RLC Impedance & Resonance Calculator
Reactance, |Z| and phase, resonance, Q and bandwidth, and star–delta conversion.
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- Free preview: the names of the table’s first rows and a watermarked chart, with the impedance, the reactance and every other figure hidden.
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Resonance
Current and power
Impedance against frequency
Across frequency
How it was calculated
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About the RLC Impedance & Resonance Calculator
Resistors, inductors and capacitors together have an impedance Z = R + jX: a resistance and a reactance that changes with frequency. An inductor’s reactance rises with frequency (XL = 2πfL), a capacitor’s falls (XC = 1 ÷ 2πfC), and where they are equal the circuit resonates. Pick a series or parallel circuit, switch on the parts you have — RL, RC, LC or RLC — and type their values and the frequency: you get |Z| and its phase, R + jX, the admittance, the power factor and what the circuit behaves like at that frequency, with a chart of |Z| and phase across frequency.
With both L and C the calculator adds the resonant frequency, the quality factor Q, the bandwidth and the half-power frequencies, and the damping ratio ζ that says whether the circuit rings. Type a voltage to get the current and the real, reactive and apparent power. Two more modes give the reactances of a part (and the part for a reactance) and the star ↔ delta (Y–Δ) conversion of three impedances, complex or resistive.
Without a pass, the free preview works on your own values and shows the names of the table’s first rows and the chart under a watermark, without its numbers; |Z|, the reactances, the converted impedances, every other figure, the working, Copy result, the CSV and the chart PNG come with a Pro pass.
How to use it
- Choose Impedance & resonance, Reactance or Star ↔ delta.
- For impedance, choose series or parallel and tick the parts that are in the circuit. Type their values with prefixes (10, 4.7k, 10m for 10 mH, 1u for 1 µF) and the frequency.
- Optionally type the RMS voltage across the circuit to get the current and the power.
- Read |Z|, the phase and the resonance figures, and check the chart for where the circuit resonates. Copy result, the CSV of the sweep and the chart PNG need a pass, or unlocking this result.
Examples
L 10 mH, C 1 µF
XL = 62.83 Ω, XC = 159.2 Ω; they are equal at 1.592 kHz
R 10 Ω, L 10 mH, C 1 µF at 1 kHz
Z = 10 − j96.32 Ω, |Z| = 96.84 Ω at −84.07° (capacitive); f0 1.592 kHz, Q 10, bandwidth 159.2 Hz
R 1 kΩ, L 10 mH, C 1 µF
Q = R√(C/L) = 10; |Z| = 1 kΩ at f0, its maximum
R 1 kΩ, C 1 µF in series
corner 159.2 Hz, where |Z| = 1.414 kΩ at −45°
Z1 10 Ω, Z2 20 Ω, Z3 30 Ω
Za 110 Ω, Zb 55 Ω, Zc 36.67 Ω
Reactance and impedance
- Inductive reactance XL = 2π × f × L: 10 mH has 62.83 Ω at 1 kHz and 6.283 Ω at 100 Hz.
- Capacitive reactance XC = 1 ÷ (2π × f × C): 1 µF has 159.2 Ω at 1 kHz.
- Series: Z = R + j(XL − XC). |Z| = √(R² + X²) and the phase φ = atan2(X, R): positive means inductive (the current lags), negative capacitive (it leads).
- Parallel: the admittances add, Y = 1/R + j(ωC − 1/(ωL)), and Z = 1 ÷ Y.
- At one frequency any circuit behaves like a resistor with one inductor or capacitor, in series or in parallel; the calculator gives both forms. Power factor = cos φ.
Resonance, Q, bandwidth and damping
L and C resonate at f0 = 1 ÷ (2π√(LC)), where XL = XC: a series circuit’s impedance falls to R (its minimum), a parallel circuit’s rises to R (its maximum).
- Q — series: Q = (1/R)√(L/C); parallel: Q = R√(C/L). √(L/C) is the characteristic impedance.
- Bandwidth between the half-power (−3 dB) points: BW = f0 ÷ Q, with f1,2 = f0 × (√(1 + 1/4Q²) ∓ 1/2Q).
- Damping ratio ζ = 1 ÷ (2Q): below 1 the circuit rings (underdamped), at 1 it is critically damped, above 1 overdamped.
- At resonance a series circuit puts Q times the supply voltage across L and across C, and a parallel circuit circulates Q times the supply current between them: rate the parts for it.
Star ↔ delta (Y–Δ) conversion
Three impedances joined at one point (a star, Y) can be replaced by three joined in a loop (a delta, Δ) without changing what any outside connection sees, and back. With Z1, Z2 and Z3 the star arms at nodes 1, 2 and 3, and Za, Zb and Zc the delta branches opposite those nodes (Za between nodes 2 and 3):
- Y → Δ: Za = (Z1Z2 + Z2Z3 + Z3Z1) ÷ Z1, Zb = … ÷ Z2, Zc = … ÷ Z3.
- Δ → Y: Z1 = Zb·Zc ÷ (Za + Zb + Zc), Z2 = Za·Zc ÷ …, Z3 = Za·Zb ÷ ….
- Balanced (all three equal): ZΔ = 3 × ZY.
The formulas hold for complex impedances too, so the calculator takes R + jX (10+j5, 3-4j) or polar (10∠30) values and checks the result by the impedance between each pair of nodes.
Sources
Limitations
- Parts are ideal. Real inductors have winding resistance and self-capacitance, real capacitors ESR and ESL, and both resonate on their own at high frequency: above a part’s self-resonant frequency it no longer behaves as its value says.
- The parallel circuit has R, L and C each in its own branch. A tank whose only loss is the inductor’s series resistance behaves slightly differently; use the series equivalent at your frequency.
- Values are steady-state (sinusoidal) at one frequency; switching transients are a job for the RC & RL Time Constant Calculator.
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Frequently asked questions
What do I get without a pass?
Without a pass, RLC Impedance & Resonance Calculator shows the names of the table’s first rows and a watermarked chart, with the impedance, the reactance and every other figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the impedance of an RLC circuit?
In series, Z = R + j(XL − XC) with XL = 2πfL and XC = 1/(2πfC), and |Z| = √(R² + (XL − XC)²). 10 Ω, 10 mH and 1 µF at 1 kHz give XL = 62.83 Ω, XC = 159.15 Ω and |Z| = √(10² + 96.32²) = 96.84 Ω. In parallel, add the admittances 1/R, 1/(jXL) and jωC and take the reciprocal.
What is the resonant frequency of an LC circuit?
f0 = 1 ÷ (2π√(LC)). For 10 mH and 1 µF: 1 ÷ (2π × √(10⁻⁸)) = 1,592 Hz. It is the same for series and parallel circuits; R only sets how sharp the resonance is (Q).
How is Q related to bandwidth?
Bandwidth = f0 ÷ Q, between the two frequencies where the power is half (−3 dB). A series RLC with Q = 10 at 1,592 Hz has a bandwidth of 159 Hz, from 1,514 Hz to 1,673 Hz.
What does the phase angle tell me?
A positive phase means the circuit is inductive at that frequency (the current lags the voltage); a negative phase means capacitive (the current leads). At resonance the phase is 0° and the circuit looks purely resistive.
How do I convert a star (Y) network to a delta (Δ)?
Divide the sum of the products of the star arms by the arm opposite each delta branch: Za = (Z1Z2 + Z2Z3 + Z3Z1) ÷ Z1. For 10, 20 and 30 Ω the sum is 1,100 Ω², so Za = 110 Ω, Zb = 55 Ω and Zc = 36.67 Ω.