (mH), or microhenries (µH); capacitance in farads (F), microfarads (µF), nanofarads (nF), or picofarads (pF); frequency in hertz (Hz), kilohertz (kHz), or megahertz (MHz). Impedance is always reported in ohms and phase angle in degrees, regardless of which input units you chose.
How do I find the resonant frequency?+
Resonant frequency is f₀ = 1/(2π√(LC)) — it depends only on inductance and capacitance, not on resistance or the frequency you actually drive the circuit at. Use the Resonance tab to see f₀ computed directly from your L and C values.
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