RLC Circuit & Resonance Calculator
Calculate impedance Z, phase angle θ, resonance frequency f₀, Q factor, current, and component voltage drops for series and parallel RLC circuits with interactive phasor diagrams, resonance curves, and reverse LC tuning.
Inputs are not collected. Usage measurement requires your consent.
Series RLC Inputs
Z = √(R² + (X_L − X_C)²)Worked Derivation & Formula Steps
Real-time breakdownDone
RLC Circuit & Resonance Calculator
Next time, open this tool from My Tools. Only the tool list is saved in this browser, not your inputs or results.
⌥DPress Option+D anytime to toggle My Tools instantly
How to use
- 1
Select circuit topology
Choose Series RLC Circuit, Parallel RLC Circuit, or LC Resonance Tuner (reverse solver).
- 2
Enter component and AC source parameters
Input resistance R (Ω/kΩ), inductance L (μH/mH/H), capacitance C (pF/nF/μF), frequency f, and source voltage V.
- 3
Inspect impedance, resonance & phasors
Review impedance Z, phase angle θ (power factor), current I, component voltage drops, resonance frequency f₀, Q factor, bandwidth Δf, and live phasor/curve plots.
Features
- Instant calculation of series RLC impedance Z, reactances X_L & X_C, and phase angle θ (power factor)
- Simultaneous evaluation of RMS line current, peak current, and individual voltage drops (V_R, V_L, V_C)
- High-precision calculation of resonance frequency f₀, angular frequency ω₀, Q factor, and 3dB bandwidth Δf
- Automatic detection and warning for resonant voltage magnification (V_L, V_C scaling by Q × V_in)
- Parallel RLC admittance Y, parallel impedance, total current, and individual branch currents (I_R, I_L, I_C)
- Reverse LC tuner mode to solve for required inductance L or capacitance C given a target frequency f₀
- Real-time SVG phasor diagram displaying RMS vectors (V_R, V_L, V_C, V) and phase angle on the complex plane
- Interactive resonance response curve plotting current vs frequency with -3dB cutoff markers (f₁, f₂)
- Practical engineering presets including AM radio, FM radio, physics lab, mains 60Hz, and audio crossovers
- Seamless engineering unit conversion across pF, nF, μF, mF, μH, mH, H, Ω, kΩ, MΩ, Hz, kHz, MHz
- One-click formatted text export tailored for physics laboratory reports and circuit design documentation
Use cases
Physics & Electrical Engineering coursework
Eliminate complex number and unit conversion mistakes, verifying impedance, phase angles, and phasor diagrams step by step.
Laboratory resonance experiment reports
Verify measured resonance frequencies, Q factors, bandwidths, and component voltage magnifications against theory.
RF, wireless & audio filter design
Calculate required L and C values for LC tanks, radio tuners, notch filters, and audio speaker crossover networks.
Details
In alternating current (AC) circuit analysis, RLC circuits combining resistors (R), inductors (L), and capacitors (C) constitute the fundamental backbone of radio communications, audio crossovers, power transmission, and electronic filtering. Unlike direct current (DC) circuits, the inductive reactance X_L = ωL and capacitive reactance X_C = 1/(ωC) depend dynamically on AC frequency f (angular frequency ω = 2πf), introducing a relative phase shift θ between voltage and current.
In a series RLC circuit, identical current I flows through all components. Resistor voltage V_R is in phase with current, inductor voltage V_L leads current by 90° (+j direction), and capacitor voltage V_C lags current by 90° (-j direction). Complex impedance is Z = R + j(X_L - X_C), with magnitude Z = √(R² + (X_L - X_C)²) and phase angle θ = arctan((X_L - X_C)/R). When X_L = X_C, series resonance occurs at f₀ = 1 / (2π√(LC)), where total reactance cancels to zero, impedance drops to its minimum Z = R, and current reaches its maximum. At resonance, voltages across the inductor and capacitor magnify to Q times the input voltage (where Q = (1/R)√(L/C)).
In a parallel RLC circuit, a common AC voltage V is applied across all branches. Analysis proceeds via admittance Y = 1/Z = G + j(B_C - B_L), yielding impedance Z = 1 / √(G² + (B_C - B_L)²). At parallel resonance (anti-resonance) f₀ = 1 / (2π√(LC)), net susceptance vanishes, admittance reaches its minimum (impedance reaches its maximum Z = R), and total line current from the source drops to its minimum while circulating tank currents are magnified by Q = R√(C/L).
The reverse LC tuner mode applies rearranged resonance equations C = 1 / (4π²f₀²L) and L = 1 / (4π²f₀²C) to immediately determine required component values for tuning to target radio frequencies (AM, FM, RFID, etc.).
This tool combines exact series/parallel formulas, automated engineering unit scaling, dynamic SVG phasor diagrams, resonance frequency response curves with -3dB bandwidth indicators, and one-click laboratory report export.
