RLC Circuit Calculator

For a series RLC circuit, first compute inductive reactance XL = 2πfL and capacitive reactance XC = 1/(2πfC). The net reactance is X = XL − XC, and total impedance is Z = √(R² + X²). The phase angle is φ = atan(X/R). For example, with R = 100 Ω, L = 50 mH, C = 10 µF at f = 1000 Hz: XL = 314.16 Ω, XC = 15.92 Ω, so Z = √(100² + 298.24²) = 314.56 Ω and φ = 71.46°. The current is I = V/Z, so 10 V gives 31.79 mA.

Resonant frequency is f₀ = 1/(2π√(LC)), the frequency where inductive and capacitive reactances cancel (XL = XC). At resonance a series RLC circuit has minimum impedance Z = R and zero phase angle, while a parallel RLC circuit has maximum impedance Z = R. For example, L = 50 mH and C = 10 µF give f₀ = 1/(2π√(0.05 × 1e-5)) = 225.08 Hz.

The Q factor measures resonance sharpness. For series RLC: Q = ω₀L/R. For parallel RLC: Q = R/(ω₀L), where ω₀ = 2πf₀. Bandwidth is BW = f₀/Q in both cases. For example, with L = 50 mH, C = 10 µF, R = 100 Ω: f₀ = 225.08 Hz, ω₀L = 70.71 Ω, so Q(series) = 0.7071 with BW = 318.31 Hz, and Q(parallel) = 1.4142 with BW = 159.15 Hz.

In series RLC, impedance is Z = √(R² + (XL−XC)²) and is minimum (Z = R) at resonance. In parallel RLC, admittance is Y = 1/R + j(ωC − 1/(ωL)), impedance Zp = 1/|Y| is maximum (Zp = R) at resonance, and branch currents can each exceed the total current (current magnification by Q). At 1000 Hz with R = 100 Ω, L = 50 mH, C = 10 µF, 10 V: series gives Z = 314.56 Ω (I = 31.79 mA), while parallel gives Zp = 16.53 Ω (I = 0.605 A), with branch currents IR = 0.1 A, IL = 31.83 mA, IC = 0.628 A.

Rearrange f₀ = 1/(2π√(LC)): L = 1/((2πf₀)²C) and C = 1/((2πf₀)²L). For example, to resonate at f₀ = 1000 Hz with C = 10 µF: L = 1/((2π×1000)² × 1e-5) = 2.533 mH. Or with L = 10 mH at 1000 Hz: C = 2.533 µF. The inverse solver tab does this automatically and verifies the result by recomputing f₀.

The phase angle φ = atan((XL−XC)/R) tells whether voltage leads or lags current. φ > 0 (inductive, XL > XC): voltage leads current. φ < 0 (capacitive, XC > XL): current leads voltage. φ = 0 at resonance: the circuit behaves purely resistively. At 1000 Hz with R = 100 Ω, L = 50 mH, C = 10 µF, φ = +71.46°, so voltage strongly leads current (inductive).

Yes. This RLC circuit calculator analyzes second-order resonant circuits with an inductor, a capacitor, and a resistor (resonance, Q factor, impedance across frequency). A cutoff frequency calculator (see our cutoff-frequency tool) covers first-order RC and RL low-pass/high-pass filters, where fc = 1/(2πRC) or fc = R/(2πL). If your circuit has both L and C and you care about resonance, use this tool; if it is a simple RC or RL filter stage, use the cutoff tool.

No. A 555 astable calculator (see our ne555-astable tool) computes the oscillation frequency and duty cycle of a 555 timer chip from resistor and capacitor values, f = 1.44/((R1+2R2)C). That is a nonlinear switching oscillator, not a linear resonant circuit. This RLC calculator solves linear AC steady-state behavior (impedance, phase, resonance, Q) of passive resistor-inductor-capacitor networks.

Yes. The standalone RLC impedance calculator idea (Z = √(R²+(XL−XC)²)) is fully absorbed into the Series tab of this tool, which also adds phase angle, current, power, a phasor diagram, parallel analysis, resonance, frequency sweep, and an inverse solver, so there is no need for a separate impedance-only tool.

Ideal lumped components: the resistor has no parasitic inductance, the inductor has no series resistance or self-capacitance, and the capacitor has no equivalent series resistance (ESR). All results are AC steady-state phasor analysis at a single frequency; transient behavior, component tolerances, temperature drift, and core saturation are not modeled. For real coils, add the winding resistance into R for better accuracy.