SizingKitElectronics · AC networks
Impedance calculator
Enter a resistance, an inductance and a capacitance in series or in parallel, name a frequency, and this returns the impedance in polar and rectangular form side by side — magnitude and phase angle, resistance and reactance — along with both reactances, the admittance, the resonant frequency, the Q factor and the bandwidth that follows from it. Leave a component out and it is treated as absent rather than as zero, which means a different thing in each topology. Free, no signup, and it keeps answering once the page has loaded and the connection has gone.
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- Series and parallel
- Polar and rectangular
- Resonance, Q and BW
The network and the frequency you are asking about
Leave out anything the circuit does not contain. A blank field is a wire: it adds no impedance to the branch.
Includes the winding resistance of a real inductor, which is where most of it lives.
Impedance is a value at one frequency, not a property of the parts.
Blank means there is no inductor here.
Blank means there is no capacitor here.
POLAR
1.563 kΩ ∠ -88.277°
RECTANGULAR
47.000 Ω − j1.562 kΩ
| What the network is doing here | capacitive — the current leads the voltage |
|---|---|
| Inductive reactance, 2πfL | 29.5310 Ω |
| Capacitive reactance, 1 ÷ 2πfC | 1.5915 kΩ |
| Admittance, 1 ÷ Z | 639.908 µS |
| Conductance / susceptance | 19.246 µS / 639.618 µS |
| Resonant frequency, 1 ÷ 2π√(LC) | 7.3413 kHz |
| Characteristic impedance, √(L ÷ C) | 216.795 Ω |
| Quality factor at resonance | 4.613 |
| −3 dB bandwidth | 1.5915 kHz |
Written in the engineering convention: Z = R + jX with X positive for an inductor, so a positive phase angle means the voltage leads the current. Reactances come straight from 2πfL and 1/(2πfC); the parallel case is summed as admittance and inverted once, so a missing part is an open circuit rather than a short. Every figure here is the ideal component — a real inductor carries winding resistance and self-capacitance, and a real capacitor carries equivalent series resistance and inductance of its own, all of which take over above the part’s self-resonant frequency.
How to read an RLC network at the frequency you actually care about
Impedance is a value at a frequency, not a property of the parts. Change the frequency and every number on the page changes with it.
Say how the parts are connected before you type any of them
Series and parallel are not two arrangements of one formula — they are computed in different domains. A series branch adds impedances, so a missing component contributes nothing and behaves as a wire. A parallel network adds admittances, so a missing component contributes nothing and behaves as an open circuit. Picking the wrong one turns an open into a short and produces an answer that looks entirely reasonable.
Include the resistance that is already in the circuit
An inductor's winding resistance is usually the largest resistive term in an LC network, and leaving it out sends Q to infinity and the bandwidth to zero. Measure the coil with a meter and put that figure in the resistance field. For a capacitor, the equivalent series resistance on the datasheet plays the same role and matters most in a switching supply.
Read the phase, not just the magnitude
The magnitude tells you the current a voltage will push through; the phase tells you when it arrives. Positive is inductive and the current lags, negative is capacitive and it leads, and zero means the two reactances have canceled and the network is behaving as a plain resistor. That last case is resonance, and the page flags it when you land on it.
Technical specifications
| Topologies | Series RLC and parallel RLC, each solved in its own domain — series summed as impedance, parallel summed as admittance and inverted once |
|---|---|
| Sign convention | Z = R + jX with X positive for an inductor, so a positive phase angle means the voltage leads the current |
| Frequency range accepted | 1 µHz to 1 THz. Zero is refused: at DC a capacitor is an open circuit and an inductor is a wire, and neither has a reactance |
| Component ranges | 1 µΩ to 1 TΩ, 1 pH to 10 kH, 1 fF to 1 F — a span that covers a trace inductance at one end and a supercapacitor at the other |
| Derived from the same inputs | XL, XC, |Z|, phase, admittance, conductance, susceptance, resonant frequency, characteristic impedance √(L/C), Q and −3 dB bandwidth |
| Q definition used | Series: √(L/C) ÷ R. Parallel: R ÷ √(L/C). These are reciprocals of one another, which is why the same three parts give different Q in the two topologies |
| What is idealized | Every part is ideal. Winding resistance, self-capacitance, dielectric loss and lead inductance are not modeled, and above a part's self-resonant frequency they dominate |
| Privacy | Component values stay in the page; no measurement or network you enter is transmitted |
Frequently asked questions
Why does the same L and C give a different Q in series and in parallel?
Because resistance does the opposite job in each. In a series network the resistance is in the current path and damps the oscillation, so Q is √(L/C) divided by R and a small resistance means a sharp response. In a parallel network the resistance shunts the tank and drains it, so Q is R divided by √(L/C) and a large resistance means a sharp response. The two expressions are reciprocals, and applying one to the other topology inverts the answer.