Ohm’s Law, Resistance & AC Impedance
From DC/AC voltage/current/power to series/parallel resistor combinations and RLC AC impedance.
FAQ
Why can voltage across the inductor or capacitor exceed the supply voltage in series resonance?
At series resonance (X_L = X_C), inductor voltage V_L and capacitor voltage V_C are exactly 180° out of phase, canceling each other completely. The net reactive voltage drop is zero, leaving the total current limited only by resistance (I = V/R). Consequently, component voltages V_L = V_C = I × X_L reach Q × V, which can be dozens or hundreds of times the supply voltage. This is called voltage magnification, requiring high voltage ratings on capacitors in tuned circuits.
What is the difference between series resonance and parallel resonance (anti-resonance)?
In series resonance, impedance reaches its minimum (Z = R) at f₀, maximizing source current. In parallel resonance (anti-resonance), impedance reaches its maximum (Z = R) at f₀, minimizing total current drawn from the AC source. However, circulating current between L and C within the parallel tank magnifies to Q times the input line current.
What does the Q factor (Quality factor) signify?
The Q factor is a dimensionless ratio measuring the sharpness or selectivity of a resonant circuit. Higher Q means a narrower, sharper frequency peak, providing higher selectivity for radio tuners. For series RLC, Q = (1/R)√(L/C), so lower resistance yields higher Q. The -3dB half-power bandwidth is inversely proportional: Δf = f₀ / Q.
What is the difference between impedance Z and reactance X?
Reactance X is the frequency-dependent opposition to AC current caused by electric fields (capacitance) or magnetic fields (inductance), storing and releasing energy without consuming real power. Impedance Z is the total combined opposition to AC current taking into account both resistive power loss R and reactive storage X: Z = √(R² + X²).
How is resonance used in radio tuners?
Antennas receive radio waves at many different frequencies simultaneously. By matching the LC resonant frequency f₀ = 1/(2π√(LC)) to the carrier frequency of a desired radio station, the circuit selectively accepts that frequency while rejecting all others. Tuning dials historically rotated a variable capacitor to adjust C and select stations.
Related guide
GuideHow to Use Ohm’s Law: Voltage, Current, Resistance and Power
Learn to use Ohm’s law V = IR to find voltage, current and resistance, plus the three power formulas P = VI, P = I²R and P = V²/R — with a 6-pair lookup table, comparison charts, and worked LED resistor examples.
GuideRLC Circuit Impedance & Resonance: Series, Parallel, Phasors & Q Factor
Master RLC circuit analysis: impedance formulas Z = √(R² + (X_L - X_C)²), resonance frequency f₀ = 1/(2π√LC), series voltage magnification (V_L = V_C = Q×V), parallel antiresonance, phasor diagrams, power factor, and lab hand calculations.
GuideSimple Harmonic Motion & Pendulum Period: Equations, Experiments & Energy
Master simple harmonic motion: pendulum period T = 2π√(L/g), Borda’s finite amplitude correction, lab gravity inversion g = 4π²L/T², spring series and parallel stiffness, vertical equilibrium stretch, and phase relationships (90°/180°) with energy conservation.
Related Tools
Ohm's Law Calculator
Enter any two of voltage V, current I, resistance R and power P to compute the other two via V = IR and P = VI. All six combinations with substituted working — pairs naturally with the equivalent resistance tool.
Equivalent Resistance Calculator
Compute the equivalent resistance of resistors in series or parallel with fully substituted working. Handles 2 to 4 resistors and cross-checks the two-resistor parallel shortcut R₁R₂ ÷ (R₁ + R₂) — handy for physics circuits.
Complex Number Calculator
Add, subtract, multiply and divide complex numbers a + bi, with the expansion using i² = −1 and conjugate-based division shown step by step. Also shows the modulus, argument, conjugate and polar form.
Wave Optics & Light Interference Calculator
Calculate Young’s double-slit experiment (fringe spacing, path difference, intensity profile), diffraction grating (grating pitch, diffraction angle, max order, angular dispersion), and thin-film interference (phase reversal, visible interference colors, anti-reflection coating) with real-time spectrum simulation.
All processing happens in your browser. Your files are never uploaded.
Verified: Verified series resonance (10Ω, 10mH, 0.1μF -> f0=5.033kHz, Q=31.62, Z=10Ω, VL=VC=158.1V), parallel resonance (1kΩ, 10mH, 10nF -> f0=15.915kHz, Q=31.62), AM radio tuning (330μH, 100pF -> f0=876.1kHz), phasor and response curves, and unit scaling with automated tests
Did you know?
Crystal radios require zero external power or batteries: an LC resonant circuit tuned to a transmitter frequency captures micro-power RF signals directly from the antenna, rectified to drive high-impedance headphones. Electrical resonance was experimentally demonstrated by Sir Oliver Lodge in 1889 using Leyden jar spark circuits.