RLC Impedance Calculator - Z, Phase Angle, and Resonance

An RLC impedance calculator returns the complex opposition a series or parallel RLC circuit presents to a sinusoidal source: the magnitude of Z in ohms, the phase angle phi in degrees, the inductive and capacitive reactances XL and XC, the resonant frequency f0, and the quality factor Q. Enter R, L, C, and f and the RLC impedance calculator does the sqrt, arctan, and 2 pi f math, with the result panel ready to read next to the textbook formula.

• • AC circuit homework and exams: Confirm the impedance, phase, and resonance against textbook tables.
• • Filter design: Pick R, L, and C to put the cutoff on target, then read the impedance at the design frequency.
• • Resonant tank tuning: Match L and C so f0 lands on the wanted channel, then check Q for bandwidth.
• • Speaker crossovers and matching networks: Use |Z| and phi to size the amplifier and match the load.

RLC circuits are the building blocks of every AC filter, oscillator, and tuned amplifier. R dissipates energy, L stores energy in a magnetic field, and C stores energy in an electric field. The impedance Z combines all three as Z = R + j(XL - XC) for series and 1/Z = 1/R + j(1/XC - 1/XL) for parallel.

When the capacitor branch dominates, the capacitive reactance calculator isolates the same 1 / (2 pi f C) value used inside this RLC impedance calculator.

The calculator reads R, L, C, f, and the topology toggle, computes the two reactances XL and XC, and combines them with R using the formula for the chosen topology.

• R (resistance): Series resistance in ohms. R is the only dissipative element; it sets the real part of the impedance and the loss that Q measures.
• L (inductance): Inductance in henries. With f, it contributes inductive reactance XL = 2 pi f L in ohms.
• C (capacitance): Capacitance in farads. At f, it contributes capacitive reactance XC = 1 / (2 pi f C) in ohms.
• f (frequency): Operating frequency in hertz. Together with L and C it sets XL, XC, and the resonance condition.
• mode (series or parallel): Topology of the RLC network. The magnitude formula and the phase angle sign both depend on this toggle.

Series and parallel RLC networks use the same reactances, but they combine differently. In the series case the impedances add directly, so Z = R + j(XL - XC) and |Z| = sqrt(R^2 + (XL - XC)^2). In the parallel case the admittances add, so 1/Z = 1/R + j(1/XC - 1/XL). The phase angle switches sign because the parallel formula is the reciprocal of the series formula.

Resonance, where XL = XC, has the same frequency in both topologies: f0 = 1 / (2 pi sqrt(L C)). For series RLC, Q = (1/R) sqrt(L/C) and |Z| at resonance is at a minimum equal to R. For parallel RLC, Q = R sqrt(C/L) and |Z| at resonance is at a maximum equal to R.

Above f0, XL > XC so the circuit looks inductive. Below f0, XC > XL so it looks capacitive. In both cases |Z| rises above R and phi moves off zero.

According to AllAboutCircuits - Series RLC and Parallel RLC, the impedance of a series RLC circuit has magnitude Z = sqrt(R^2 + (XL - XC)^2) and phase phi = arctan((XL - XC) / R), with XL = 2 pi f L and XC = 1 / (2 pi f C).

When the operating frequency f is the unknown and the RLC network only needs to be tuned, the resonant frequency LC calculator solves f0 = 1 / (2 pi sqrt(L C)) directly from L and C.

Four ideas explain the result panel: reactance, the impedance triangle, resonance, and the quality factor.

These four ideas show up directly in the result panel: reactances feed the magnitude, the impedance triangle feeds the phase angle, the resonance formula feeds f0, and the Q formula feeds the bandwidth estimate. In a real circuit the inductor has series resistance, the capacitor has leakage, and parasitic capacitance shows up across the inductor, so the measured Q sits below the textbook value.

For the rad/s value of omega = 2 pi f used inside the reactance formulas, the angular frequency calculator returns the rad/s figure alongside the hertz value.

Five steps give the impedance, phase, reactances, resonance, and Q factor for a series or parallel RLC network.

1. 1 Pick the topology: Choose Series RLC or Parallel RLC. The magnitude formula, the phase angle sign, and the Q formula depend on this choice.
2. 2 Enter resistance R: Type the resistance in ohms. R sets the dissipative part of the impedance and the loss that Q measures.
3. 3 Enter inductance L: Type the inductance in henries. With f, it sets XL and contributes to f0.
4. 4 Enter capacitance C: Type the capacitance in farads. With f, it sets XC and contributes to f0 alongside L.
5. 5 Enter frequency f and read the result: The result panel returns |Z|, phi, XL, XC, f0, and Q in real time. Try f = f0 to see the resonance behaviour.

R = 50 ohm, L = 10 mH, C = 1 uF, series RLC, f = 2000 Hz gives |Z| = 68.00 ohm, phi = 37.18 deg, f0 = 1591.55 Hz, Q = 2. Move f to 1591.55 Hz and watch phi collapse to 0 and |Z| to 50 ohm: that is the resonance check.

Once |Z| and phi are known, the Ohm's law calculator takes the magnitude and phase to give the steady-state current for a given source voltage.

The result panel condenses the RLC quantities a student, hobbyist, or engineer needs to read a circuit into one place.

• • Series and parallel in one panel: A topology toggle switches between Z = sqrt(R^2 + (XL - XC)^2) for series and 1/Z = sqrt((1/R)^2 + (1/XL - 1/XC)^2) for parallel.
• • Z, XL, XC, phi, f0, and Q side by side: The result panel returns magnitude, both reactances, phase angle in degrees, resonant frequency, and quality factor.
• • Real-time updates as inputs change: Editing R, L, C, f, or the topology updates every result on the same tick, so resonance and bandwidth can be explored by sweeping f across f0.
• • Numerical stability across the AC range: The reactance formulas remain accurate from sub-hertz audio filters up through RF tanks without overflow.
• • Open-form, source-backed formulas: The magnitude, phase, f0, and Q formulas are written out next to the result panel and trace back to the AllAboutCircuits and Wikipedia RLC pages.

Compared with separate XL and XC calculators plus a hand calculation, the result panel answers the typical RLC question in one step and also exposes how R trades against Q, the central design knob for filters and tanks.

After reading |Z| and phi from this panel, the AC wattage calculator turns the same RLC network into real and reactive power for a known source voltage.

Four factors change the numbers on the screen, plus two practical limits when the textbook formulas are used on real components.

• • The formulas assume ideal, lumped R, L, and C. Real inductors have series resistance, real capacitors have leakage, and wiring adds parasitic inductance at high frequency.
• • The panel assumes a single sinusoidal source at f. Pulsed or modulated drives need a Fourier treatment because the impedance differs at each harmonic.

These four factors are the design knobs. L and C place f0 on the wanted channel, R sets how sharp the resonance is, and f reads the resulting impedance and phase at the operating point.

For tolerance analysis, the L and C tolerances set the spread of f0. A 10 percent L or C tolerance moves f0 by roughly 5 percent, while a 20 percent R tolerance moves Q by roughly 20 percent in the series case.

According to Wikipedia - RLC circuit, the Q factor of a series RLC circuit is Q = (1/R) sqrt(L / C), and the half-power bandwidth of the resonance peak is BW = f0 / Q.

For the time-domain counterpart of the same RC branch, the capacitor charge time calculator returns the RC time constant tau = R C and the exponential charging curve.