What happens at the resonant frequency?
The two reactances are equal and opposite and cancel, leaving a purely resistive network. In series that is the minimum impedance the circuit reaches and it equals the resistance alone, which is why a series LC across a supply is a short at one frequency. In parallel it is the maximum, and in an ideal model with no resistance it has no finite value at all — the page reports that as unbounded rather than as a large number.
Can I use this for a speaker, a transformer winding or an antenna?
As a first approximation and no further. Those are distributed or nonlinear devices whose impedance is measured rather than derived: a loudspeaker's nominal 8 Ω is a marketing figure that its real curve crosses briefly, a transformer winding carries a frequency-dependent core loss no lumped RLC captures, and an antenna's radiation resistance is not a component at all. Model a measured curve with an equivalent RLC if you must, but do not expect the parts to be the physical ones.
Is impedance the same thing as AC resistance?
No — impedance has a phase and AC resistance does not. The resistive part is the component in phase with the current and it is the only part that dissipates power; the reactive part stores energy and hands it back each cycle, moving no net power at all. That distinction is why a heavily reactive load draws current a supply must carry but does no work with, and why the two are counted separately on every electricity bill above domestic scale.
Why is my measured impedance higher than this page says above a few megahertz?
Because the parts stopped being what their labels say. Every capacitor has lead and plate inductance and every inductor has turn-to-turn capacitance, so each one self-resonates and then behaves as its opposite: above self-resonance a capacitor is an inductor and an inductor is a capacitor. This page models ideal components, so its answer diverges from a network analyzer exactly where the parasitics take over — usually tens of megahertz for a leaded part, hundreds for a small surface-mount one.
How do I get impedance from a voltage and a current I measured?
Divide the magnitudes for |Z| and take the phase difference between the two waveforms for the angle — a two-channel scope gives both. That path is worth taking whenever the circuit contains anything you did not build, because a measured impedance carries all the parasitics, the core losses and the temperature effects that a three-component model leaves out. Feed the result back into this page as an equivalent R and X to see what network reproduces it.
What is the characteristic impedance the page prints?
√(L/C) — the impedance the reactances both equal at resonance, and the natural scale of the network. It is useful because Q is nothing more than the ratio between it and the resistance, so the two figures together tell you how the circuit will behave before you compute anything. It is not the same quantity as the characteristic impedance of a transmission line, which is derived from inductance and capacitance per unit length rather than from two discrete parts.
About phasors, the two topologies, and what an ideal component is not
The reason impedance needs two numbers is that a capacitor and an inductor do not oppose current, they delay it. Push a sinusoidal voltage across a capacitor and the current is already at its peak a quarter cycle before the voltage gets there; across an inductor it arrives a quarter cycle late. A single magnitude cannot express that, so the whole subject is written as a complex value — a resistive part in phase with the current, and a reactive part ninety degrees out of it, positive for inductance by the engineering convention this page follows. Which of the two forms you want depends entirely on the next step: polar to get a current out of a voltage, rectangular to add one branch to another. That is why both are printed at once here rather than behind a switch.
The series and parallel cases look symmetric on a schematic and are not symmetric to compute. Series impedances add directly, so an omitted component contributes zero impedance and behaves as a piece of wire. Parallel branches add as admittances — the reciprocals — so an omitted component contributes zero admittance and behaves as an open circuit. Those are opposite physical statements, and a calculator that runs both through one formula reports a short where the circuit has a gap. This page sums each topology in its own domain and inverts once at the end, which is also why the parallel case can legitimately return an unbounded impedance: an ideal LC tank with nothing to dissipate in it genuinely has no finite impedance at resonance.
What no lumped model gives you is the behavior of a real part. Above its self-resonant frequency every capacitor is an inductor and every inductor is a capacitor, because the lead inductance and the interwinding capacitance that were negligible below it are now the dominant terms — which is the reason a decoupling network uses several capacitors of different sizes rather than one large one. Below that the model holds well, and the figures here are the ones that matter: the reactance that sets the current, the phase that sets the timing, and the Q that sets how narrow the response is. If the network is a resistor and a capacitor rather than a full RLC, the same physics is easier to read in the time domain — the RC time constant calculator reads the same corner frequency as a settling time instead. If it is a resistor pair feeding something reactive, the voltage divider calculator gives the source resistance that meets it, and the Ohm’s law calculator handles the purely resistive case where the phase angle is zero and none of this arises. When you need a ratio of two impedances expressed in decibels rather than as a number, the decibel calculator is where the 10 log and 20 log distinction is set out.
Where these component values are solved
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
The complex arithmetic runs in the tab on every keystroke. No network topology or measurement you enter is logged, which matters when the values on your bench belong to somebody else’s product.